(Test Bank) Psychological Research Exam Questions and Answers/PYC3704 Psychological Research Test Bank (A+ Rated)

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PYC3704 Psychological Research Exam Questions and Answers PYC3704 Psychological Research Test Bank Complete study Guide. A+ Rated Very Reliable This document is a compilation of UNISA Ex am Questions and Answers Answers are motivated by a combination of: • Short summaries/reasoning regarding the relevant topic(s) in question. (Incorrect options are also marked where applicable, in order to identify and disregard red -herring alternatives) Exams covered are: • 2016 May -June • 2016 October -November • 2017 May -June • 2017 October November • Mock Exam 1 • Mock Exam 2 • Test yourself Questions and Answers from the Study Guide Please note: This document is an additional tool for exam preparation. The Stuvia -user that compiled and uploaded this document takes no responsibility for incorrect answers. Students must ensure that they study the prescribed material and understand the content. May June 2016 Question 1 A theory can be described as an interdependent set of - - - - - relations between - - - - - 1. proposed, constructs 2. empirical, hypotheses 3. verified, variables Answer: The correct option is 1 Reasoning: • Alternative 1 is correct because a theory is defined as a “network of postulated relations between constructs”. • Alternative 2 is wrong because one does not test relations between hypotheses, but between variables. • The relations are postulated (and ther efore not verified) so that alternative 3 is also incorrect. Question 2 A measurement model of attention deficit disorder relates this - - - - - to its - - - - - 1. construct, intervening variables 2. hypothetical variable, observable instances 3. variable, parameters Answer: The correct option is 2 Reasoning: • Alternative 2 is correct because (a) ‘attention deficit disorder’ is a hypothetical variable used to refer to a cluster of observable symptoms, and (b) the symptoms are the observable instances (of behaviour) which are used to measure (e.g. indicate the se verity) of the disorder. • Alternative 1 is incorrect because one requires manifest, not latent variables for measurement. • Alternative 3 is also incorrect because a model is not a variable, but a theory of the relationship between ‘referents’ (or hypothet ical entities). Use the following scenario to answer Questions 3 to 5 "Acute stress disorder among patients who suffer from this disorder can be explained in terms of how the intensity of stress is affected by personality factors, by the nature of the stressors which they experience, and by the support they experience in their social system. My research will investigate whether the level of anxiety of these patients can be reduced by providing social support through group therapy. More specifically, patients receiving group therapy are expected to score lower on the Manifest Anxiety Scale than patients not receiving therapy" Question 3 "Acute stress disorder among patients who suffer from this disorder can be explained in terms of how the intensity of stress is affected by personality factors, by the nature of the stressors which they experience, and by the support they experience in the ir social system” is a(n) - - - -- 1. hypothesis 2. theory 3. operational definition Answer: The correct option is 2 Question 4 The dependent variable(s) in my research is/a re - - - - - 1. personality factors, nature of stressors, support received 2. whether or not group therapy is received 3. level of anxiety experienced by patients Answer: The correct option is 3 Reasoning: In the hypothesis it is indicated the level or intensity of anxiety experienced ‘depends’ on other variables such as personality factors, the nature of the stressors and support experienced in the social system, showing that it functions as a dependent or Y-variable which is to be predicted or explained in the study. [The dependent variable is usually the one that the researcher is interested in, the variable that is the focus of the research. The independent variable is something that the researcher man ipulates, to see how this affects the dependent variable (in other words, the dependent variable is dependent on the independent variable).] Question 5 When interpreting the results of this research I will assume that personality factors and the nature of the stressors - - - - - 1. do affect level of anxiety, but their effects more or less cancel out over all my patients in the research sample 2. do not affec t level of anxiety 3. do affect level of anxiety, but according to the central limit theorem their average effect will be zero Answer: The correct option is 1 Reasoning: • Alternative 1 is correct because it is obvious that the type of stressor may have an effect on the level of anxiety experienced, but if an unbiased (e.g. random) sample is selected from the population, the influence of the type of stressor will be averaged over the sample. • Alternative 2 is incorrect because there are no grounds for assuming that the type of stressor will not affect anxiety. • Alternative 3 is also incorrect because the central limit theory is not applicable here (it refers to the nature of the sampling distributions of sampling statistics and not to the value of specific variables). Question 6 A psychologist conducts a study in which she measures the reaction times of students doing a psychometric test. She proceeds from the assumption