PSYC 354 HOMEWORK 6 Percentiles and Hypothesis Testing with Z-Tests When submitting this file, be sure the filename includes your full name, course and section. Example: HW6_JohnDoe_354B01 Be sure you have reviewed this module/week's lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Questions 1-4 Part I: Concepts These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. Part I: Questions 1-7 End-of-chapter problems: Answer the following questions. If applicable, remember to show work in your homework document for partial credit. 1) What are the 6 steps of hypothesis testing? (State the 6 steps) A) B) C) D) E) F) 2) Using the z table in Appendix B, calculate the following percentages for a z score of -0.45 2-a) % above this z score: Answer 2-b) % below this z score: Answer Work: Work: Page 1 of 7 PSYC 354 2-c) At least as extreme as this z score (on either side): Work: Answer 3) Rewrite each of the following percentages as probabilities, or p levels: 3-a) 5% = Answer 3-b) 95% = Answer 3-c) 43% = Answer 4) If the critical values, or cutoffs, for a two-tailed z test are -2.05 and +2.05, determine whether you would reject or fail to reject the null hypothesis in each of the following cases: 4a) z = 2.23 4b) z = -0.97 5) Answer Answer Imagine a class of twenty-five 12-year-old girls with an average height of 62 inches. We know that the population mean and standard deviation for this age group of girls is m=59 inches, s = 1.5 inches. (Note that this is a z statistic problem.) 5a) Calculate the z statistic for this sample (not the z score). Answer 5b) How does this sample mean compare to the distribution of sample means? In other words, how does the height of the girls in the sample compare to the height of girls in th general population? Answer 6) For the following scenarios, identify whether the researcher has expressed a directional or a nondirectional hypothesis: 6a) Social media has changed the levels of closeness in long-distance relationships. Answer 6b) A professor wonders whether students who eat a healthy breakfast score better on exams in morning courses than those who do not eat a healthy breakfast. Answer For the following scenario, state the null and research hypotheses in both words and symbolic notation. Symbolic notation must include the symbols \" \" and \" \" and a comparison operator (=, , <, >, , ), as described in Nolan and 7) Heinzen (2014). Remember to consider whether the hypothesis is nondirectional or directional. Scenario: A professor wonders whether students who eat a healthy breakfast score better on exams in morning courses than those who do not eat a healthy breakfast. Null Hypothesis (H0): Symbolic Notation Answer Page 2 of 7 PSYC 354 Null Hypothesis: Answer Written Statement Research Hypothesis (H1): Symbolic Notation Research Hypothesis: Written Statement Answer Answer Part I: Questions 8a-8g Fill in the highlighted blanks with the best word or words. 8-a) Values of a test statistic beyond which you reject the null hypothesis are called ________. 8-b) The ________ is the area in the tails in which the null can be rejected. The probability used to determine the critical values, or cutoffs, in hypothesis testing 8-c) is known as a ________ level, also known as alpha. If your data differ from what you would expect if chance were the only thing 8-d) operating, you would call your finding ________. 8-e) A hypothesis test in which the research hypothesis is directional is a(n) ________ test. 8-f) A hypothesis test in which the research hypothesis specifies that there will be a difference but does not specify the direction of that difference is a(n) ________ test. 8-g) If your z-statistic exceeds the critical cutoff, you can ________ the null hypothesis. Page 3 of 7 PSYC 354 Part I: Questions 9a-9c The police department of a major city has found that the average height of their 1,200 officers is 71 inches (in.) with = 2.6 inches. Use the normal distribution and the formulas and steps in this week's presentations to answer the following questions: Note: Showing work is required for this section. Remember that it helps to transfer the raw mean and SD from the description above to the standardized curve shown here (though you don't need to show this). This helps compare raw and z scores and check your work. What is the z score for an officer who is 72 inches tall? Based on the z score and the 9a) z table, what is the officer's percentile? (Hint: See slide 7 of this week's related presentation) Answer (z Work (required): score): Answer Work/reasoning using z table (required): (percentile): 9b ) What is the height (in inches) that marks the 80th percentile