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# Statistical Principles PSY 200

UNM

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This 12 page Class Notes was uploaded by Rocky Weimann on Wednesday September 23, 2015. The Class Notes belongs to PSY 200 at University of New Mexico taught by Steven Gangestad in Fall. Since its upload, it has received 19 views. For similar materials see /class/212223/psy-200-university-of-new-mexico in Psychlogy at University of New Mexico.

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Date Created: 09/23/15

GangestadF 10 Psychology 200 Introduction to Statistics Sample Exam Questions Exam 4 Part I True False Circle the best answer 2 points each T F 1 In a statistical test of two correlated means a version of the formula for testing a single mean is used T F 2 Ifa difference between two sample means is found to be nonsigni cant you should accept the null hypothesis that there is no difference between the population means T F 3 One reason why a correlation coef cient is transformed to a zr is because the standard error of r is not constant across levels of r Part II Multiple choice Circle the best answer 3 points each 1 Suppose a researcher rejects the null hypothesis that p rho between variable X and variable Y is the same in men than women Which of the following statements is implied by this nding a Variable X has a greater mean in men than women b Variable Y has a greater mean in men than women c Variable X is more positively associated with variable Y in men than women or vice versa d all of the above N To test whether two population correlation coef cients differ from one another a researcher should use a a t statistic b an F statistic c a 12 statistic d a Zstatistic Part II Short answer Provide a short answer to each question 5 points each 1 Describe the difference between a t test performed on independent samples and one performed on correlated samples What are the conditions under which you d choose to perform these tests Part IV Calculation questions Show your work 1 A psychologist examined the improvement in children s verbal skills resulting from watching Sesame Street over a period of 6 weeks A pretest was given prior to the treatment period and a posttest was given at the end of the six weeks On average kids verbal skill scores improved 24 points The standard deviation of the change scores was 32 A total of 10 kids were in the study Test whether or not kids scores changed from the pretest to the posttest Be sure to state the statistical hypotheses state the alpha level compute your test statistic state your degrees of freedom for the test state the critical value for the test and make your conclusions 10 points 2 Thirty young infants were shown pictures of faces in a controlled situation Half were shown a picture of an attractive face as judged by adults The other half were shown a picture of a less attractive face Time of staring at the picture was used as a measure of interest Infants shown the attractive face stared at it an average of 186 seconds standard deviation 51 seconds Infants shown the less attractive face stared at it an average of 141 seconds standard deviation 58 seconds Test whether the two groups of infants stared at the picture the same amount of time Give the statistical hypotheses the alpha level a test statistic degrees of freedom for the test the critical value for the test statistic and your conclusions 10 points 3 In a study examining the effect of raceethnicity of a defendant participants were presented with a transcript of a trial and asked to indicate the probability that the defendant was guilty Judgments were made on a 10pointscale where 1 definitely not guilty to 10 definitely guilty All participants read the same transcript However onethird of them were told the defendant was white onethird were told the defendant was AfricanAmerican and onethird were told the defendant was MexicanAmerican Results are presented below Analyze the data and draw a conclusion 15 points White defendant AfricanAmerican defendant MexicanAmerican defendant 6 7 10 6 2 9 10 3 4 5 5 4 10 1 8 7 GangestadF 09 Psychology 200 Introduction to Statistics Sample Exam Answers Exam 4 Part I True False Circle the best answer 2 points each 1 T 2 F 3 T Part 11 Multiple choice Circle the best answer 3 points each 1 c 2 d Part 11 Short answer Provide a short answer to each question 5 points each 1 Describe the difference between a I test performed on independent samples and one performed on correlated samples What are the conditions under which you d choose to perform these tests A ttest on independent samples tests whether the observed difference between two sample means could have occurred by chance as large at least 5 of the time under the null hypothesis that the population means are identical A ttest on correlated samples tests whether the mean difference between the two variables could have occurred by chance under the null hypothesis that the population means are identical A ttest on independent samples is used when observations are made on two samples of different individuals a betweensubject design A ttest on correlated samples is used when observations in two different conditions are made on a single sample of individuals a withinsubject design Part IV Calculation questions Show your work 1 A psychologist examined the improvement in children s verbal skills resulting from watching Sesame Street over a period of 6 weeks A pretest was given prior to the treatment period and a posttest was given at the end of the six weeks On average kids verbal skill scores improved 24 points The standard deviation of the change scores was 32 A total of 10 kids were in the study Test whether or not kids scores changed from the pretest to the posttest Be sure to state the statistical hypotheses state the alpha level compute your test statistic state your degrees of freedom for the test state the critical value for the test and make your conclusions 10 