that a fast reaction time is a good indication of high intelligence. In this study 'intelligence' is the - - - - - variable 1. operational 2. latent 3. manifest Answer: The correct option is 2 Reasoning: Intelligence is a latent variable because it cannot be observed directly. The results of the psychometric test can however be observed directly and can therefore be regarded as the manifest variable. Use the following scenario to answer Questions 7 and 8 Jeff's explanation of size perception in the natura l environment states that the estimated size of a distant object is affected by its true size, distance from the observer, and transparency of the atmosphere. He decides to investigate whether the claim that estimated size increases with haziness is valid. Question 7 The statement "estimated size increases with haziness" represents the - - - - - 1. observed relation between two variables 2. research hypothesis 3. operational definition Answer: The correct option is 2 Reasoning: • Alternative 2 is correct, because a specific hypothesis is now derived from the theory presented in the scenario. • Alternatives 1 and 3 is incorrect because the terms ‘estimated size’ and ‘haziness’ have not been operationally defined in the statement given. Question 8 The dependent variable(s) in Jeff's research is/are - - - -- 1. true size, distance from the observer, and tran sparency of the atmosphere 2. haziness 3. estimated size Answer: The correct option is 3 Reasoning: (The dependent variable is usually the one that the researcher is interested in, the variable that is the focus of the research. The independent variable is something that the researcher manipulates, to see how this affects the dependent variable (in other words, the dependent variable is dependent on the independent variable).) In the hypothesis mentioned it is indicated the estimated size ‘depends’ on othe r variables such as true size, distance from the observer, and transparency of the atmosphere, s howing that it functions as a dependent or Y -variable which is to be predicted or explained in the study. Question 9 In a study, the relationship between level of physiological arousal (high and low) and mood (measured on three levels) is considered. A suitable hypothesis for the study can be viewed as a - - - - 1. rule associating the values of 'physiological arousal' w ith the values of 'mood' 2. correlation between the constants 'physiological arousal' and 'mood' 3. procedure to make it possible to measure the values of the variables 'physiological arousal' and 'mood' Answer: The correct option is 3 Reasoning: A hypothesis can be informally described as an educated guess. The research hypothesis expresses the problem in terms of very specific relationships among constructs that we expect to find (if our guess is true). It is important that this po ssible relationship should be clear and unambiguous. A hypothesis that is stated clearly and specifies exactly what is to be observed and what should be true if it is valid, is often called an operational hypothesis. A research hypothesis : a statement abo ut a possible relationship among constructs that may explain some set of observations that one intends to investigate. Option 2 is incorrect, as physiological arousal and mood are not constants, but variables. Question 10 Assume that a researcher believes that education plays a role in promotion. He intends to investigate this on a sample of workers at Computer Solutions Inc. Which one of the following is the most appropriate statement of the operational hypothesis? 1. Educat ion is relevant to the promotion of employees at Computer Solutions Inc 2. Employees with higher levels of education earn more than employees with lower levels of education at Computer Solutions Inc 3. Employees with higher levels of education are more likely to be promoted at Computer Solutions Inc than employees with lower education at corresponding post levels Answer: The correct option is 3 Reasoning: A hypothesis that is stated clearly and spec ifies exactly what is to be observed and what should be true if it is valid, is often called an operational hypothesis. • Alternative 1 is not stated clearly, and therefore incorrect. • Alternative 2 is also more vague than alternative 3, and relates to earnings, not promotions. Question 11 A standard normal distribution has a standard deviation of - - - - - and a mean of - - - -- 1. 0, 1 2. 1, 0 3. 1, 10 Answer: The correct option is 2 Reasoning: A standard normal distribution has a mean of 0 and a standard deviation of 1. Question 12 Consider the hypothesis: There is a relationship between self -esteem and eating disorders. People with low self -esteem are more likely to have eating disorders because they tend to have less healthy eating habits than people with high self -esteem. Suppose that µhs indicates be the average of a measurement on a scale that measures 'healthy eating patterns' (where a higher score means a person exhibits more healthy eating habits), for people with high self -esteem, and µls, the average eating pattern score for people with low selfesteem. Which of the following is an app ropriate way to state the hypothesis in symbolic form? 1. µhs ≠ µls 2. µhs > µls 3. µhs < µls Answer: The correct option is 2 Question 13 Which of the options represents a valid description of the law of large numbers? 