for this group of officers? (Hint: See slides 14-16 of this week's related presentation) Answer Work (required): 9c) What percent of officers are between 68 and 72 inches tall? (Hint: See slide 12 of this week's related presentation) Work (required): Answer Page 4 of 7 PSYC 354 Part I: Questions 10a-10c The verbal part of the Graduate Record Exam (GRE) has a of 500 and = 100. Use the normal distribution and the formulas and steps in this week's presentations to answer the following questions: Note: Showing work is required for this section. Remember that it helps to transfer the raw mean and SD from the description above to the standardized curve shown here (though you don't need to show this). This helps compare raw and z scores and check your work. What is the z score for a GRE score of 583? 10a) What is the percentile rank of this z score? (Hint: See slide 7 of this week's related presentation) Answer (z Work (required): score): Answer Work (required): (percentile): 10b What GRE score corresponds to a percentile rank of 25%? (Hint: See slide 17 of this week's related presentation) ) Answer Work (required): If you wanted to select only students at or above the 82nd percentile, what GRE 10c) score would you use as a cutoff score (i.e. what GRE score corresponds to this percentile)? (Hint: See slides 14-16 of this week's related presentation) Answer Work (required): Part II: SPSS Analysis For this section, you will be using last module/week's data set containing IQ scores. Open the file; it should also contain the standardized IQ variable you created last module/week. Page 5 of 7 PSYC 354 Part II: Question 1a & 1b Use last week's HW file that you created using IQ scores, and the SPSS reading and presentation from this week. Using the z-scored IQ variable, create percentile ranks assuming the scores are normally distributed. o Call the new percentile variable \"IQ rank.\" 1a) List the first 5 IQ ranks from your file (rows 1-5). Answer: Row 1: Row 2: Row 3: Row 4: Row 5: 1b ) Which raw IQ score seems to best divide the top 50% from the bottom 50% of scores? (This score can be found by looking carefully over the values in the IQ rank column) Answer Part III: SPSS Data Entry and Analysis There is no Part III material this module/week. Part IV: Cumulative Data provided below for respective questions. Part IV: (Non-SPSS) Questions 1-4 For a distribution with M = 40 and s = 5: Page 6 of 7 PSYC 354 1) What is the z-score corresponding to a raw score of 32? Answer 2) What is the z-score corresponding to a raw score of 50? Answer 3) Work: If a person has a z-score of 1.8, what is his/her raw score? Answer 4) Work: Work: If a person has a z-score of -.63, what is his/her raw score? Answer Work: Part IV: (Non-SPSS) Question 5-8 For the following types of data, state the graph that would be the best choice to display the data. Two items have more than one correct answerfor these, either answer is acceptable. 5) A nominal independent variable (IV) and a scale dependent variable (DV) Answer 6) One scale variable with frequencies (when you want to see the general shape of the distribution). Answer 7) One scale IV and one scale DV Answer 8) One nominal variable broken down into percentages Answer Submit Homework 6 by 11:59 p.m. (ET) on Monday of Module/Week 6. Remember to name file appropriately. Done! Page 7 of 7 PSYC 354 HOMEWORK 7 Confidence Intervals, Effect Size, and Statistical Power When submitting this file, be sure the filename includes your full name, course and section. Example: HW7_JohnDoe_354B01 Be sure you have reviewed this module/week's lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Questions 1-8 Part I: Concepts These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. Part I: Questions 1a-1e Fill in the highlighted blanks with the best word or words. 1-a) The confidence interval is centered around the ________ of the sample. 1-b) Cohen's d measures the difference between means in terms of ________. 1-c) According to Cohen's conventions, a d value of ________ indicates a small effect. 1-d) A study that calculates the mean effect size from the individual effect sizes of many studies is called a(n) ________. 1-e) Statistical power refers to the probability of successfully rejecting the ________. Part I: Questions 2-5 End-of-chapter problems: Complete the following problems. Page 1 of 5 PSYC 354 If applicable, remember to show work in your homework document to receive partial credit. 