points Ho 1 In a 05 t9 2432 110 237 lt 05 Reject null hypothesis Kids skills improve H1 1 1 df 9 tam 2262 between testings 2 Thirty young infants were shown pictures of faces in a controlled situation Half were shown a picture of an attractive face as judged by adults The other half were shown a picture of a less attractive face Time of staring at the picture was used as a measure of interest Infants shown the attractive face stared at it an average of 186 seconds standard deviation 51 seconds Infants shown the less attractive face stared at it an average of 141 seconds standard deviation 58 seconds Test whether the two groups of infants stared at the picture the same amount of time Give the statistical hypotheses the alpha level a test statistic degrees of freedom for the test the critical value for the test statistic and your conclusions 10 pornts H0 1 p a 05 t28 186 141 J14 x 511 14 x 581I28 x 115 115 226p lt 05 H1 1 1 df 28 tum 2048 Reject null hypothesis infants stare more at attractive faces 3 In a study examining the effect of raceethnicity of a defendant participants were presented with a transcript of a trial and asked to indicate the probability that the defendant was guilty Judgments were made on a lOpointscale where l definitely not guilty to 10 definitely guilty All participants read the same transcript However onethird of them were told the defendant was white onethird were told the defendant was AfricanAmerican and onethird were told the defendant was MexicanAmerican Results are presented below Analyze the data and draw a conclusion 15 points White defendant AfricanAmerican defendant MexicanAmerican defendant 6 36 10 100 10 100 7 49 10 100 6 36 2 4 9 81 10 100 3 9 4 16 5 25 5 25 4 16 10 100 l l 8 64 7 49 H o 1 2 l 3 H1 at least two means differ SST 911 117218 1505 d B 2 MS 285 F215 285623 457 lt 05 f SS 9633753841172118 57 d W 15 MSW 623 Reject the null hypothesis ethnicity SSW 1505 57 935 Fem 215 368 affectsjudgments in this trial Psychology 200003 Fall 2010 Sample Exam Questions Exam 1 The following questions were actual test questions on a previous exam They will not appear on this year s exam but questions like these may appear Pad 1 Multiple choice Circle the best answer 3 points each 1 An ordinal scale has which of the following properties equal intervals meaningful absolute zero magnitude all three E 9997 2 The percentage of scores at or below a given interval in a grouped frequency distribution may be read directly from a simple frequency distribution cumulative frequency distribution relative frequency distribution cumulative distribution 9 0quotm 3 Here is a frequency distribution of scores score 6 l 5 2 4 5 3 10 2 10 l 5 This distribution is a negatively skewed b positively skewed c platykurtic d leptokurtic Palt II Shon answer 1 For each of the following indicate the type of measurement scale 2 points each 1 make of car 2 number of brothers 2 Which of the following summary statistics of the mean median mode and variance must be wrong Why 3 points Mean 24 Median 45 Mode 5 Variance 972 Part III Calculation problems Show all of your work 1 2 points each 10 points total Answer with regard to the following scores X1 9 X2 6 X3 3 X4 6 X5 11 a 25X b Zoo5 c Eon2 d ZX7z e Which of the above is equal to what is referred to as the sum of squares in the calculation of the variance in the definitional formula in this set of numbers 2 8 points total Answer with regard to the following scores 21 1218 24 21 30 a 3 points What s the mean b 3 points What s the standard deviation c 2 points What s the median Note In total there were 30 points based on multiple choice questions Part I 20 points based on short answer questions Part II and 50 points based on calculation questions Part III Psychology 200003 Fall 2010 Sample Exam Answers Exam 1 The following questions were actual test questions on a previous exam They will not appear on this year s exam but questions like these may appear Part 1 Multiple choice Circle the best answer 3 points each 1 An ordinal scale has which of the following properties equal intervals meaningful absolute zero magnitude all three E 9957 2 The percentage of scores at or below a given interval in a grouped frequency distribution may be read directly from a a simple frequency distribution b cumulative frequency distribution c relative frequency distribution d cumulative distribution 3 Here is a frequency distribution of scores score f 6 1 5 2 4 5 3 7 2 8 1 5 This distribution is a negatively skewed b positively skewed c platykurtic d leptokurtic Part II Short answer 1 For each of the following indicate the type of measurement scale 2 points each nominal 1 make of car ratio 2 number of brothers 2 Which of the following summary statistics of the mean median mode and variance must be wrong Why 3 points Mean 24 Median 45 Mode 5 Variance 972 The variance A variance must be positive Part III Calculation problems Show all of your work 1 2 points each 10 points total Answer with regard to the following scores X 2 X 3 3 X4 6 X5 11 a ZSXi5x95x65x35x65x11175 b ZX5 9 6 3 6 115 7 c 2Xi292623262112283 d 2Xi729 726 723 726 7211 7238 e Which of the above is equal to what is referred to as the sum of squares in the calculation of the variance in the definitional formula in this set of numbers 1 2 8 points total Answer with regard to the following scores 21 1218 24 21 30 a 3 points What s the mean 21 i21121s242130621 b 3 points What s the standard deviation s 121 212 12 212 18 212 24 212 21 212 30 2125 6 c 2 points What s the median 21 GangestadF 10 Psychology 200 Introduction to Statistics Sample Exam Questions Exam 3 Part I True False Circle the best answer 2 points each T F 1 In a statistical test the probability of the observed sample results is computed tentatively assuming that the null hypothesis is true T F 2 As sample size increases the standard error ofthe mean increases T F 3 The alternative hypothesis is often the one the investigator wants to be able to support Part II