1. As repetitions of a probability experiment increases, the relative frequency or proportion of outcomes will approximate the most probable outcome or theoretical probability 2. All probability distributions approach the normal distribution as the sample size increases 3. For a random sample of size n selected from a population with mean µ and standard deviation σ, the sampling distribution of means obtained from all possible samples is approximately normal with mean µ and standard deviation Answer: The correct option is 1 Reasoning: Alternatives 2 and 3 refer to the central limit theorem, and not to the law of large numbers and is therefore incorrect. Law of large numbers: If an experiment is done repeatedly, and if the outcomes are independent of one another, the observed proportion of favourable occurrences of an event will eventually approach its theoret ical probability. Question 14 Suppose that over the years 10 000 students wrote an examination in a specific course, and that 6400 of them passed, of which 200 obtained exactly 50%. This means that for randomly selected students the probability of obtaining exactly 50% is - - - - - while the probability of obtaining 50% or more is - - - - - 1. 0.64, 0.02 2. 0.05, 0.64 3. 0.02, 0.64 Answer: The correct option is 3 Reasoning: Therefore: • the probability for students obtaining exactly 50% = = 0.02 • the probability for students obtaining 50 % or more (a pass) = = 0.64 Question 15 During the interpretation of psychological measurements, the normal distribution is often - - - - - 1. adapted to fit the observed frequency distribution of scores 2. used as a theoretical model for interpreting the observed distribution of scores 3. used to cal culate the relative frequency of observed scores Answer: The correct option is 2 Reasoning: The normal distribution is a theoretical distribution which is used to determine the probability of a given score provided the mean and standard deviation are known. It is not dependent on observed frequencies (alternative 1), nor is it used to calculate the relative frequency of observed scores (alternative 3) which can only be obtained empirically. Question 16 Joseph scores 62% in a History test (class mean 60%, standard deviation 10%) and 54% in a Biology test (class mean 60%, standard deviation 12%). Use z -scores to decide which statement is true. Relative to the rest of his class Joseph does - - - - - 1. bette r in History that in Biology 2. better in Biology than in History 3. equally well in History and Biology Answer: The correct option is 1 Reasoning: Joseph’s z -score for History is (62 -60)/10 = 0,2, and for Biology it is (54 -60)/12 = -0,5. Question 17 A frequency distribution of the ages in months of a class of Grade 1 children indicates for each - - - what the corresponding - - - - - is 1. frequency, age in months 2. age in months, number of children of that age 3. age in months, relative frequency at that age Answer: The correct option is 2 Reasoning: A frequency distribution will represent the number of students falling under each age group. Base your answers to Questions 18 and 19 on the following scenario A researcher is investigating job satisfaction of workers at a branch office of a particular company. The distribution of staff at this office is as follows Managerial Section 5 Adm inistrative Section 15 Technical Section 10 Human Resources Section 6 In order to conduct an interview, the researcher draws the name of a staff member at random Question 18 What is the probability that the person selected would be in the Admi nistration Section? 1. 0.07 2. 0.42 3. 0.25 Answer: The correct option is 2 Reasoning: Therefore, p = = 0.42 Question 19 What is the probability that a worker whose name is selected at random is from the Managerial Section or from the Human Resources Section? 1. 0.31 2. 0.06 3. 0.4 Answer: The correct option is 1 Reasoning: Since these are mutually exclusive possibilities, we can apply the additive rule directly. p(Managerial OR Human Resources) = p(Managerial) + p(Human Resources) 𝑛𝑢𝑚𝑏𝑒𝑟 𝑀𝑎𝑛𝑎𝑔𝑒𝑟𝑖𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝐻𝑢𝑚𝑎𝑛 𝑅𝑒𝑠𝑜𝑢𝑟𝑐𝑒𝑠 = + 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 = + = = = 0.305 Question 20 A probability distribution of the ages in months of South African Grade 1 children indicates for each - - - - - what the corresponding - - - - - is 1. child, age of that child 2. age in months, number of children of that age 3. age in months, probability of a Gr ade 1 child having that age Answer: The correct option is 3 Reasoning: Alternative 2 refers to a frequency distribution, and is therefore incorrect. (A probability distribution is a mathematical function that, stated in simple terms, can be thought of as providing the probabilities of occurrence of different possible outcomes in an experiment.) Question 21 Vusi is conducting research into the ability of people to recognize faces from photographs. A random sample of research participants are shown a group photo which they are allowed to look at for ten minutes. Each participant is then shown ten individual photographs, and asked whether the person on the photo was in the group photo. The table represents a frequency distribution of the number photos that were identified correctly by the research part icipants. Number of correct responses 0 1 2 3 4 5 6 7 8 9 10 Frequency count of participants 0 1 4 11 14 18 22 17 9 6 0 Based on this data, what is the probability be that a person who is selected at random would correctly identify 7 or more faces from the group photo? 1. 0.07 2. 0.15 3. 