2) List five factors that affect statistical power. For each, indicate how a researcher can leverage/manipulate that factor to increase power in a study. A) B) C) D) E) 3) Exercise 8.22 from N&H text: In 2006, approximately 47% of Americans, when surveyed by a Gallup poll, felt that having a gun in the home made them safer than having no gun. The margin of error reported was 3%. Construct an interval estimate using these figures. Answer 4) For each of the following confidence levels, look up the critical z values for a two-tailed test. 4a) 80% (Hint: 10% in each tail): Answer Work: 4b) 88% Answer Work: 5) Remembering that a meta-analysis calculates one mean effect size using the effect sizes of several studies, assume you are conducting a meta-analysis over a set of five studies. The effect sizes for each study are: d= .80, d = .09, d = .46, d = .65, d = .28 5a) Calculat e the mean effect size of these studies. Answer 5b) Use Cohen's conventions to describe the mean effect size you calculated in part (a). Answer Page 2 of 5 PSYC 354 Part I: Questions 6-8 Compute effect size in the following questions: 6 ) A company decides to add a new program that prepares randomly selected sales personnel to increase their number of sales per month. The mean number of sales per month for the overall population of sales personnel at this national company is 25 with a standard deviation of 3. The mean number of sales per month for those who participated in the new program is 30. Compute the effect size of the new sales program. Answer 7 ) On a certain anxiety questionnaire, the general population is known to have a mean of 16 and a standard deviation of 2.4. A higher score represents higher levels of anxiety. Participants in a new relaxation program complete the questionnaire after completing the program and have a mean score of 12.5. What is the effect size of the relaxation program? Answer 8 ) Work: Work: A residential treatment facility tests a new group therapy for patients with selfdestructive behaviors. The therapists hope to decrease scores on a measure of selfdestructive behaviors that has a mean in the overall residential treatment population of 15 and a standard deviation of 1.6. The mean score for the patients after the new group therapy is 13.7. What is the effect size of the new group therapy? Answer Work: Part II & Part III There is no new SPSS material this module/week. No questions for Part II or III . Part IV: Cumulative Data provided below for respective questions. Page 3 of 5 PSYC 354 Helping Behaviors 47 56 52 39 40 63 39 45 50 46 32 54 47 35 65 61 43 56 59 52 Part IV: Questions 1-4 A test designed to measure helping behavior was administered to 20 university students. The data from this test are shown in the column to the left. (higher scores more helping). Enter the Helping Behaviors data into a new SPSS file. 1-a) Using SPSS, calculate descriptive statistics for this variable. Be sure to include the mean and standard deviation. Answer: Descriptive Statistics Table 2) Create the appropriate graph in SPSS for the variable \"Helping Behaviors.\" Justify your choice of graph. Answer: Appropriate graph Justification 3) Using the mean and standard deviation of the helping behaviors data above (from your SPSS output), calculate (by hand) the raw score that marks the 45th percentile of this data set. (See last week's material for review.) Answer Work: 4) Using the mean and standard deviation of the helping behaviors data above, calculate the percentile of a raw score of 37. (See last week's material for review.) Answer Work: Page 4 of 5 PSYC 354 Part IV: Question 5a-5e For the following scores, state the: a) mean; b) median; c) mode; d) range; e) standard deviation. 39 35 43 27 35 5-a) Mean Answer Work: 5-b) Median Answer Work: 5-c) Mode Answer Work: 5-d) Range Answer Work: Standard Deviation (Note: Compute by hand using the formula from Module 3. 5-e) Programs like SPSS or Excel use a slightly different formula that we won't use until Module 8 and will give you the wrong answer for this section.) Answer Work: Submit Homework 7 by 11:59 p.m. (ET) on Monday of Module/Week 7. Remember to name file appropriately. Done! Page 5 of 5 PSYC 354 HOMEWORK 7 Confidence Intervals, Effect Size, and Statistical Power When submitting this file, be sure the filename includes your full name, course and section. Example: HW7_JohnDoe_354B01 Be sure you have reviewed this module/week's lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file. Questions 1-8 Part I: Concepts These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. Part I: Questions 1a-1e Fill in the highlighted blanks with the best word or words. 1-a) The confidence interval is centered around the ________ of the sample. 1-b) Cohen's d measures the difference between means in terms of ________. 