Multiple choice Circle the best answer 3 points each N E The standard error of the mean is the sample standard deviation standard deviation of a distribution of sample means standard deviation of the population of raw scores typical deviation of a score from the sample mean 51 0quotm The standard deviation of a raw variable is 5 The standard error of the mean for some N can possibly be a 25 b 5 c 5 d none of the above In a particular study H0 is rejected with a 05 This result means that a the probability that the null hypothesis is correct is less than 05 b if H 0 is true the probability of a sample mean as extreme as that observed is less than 05 c the alternative hypothesis has a 95 chance of being true d if H 1 is true the probability of a sample mean as extreme as that observed is at least Part II Short answer Provide a short answer to each question 5 points each 1 State the Central Limit Theorem and explain why it is so important to inferential statistic s Palt IV Calculation questions Show your work 1 The Minnesota Multiphasic Personality Inventory MMPI is a widely used test of personality in clinical settings The scores on each of its 11 main scales have a population mean of 50 and a population standard deviation of 10 Suppose we randomly draw a sample of 25 individuals What is the standard error of the mean 3 points 2 You re interested in estimating the mean number of times individuals brush their teeth a day in the population of UNM students You draw a sample of 100 individuals The sample mean is 17 and the sample standard deviation is 9 What is your best estimate of the population mean State the 95 con dence limits of the mean Note Please keep in mind that the standard deviation is estimated from a sample and is not the population value 6 points 3 In a study of subliminal perception 36 participants were exposed to letters for very brief durations After each exposure they were asked to indicate which letter they saw out of a list of 4 Each participant was given 40 trials Out of the 40 trials participants got a mean of 1060 correct with a standard deviation of 260 Test the hypothesis that participants perform the task at chance levels Be sure to state the null and alternative hypotheses an alpha level a test statistic a critical value for the test statistic and a conclusion Note Chance levels here amount to getting one quarter of the trials right that is getting 10 out of the 40 correct 10 points GangestadF 10 Psychology 200 Introduction to Statistics Sample Exam Answers Exam 3 Part I True False Circle the best answer 2 points each T F 1 In a statistical test the probability of the observed sample results is computed tentatively assuming that the null hypothesis is true T F 2 As sample size increases the standard error ofthe mean increases T F 3 The alternative hypothesis is often the one the investigator wants to be able to support Part II Multiple choice Circle the best answer 3 points each N E The standard error of the mean is the a sample standard deviation b standard deviation of a distribution of sample means c standard deviation of the population of raw scores d typical deviation of a score from the sample mean The standard deviation of a raw variable is 5 The standard error of the mean for some N can possibly be a 25 b 5 c 5 d none of the above In a particular study H0 is rejected with a 05 This result means that a the probability that the null hypothesis is correct is less than 05 b if H 0 is true the probability of a sample mean as extreme as that observed is less than 05 c the alternative hypothesis has a 95 chance of being true d if H 1 is true the probability of a sample mean as extreme as that observed is at least 95 Part II Short answer Provide a short answer to each question 5 points each 1 State the Central Limit Theorem and explain why it is so important to inferential statistic s The Central Limit Theorem states that as N becomes large the sampling distribution of the mean approaches a normal distribution It is important to inferential statistics because our test statistics assume that the sampling distribution of the mean is normal the Central Limit Theorem says that in general we can safely do so Part IV Calculation questions Show your work 45 points total 1 The Minnesota Multiphasic Personality Inventory MMPI is a widely used test of personality in clinical settings The scores on each of its 11 main scales have a population mean of 50 and a population standard deviation of 10 Suppose we randomly draw a sample of 25 individuals What is the standard error of the mean 3 points ch GX IN 10 125 105 2 2 You re interested in estimating the mean number of times individuals brush their teeth a day in the population of UNM students You draw a sample of 100 individuals The sample mean is 17 and the sample standard deviation is 9 What is your best estimate of the population mean State the 95 con dence limits of the mean Note Please keep in mind that the standard deviation is estimated from a sample and is not the population value 6 points u Xi tmt x sx lN 17 i 1984 x 9 l100 17 i 18 ie 152 to 188 You can interpolate a tmt value of 1984 from your table and be close enough 3 In a study of subliminal perception 36 participants were exposed to letters for very brief durations After each exposure they were asked to indicate which letter they saw out of a list of 4 Each participant was given 40 trials Out of the 40 trials participants got a mean of 1060 correct with a standard deviation of 260 Test the hypothesis that participants perform the task at chance levels Be sure to state the null and alternative hypotheses an alpha level a test statistic a critical value for the test statistic and a conclusion Note Chance levels here amount to getting one quarter of the trials right that is getting 10 out of the 40 correct 10 points H0 y 10 H1 u 10 a 05 t35 106 1026 l36 6433 139 with 35 df tcm 203 Decision Do not reject the null hypothesis

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