0.32 Answer: The correct option is 3 Reasoning: ∑(𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡 𝑜𝑓 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒𝑠 7 𝑡𝑜 10) ∑𝑡𝑜𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑐𝑜𝑢𝑛𝑡 = = = 0.32 Question 22 John received 55 marks for his psychology test. The average mark for this test is 63, and the standard deviation is 8. What proportion of the students received higher marks than John? 1. 0.16 2. 0.84 3. 0.34 Answer: The correct option is 2 Reasoning: John’s z -score is -1. (55 -63)/8 Look up the larger portion (higher marks) of this z -score on the z -score table. = 0.84 Question 23 The asymptotic property of the normal curve refers to the fact that - - - - - 1. the curve is symmetrical and bell -shaped 2. the endpo ints of the curve get closer to, but never touch, the horizontal axis 3. the curve represents a distribution of data that was standardized to a mean of 0 and a standard deviation of 1 Answer: The correct option is 2 Reasoning: Asymptotic means that the two tails never touch the horizontal axis, moving ever closer to infinity, because there is always some probability that more extreme values will occur. Question 24 The central limit theorem states that the - - - - - 1. sampling distribution of a specific variable will approach a normal distribution as the size of the sample increases 2. sampling error will gradually assume a normal distribution for larger samples 3. distribution of the mean of a large number of samples of a specific variable will be approximately normal, regardless of the underlying distribution of the variable Answer: The correct option is 3 Reasoning: The central limit theorem states that, for a large sample size, the sampling distribution of a mean is close to normal, irrespective of the shape of the population distribution of the original data. Question 25 When testing a hypothesis, the p -value r epresents the probability that we would find the specific relationship between variables that we see in our measurements, given that the - - - - - 1. null hypothesis is false 2. alternative hypothesis is true 3. null hypothesis is true Answer: The correct option is 3 Reasoning: The p -value is an area below the sampling distribution of the statistic (or test statistic). Such a sampling distribution can only be derived under H 0. The p -value represents the probability that the null hypothesis i s true. Question 26 When a research hypothesis is formally expressed as a statistical hypothesis, it should be expressed in terms of - - - - - 1. population parameters 2. sample statistics 3. both of the above Answer: The correct option is 1 Reasoning: Note that the alternative and null hypotheses here are about the value of μ which of course is a population parameter. Question 27 When comparing an observed sample mean with a given population mean, the rejection of H 0 implies that a difference between the calculated sample mean and its expected value under H 0 is probably due to ----- 1. chance 2. the independent variable 3. sampling error Answer: The correct option is 2 Reasoning: The null hypothesis states that the true population mean is i.e. 100, and that any sample deviation from this - such as a mean of 104 - is due to chance or random sampling error. The p -value is a probability value that indicates what the chances are that our sample value would be 104 or greater when it should `really' reflect the population mean of 100, but misses the mark due to measurement error. Our task is to make up our minds whethe r we suspect that 104 is probably due to chance and is, therefore, really an approximation for 100, or whether we believe that 104 is sufficiently higher than 100 to support our alternative hypothesis, in spite of possible measurement error. If we accept the difference as significant, we would conclude that we can reject H 0 in favour of H 1. Question 28 Suppose we have stated H 0 µ = 10, and H 1 µ < 10, and find that the sample mean corresponds to a zscore of -3. This means that the corresponding p -value is equal to - - - - - 1. 0.9987 2. 0.4987 3. 0.0013 Answer: The correct option is 3 Reasoning: Look up the c orresponding ‘smaller portion’ of 3 on the z -score appendix. Question 29 A researcher wants to determine the effectiveness of an assertiveness training course. She tests a sample of 200 participants before and after the workshop on a scale which measures assertiveness, and finds mean scores of ẋ1 = 45 before and ẋ2 = 57 after t he workshop. A statistical test shows that this difference is statistically significant. The scores are however fairly close together and she is concerned that the result may be due to the relatively large sample size. What can she do to check whether the result is also fairly important in practical terms? She should - - - - - 1. calculate the power of the test 2. determine the level of significance of the result 3. calculate the effect size Answer: The correct option is 3 Reasoning: A major determinant of the sensitivity or power of a statistical test is sample size (which is why we can increase sample size to enhance power). When the sample is large, even smaller effects will have statistical significance. One way that statisticians have suggested to deal with this problem is by the notion of effect size . Question 30 How is the significance level ( α) of a statistical test determined? It is - - - - - 1. looked up in the z -tables 2. selected by the researcher 3. calculated from the test statistic Answer: The correct option is 2 Reasoning: The