1-c) According to Cohen's conventions, a d value of ________ indicates a small effect. 1-d) A study that calculates the mean effect size from the individual effect sizes of many studies is called a(n) ________. 1-e) Statistical power refers to the probability of successfully rejecting the ________. Part I: Questions 2-5 End-of-chapter problems: Complete the following problems. Page 1 of 5 PSYC 354 If applicable, remember to show work in your homework document to receive partial credit. 2) List five factors that affect statistical power. For each, indicate how a researcher can leverage/manipulate that factor to increase power in a study. A) B) C) D) E) 3) Exercise 8.22 from N&H text: In 2006, approximately 47% of Americans, when surveyed by a Gallup poll, felt that having a gun in the home made them safer than having no gun. The margin of error reported was 3%. Construct an interval estimate using these figures. Answer 4) For each of the following confidence levels, look up the critical z values for a two-tailed test. 4a) 80% (Hint: 10% in each tail): Answer Work: 4b) 88% Answer Work: 5) Remembering that a meta-analysis calculates one mean effect size using the effect sizes of several studies, assume you are conducting a meta-analysis over a set of five studies. The effect sizes for each study are: d= .80, d = .09, d = .46, d = .65, d = .28 5a) Calculat e the mean effect size of these studies. Answer 5b) Use Cohen's conventions to describe the mean effect size you calculated in part (a). Answer Page 2 of 5 PSYC 354 Part I: Questions 6-8 Compute effect size in the following questions: 6 ) A company decides to add a new program that prepares randomly selected sales personnel to increase their number of sales per month. The mean number of sales per month for the overall population of sales personnel at this national company is 25 with a standard deviation of 3. The mean number of sales per month for those who participated in the new program is 30. Compute the effect size of the new sales program. Answer 7 ) On a certain anxiety questionnaire, the general population is known to have a mean of 16 and a standard deviation of 2.4. A higher score represents higher levels of anxiety. Participants in a new relaxation program complete the questionnaire after completing the program and have a mean score of 12.5. What is the effect size of the relaxation program? Answer 8 ) Work: Work: A residential treatment facility tests a new group therapy for patients with selfdestructive behaviors. The therapists hope to decrease scores on a measure of selfdestructive behaviors that has a mean in the overall residential treatment population of 15 and a standard deviation of 1.6. The mean score for the patients after the new group therapy is 13.7. What is the effect size of the new group therapy? Answer Work: Part II & Part III There is no new SPSS material this module/week. No questions for Part II or III . Part IV: Cumulative Data provided below for respective questions. Page 3 of 5 PSYC 354 Helping Behaviors 47 56 52 39 40 63 39 45 50 46 32 54 47 35 65 61 43 56 59 52 Part IV: Questions 1-4 A test designed to measure helping behavior was administered to 20 university students. The data from this test are shown in the column to the left. (higher scores more helping). Enter the Helping Behaviors data into a new SPSS file. 1-a) Using SPSS, calculate descriptive statistics for this variable. Be sure to include the mean and standard deviation. Answer: Descriptive Statistics Table 2) Create the appropriate graph in SPSS for the variable \"Helping Behaviors.\" Justify your choice of graph. Answer: Appropriate graph Justification 3) Using the mean and standard deviation of the helping behaviors data above (from your SPSS output), calculate (by hand) the raw score that marks the 45th percentile of this data set. (See last week's material for review.) Answer Work: 4) Using the mean and standard deviation of the helping behaviors data above, calculate the percentile of a raw score of 37. (See last week's material for review.) Answer Work: Page 4 of 5 PSYC 354 Part IV: Question 5a-5e For the following scores, state the: a) mean; b) median; c) mode; d) range; e) standard deviation. 39 35 43 27 35 5-a) Mean Answer Work: 5-b) Median Answer Work: 5-c) Mode Answer Work: 5-d) Range Answer Work: Standard Deviation (Note: Compute by hand using the formula from Module 3. 5-e) Programs like SPSS or Excel use a slightly different formula that we won't use until Module 8 and will give you the wrong answer for this section.) Answer Work: Submit Homework 7 by 11:59 p.m. (ET) on Monday of Module/Week 7. Remember to name file appropriately. Done! Page 5 of 5