researcher compares the p -value with a level of significance (a) that he/she chose before he/she did the sampling and made the observation. This is chosen by the researc her, based on the risk of being wrong when rejecting the null hypothesis that he or she is willing to take. Question 31 A Type II error occurs when the - - - - - 1. null hypothesis is not rejected when it should be rejected 2. null hypothesis is rejected when it should not be rejected 3. alternative hypothesis is rejected instead of the null hypothesis Answer: The correct option is 1 Reasoning: The Type II error of f ailing to reject a null hypothesis that is really false is indicated by the Greek symbol β which indicates the probability associated with this risk. Question 32 When applying a statistical test, we - - - - - the null hypothesis if the p -value is - - - - - or equal to the level of significance 1. reject, greater 2. accept, smaller 3. reject, smaller Answer: The correct option is 3 Reasoning: The null hypothesis is never accepted. The decision regarding the null hypothesis is to reject it or not to reject it. Therefore alternative 2 is eliminated. If the p -value is equal to or less than the chosen significance level α, we reject H 0 in favour o f H1. Otherwise, do not reject the null hypothesis in favour of the alternative hypothesis. Base your answers to Questions 33 and 34 on the following hypothesis "The mean extroversion score on the Eysenck Personality Questionnaire (EPQ) of women who support abortion is higher than that of women who oppose it” Question 33 The hypothesis indicates how the constructs - - - - - 1. are operationalized 2. are related 3. differ Answer: The correct option is 2 Reasoning: A hypothesis can be informally described as an educated guess. The research hypothesis expresses the problem in terms of very specific relationships among constructs that we expect to find (if our guess is true). It is important that this possible relatio nship should be clear and unambiguous. A hypothesis that is stated clearly and specifies exactly what is to be observed and what should be true if it is valid, is often called an operational hypothesis. A research hypothesis: a statement about a possible relationship among constructs that may explain some set of observations that one intends to investigate. Question 34 The two constructs of importance in the hypothesis are - - - - - and - - - - - 1. gender, personality 2. extroversion, whether a woman supports abortion or not 3. whether abortion is supported or not, gender Answer: The correct option is 2 Reasoning: Constructs are: a) concepts used to account for observations b) the building blocks of theories c) hypothetical or theoretical concepts Question 35 The alternative hypothesis is often a re -statement of the - - - - - hypothesis 1. statistical 2. research 3. null Answer: The correct option is 2 Reasoning: A research hypothesis always translates into two mutually exclusive hypotheses (i.e. both cannot be true at the same time): a null and an alternative hypothesis. Therefore alternative 3 is incorrect and eliminated. A statistical hypothesis is the research h ypothesis that is written in statistical language. Therefore, the alternative hypothesis is a statistical hypothesis, and not a “re -statement”. Question 36 Suppose that the memory span of adults is normally distributed with a mean of 7 items and a standard deviation of 2 items. A researcher predicts that dyslexic adults have a shorter memory span than adults in general. Which of the following is an appropria te alternative hypothesis for testing this prediction? 1. The mean memory span of the population of dyslexic adults is smaller than 7 2. The mean memory span of the population of adults is not equal to 7 3. The mean memory span of the population of dyslexic adul ts equals 7 Answer: The correct option is 1 Reasoning: H1: µD < 7 Question 37 If a p -value on a computer printout is reported as '0.0000', what should a researcher assume? It implies that the value can be interpreted as - - - - - 1. smaller than 0.00001 2. equal to exactly zero 3. too small to calculate Answer: The correct option is 1 Reasoning: In statistics, probabilities are sometimes expressed as p = 0.0000. This does not mean p = 0; it is a convention for indicating that p < 0.00005: i.e., there are at least four zeroes after the decimal point. Question 38 Which of the following statemen t about a null hypothesis is not valid? The null hypothesis is a statement of what may be expected if - - - - - 1. there are significant relationships among constructs or variables 2. there are no relationships among variables in the research question 3. all relationships among constructs are due to chance or measurement error Answer: The correct option is 1 Reasoning: The null hypothesis always contains the `equal to' symbol `='. Th e null hypothesis is the hypothesis that no effect exists, and in cases where we are testing a mean, this implies that two group means (or a group mean and a specific constant value) do not differ. The probability of obtaining the value that is equal to t he value of the null hypothesis purely by chance, due to random measurement errors, when the null hypothesis is actually true, is referred to as the p -value. Question 39 The level of significance is like a - - - - - 1. p-value under H 0 2. p-value under H 1 3. p-value from the z -tables Answer: The correct option is 1 Reasoning: Level of significance limits the probability of making a Type I error as it sets the maximum probability. The p -value represents the probability that the null hypothesis is true: that the effect we see in our observation is due to chance effects like measurement error. If this probability is small, we conclude that H 0 is not true, and we reject it. This p - value is also a direct indication of the probability that the null hypothesis is being mistakenly rejected (Type I error). Question 40 The larger that a value which a researcher chooses as the level of significance is, the greater the probability of - - - - - 1. a type I error 2. a type II error 3. not rejecting the null hypothesis Answer: The correct option is 1 Reasoning: The convention in most research projects is to fix the value of the level of significance ( α) in advance of the actual research, thereby limiting the probability of a Type I error to this value. The value of a represents the maximum risk that we are willin g to take of making a Type I error by rejecting H 0 in error. So, by setting α in advance, and only rejecting H 0 if the p -value is smaller than α, we are protecting ourselves against the probability of making a Type I error of larger than α. What if the p -value is not smaller than the a -level and we decide not to reject H 0? Now we run the risk of not rejecting H0 when - in fact - H0 is false and H1 is true . This is referred to as a Type II error. The decision not to reject H 0 is based on the test statistic, from which we determine a pvalue that is not smaller than our chosen level of significance (i.e., p -value > α). However, this outcome may also be the re sult of measurement error. The effect may be close to what H 0 predicts purely by chance. This error of failing to reject a null hypothesis that is really false is indicated by the Greek symbol β (pronounced `beta') which indicates the probability associat ed with this risk. So, while α indicates the risk that a researcher is prepared to take of making a Type I error (rejecting H 0 when the researcher should not do so), β is used to indicate the opposite risk - the risk he (or she) is taking of making a Type II error (not rejecting H 0 when in fact he should). Generally, though, the smaller α, the larger β. If we wish to avoid Type I errors, we set a to a small value such as 0.01 or even 0.001, but if we want to avoid Type II errors, we could set a to a larger value. (Note that option 2 and 3 refers to the same concept, namely a Type II error, both are incorrect, as there is only one possible answer to a multiple -choice question.) Question 41 Which of the following symbols is used to indicate the probability of making a Type II error? 1. Alpha or α 2. Beta or β 3. Cohen's d Answer: The correct option is 2 Question 42 Which one of the following alternative hypotheses would require a one -tailed te st of significance? 1. The mean anxiety score for boys differs from the mean score for girls 2. The mean verbal ability score for boys is lower than the mean verbal ability score for girls 3. There is a significant correlation between the test marks for English and marks for Mathematics for a mixed group of boys and girls Answer: The correct option is 2 Reasoning: If the symbol is “≠” then a non -directional (two -tailed) test would be required. Therefore option 1 is incorrect. Option 3 also does not state <, >, but rather a ≠, therefore this option is eliminated. (One -tailed = directional) Question 43 Suppose we want to increase the ability of a statistical test to detect a significant result. Which of the following options would not be helpful? 1. Increase the sample size 2. Decrease sampling error, measurement error, etc. 3. Set a smaller level of significa nce Answer: The correct option is 1 Reasoning: If a large effect does not yield a significant result, it may be that the statistical test lacks power (see section 3.3.2) and increasing the sample size will increase the power of the test (i.e. its abil ity to detect significant differences). Question 44 The power of a statistical test indicates the - - - - - 1. sensitivity or 'accuracy' of the test to determine whether an effect exists 2. whether a result is of practical importance, even though it may be significant 3. probability of making a Type I error Answer: The correct option is 1 Reasoning: The ability of a statistical test to detect a significant relationship between variables when such a relationship does in fact exist, is referred to as its power. This is the inverse of a Type II error: it is the probability of rejecting H 0 when, in fact , it is false and H1 is true. To put it succinctly, it is the probability of correctly rejecting a false null hypothesis. Therefore option 3 is eliminated. Question 45 Suppose H 0 µ = 100 are tested against H 1 µ ≠ 100 at the 0.10 level of significance. If the t -statistic is 3.20 and the two -tailed p -value is 0.11, what decision regarding the statistical hypothesis should be taken? 1. Reject H 0 and accept H 1 at the 0.10 level of significance 2. Reject H 1 and accept H 0 at the 0.11 level of significance 3. Do not reject H 0 at the 0.10 level of significance Answer: The correct option is 3 Reasoning: If the p -value is smaller than the level of significance of α = 0. 10, it implies that the null hypothesis can be rejected in favour of the alternative hypothesis. This p -value is greater than the level of significance, therefore it does not imply that H 0 can be rejected in favour of H 1. Option 1 is therefore incorrect. Option 2 is incorrect, because the decision rule is never to reject H 1, we only reject or accept H 0. H1 can only be accepted (once H 0 is rejected). Base your answers to Questions 46 to 49 on the following scenario An educational psychologist is doing r esearch on numeracy and has drawn a sample of university students enrolled for research methodology. It is known that the population average on a psychometric test of Numeracy equals 100, but she believes that the average numeracy level of these students w ill be higher than the population average. She sets a level of significance of α = 0.05 Question 46 Select the correct formulation of the hypothesis in this study 1. H0 µ ≠ 100, H1 µ ≥ 100 2. H0 µ = 100, H1 µ ≠ 100 3. H0 µ = 100, H1 µ > 100 Answer: The correct option is 3 Reasoning: The null hypothesis always contains the `equal to' symbol `='. The null hypothesis is the hypothesis that no effect exists, and in cases where we are testing a mean, this implies that two group means (or a group mean and a specific constant value) do not differ. Therefore alternative 1 is eliminated. (another reason to eliminate option 1, is the fact that H1 and H0 needs to be mutually exclusive. ≥ and = is not mutually exclusive.) Question 47 The hypothesis requires a - - - - - statistical test 1. directional 2. non-directional 3. two-tailed Answer: The correct option is 1 Reasoning: Where both values of the mean, either greater than or smaller than 100 are to be considered (H 1: µ ≠ 100), a non -directional or two -tailed test is required . In this case, the researcher’s hypothesis states that numeracy level is GREATER than (t herefore directional and one -tailed) Question 48 Suppose the researcher finds after statistical analysis that the average numeracy level in her sample is 105 with a standard deviation of 8. Which test statistic should she use to see if the difference is significant? 1. tẋ 2. zẋ 3. tc Answer: The correct option i s 2 Reasoning: There are 3 types of test statistics, namely t ẋ, zẋ and א². Therefore alternative 3 is incorrect and eliminated. When the standard deviation is known, we use the z ẋ test statistic. When the standard deviation is unknown, we use the t ẋ test statistic. Question 49 The researcher calculates the test statistic, and finds that the p -value associated with the resultant statistic is 0.062 . Based on the scenario above, what conclusion can the researcher make regarding her hypothesis? 1. The average numeracy of the students is significantly higher than the population average 2. The average numeracy of the students is not significantly higher tha n the population average 3. The population average differs significantly from the average numeracy of the students Answer: The correct option is 2 Reasoning: Using the values given in the scenario and placing them in the formula for z ẋ (ẋ− µ) zẋ = 𝜎ẋ Doing arithmetic, we can then see that µ = 104.5 Question 50 Consider the following statistical hypotheses H0 µ = 60 H1 µ ≠ 60 Suppose the one -tailed p -value is 0. 0345 and the level of significance is set at 0.05. The sample mean was found to be 65. What is the value of the two -tailed or non -directional p -value? 1. 0.10 2. 0.0173 3. 0.0690 Answer: The correct option is 3 Reasoning: A two -tailed p -value (used in the case of a non -directional hypothesis) is twice the size of a one tailed p -value (see page 66 of the study guide); or, conversely, a one - tailed p -value (used in the case of a directional hypothesis) is half the size of a two -tailed probability. The relationship between one -tailed and two -tailed p -values can be summarized as follows: • One-tailed p -value = (two -tailed p -value) / 2 • Two -tailed p -value = (one -tailed p -value) x 2 Base your answers to Questions 51 to 53 on the following scenario To validate a new depression scale a researcher applies it to 50 patients diagnosed with depression and 50 patients diagnosed with stress. She predicts that the depression sample will score higher on the scale (implying more depression) than the stress samp le. The mean scores of the two samples are found to be ẋDEPRESSION = 30 with a standard deviation of 12 for the depression group and ẋSTRESS = 25, with a standard deviation 10 for the stress group. Question 51 Which is an appropriate alternative hypothesis for the analysis of the results? 1. ẋSTRESS < ẋDEPRESSION 2. µSTRESS ≠ µDEPRESSION 3. µSTRESS > µDEPRESSION Answer: The correct option is 1 Reasoning: Option 2 is incorrect on two accounts, it uses a population parameter and it does not show the direction, (< or >). Option 3 is also incorrect on two accounts, as it uses a population parameter and it shows the direction incorrectly, as the hypothesis is that the depression sample will score higher than the stres s sample. Question 52 What type of statistical test is required? 1. A one -tailed test 2. A two -tailed test 3. A non -directional test Answer: The correct option is 1 Reasoning: A directional (one -tailed) test is required. Question 53 Given the information in the scenario above, which of the following assumptions need to be made before calculating the test statistic? 1. The population standard deviation is known 2. The two populations have different means 3. The two populations have the same variance Answer: The correct option is 1 Reasoning: Option 2 is a given in the scenario, and therefore no need to assume. Option 3 is incorrect, as the standard deviation for both populations (samples) are given, and no need to assume. Question 54 A researcher suspects that the average level of social engagement (need to interact socially) is higher among females than among males. She wants to test this by comparing the following hypotheses H 0 µF = µM H1 µF > µM where µ F indicates the average leve l of social engagement among females in the population, as tested on a 7 -polnt scale, and µ M is the average level of social engagement among males in the population. She draws random samples of females and males respectively, and calculates the following m ean levels of social engagement scores for each group Females ẋF = 4.1, Males ẋM = 4.8 What can the researcher infer from these observations? 1. H0 can be rejected 2. H0 cannot be rejected 3. It is necessary to do a t -test to determine whether the difference is significant Answer: The correct option is 3 Reasoning: Clearly, the observed value of ẋM is higher than the observed value of ẋF. This is a difference in the correct direction, which fits with our stated alternative hypothesis. The question is, however, whether this difference between the scores of 4.1 and 4.8 is statistically significant, or likely to be just due to chance. Only if it is significant should we have the confidence to reject the null hypothesis and accept that males have a higher average level of social engagement. We can use the t -statistic to determine this. Question 55 A standard error refers to the extent - - - - - 1. to which sample means are distributed around the actual mean of the sampling distribution 2. to which the sample standard deviation differs from the population standard deviation 3. of the error one would make i f you reject the null hypothesis falsely Answer: The correct option is 1 Reasoning: We can estimate the size of the error we would make if we used the sample mean as an estimate of the population mean. This is referred to as the standard error. Option 3 refers to a Type I error. Option 2 refers to standard deviation (which together with the mean are the only 2 variables between the population and the sample), but not to the mean as the definition of standard error requires. Question 56 The use of the t c test to compare the means of data from two independent samples of moderate size is appropriate when - - - - - a) the samples come from populations that are normally distributed b) the population variances are equal 1. (b) but not (a ) 2. (a) but not (b) 3. (a) and (b) Answer: The correct option is 3 Reasoning: Assumptions before using the t c-test: • Normally distributed with the same standard deviation • Two samples are independent samples Base your answers to Questions 57 and 58 on the following scenario An educational psychologist wants to know if learners will do significantly better on a test which measures reasoning skills if they take the same test again. She gives the test to a group of 100 grade twelve learners, and after an interval of two months she gives the same test to these same learners. Question 57 What assumption should the educational psychologist make when she tests her hypothesis for statistical significance? The sampl es of measurements from the first and second instances when the test was taken are - - - - 1. not correlated 2. independent 3. dependent Answer: The correct option is 3 Reasoning: The same 100 subjects were tested twice – initially and again after two months. In other words, each subject is matched with himself or herself, which is why the samples are regarded as dependent. This is a repeated measures design – which is an example of dependent group design. Question 58 Which test statistic is appropriate to test the difference between the first and second test for statistical significance? 1. The test statistic based on Pearson's r 2. The t d test statistic 3. The t c test statistic Answer: The correct option is 2 Reasoning: A tc test is used for independent samples and a t d test for dependent or correlated groups. Question 59 When evaluating a t -test for the comparison of two group means, what does it mean to say, "the difference between the means of two groups is statistically significant"? 1. If the null hypothesis were true, the results which were found in the sample data would be unlikely 2. The null hypothesis gives an adequate description of the relationships between the means 3. The results which were found in the sample data would be unlikely if the alternative hypothesis is true Answer: The correct option is 1 Reasoning: If the null hypothesis were true, there would not be a difference between the means of two groups. Therefore option 2 is incorrect. The result of statistically significant differences would be unlikely if the null hypothesis is true. Therefore option 3 i s incorrect. (Option 1 and 3 are opposites) Question 60 A graph which shows the extent to which a measurement of one variable is related to a measurement on another variable for variables measured on a ratio or interval scale is called a - - - - 1. histogram 2. scatter plot 3. contingency diagram Answer: The correct option is 2 Reasoning: Scatter plots represent correlations of variables on a ratio or interval scale, while histograms are better to represent variables on a nominal or ordinal level. Question 61 If the relationship between two variables where a person scoring low on one variable is most likely to score high on the other is determined with a Pearson's correlation coefficient, the value of r is likely to be 1. higher than zero 2. less than zero 3. close t o zero Answer: The correct option is 2