the following Nolan and Heinzen end-of-chapter questions for Chapter 7: o 7.8, 7.18, 7.20, 7.22, 7.28 [sections (a) and (b)] o 7.32 [sections (a)-(d)], 7.34, 7.39 o 7.40 [sections (a) and (b)]. 7.8 What are the six steps of hypothesis testing? 7.18 Using the z table in Appendix B, calculate the following percentages for a z score of -0.08: a. Above this z score b. Below this z score c. At least as extreme as this z score 7.20 Rewrite each of the following percentages as probabilities, or p levels: a. 5% b. 83% c. A51% 7.22 If the critical values for a hypothesis test occur where 25% of the distribution is in each tail, what are the cut offs for z? 7.28 If the cutoffs for z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases: a. z=-0.94 b. z=2.12 c. A z score for which 49.6% of the data fall between z and the mean 7.32 z distribution and height: Elena, a 15-year-old girl, is 58 inches tall. Based on what we know, the average height for girls at this age is 63.80 inches, with a standard deviation of 2.66 inches. a. Calculate her z score. b. What percentage of girls are taller than Elena? c. What percentage of girls are shorter? 7.34 The z statistic and height: Imagine a class of thirty-three 15-year-old girls with an average height of 62.6 inches. Remember, u= 63.8 inches and 6=2.66 inches. a. Calculate the z statistic. b. How does this sample of girls compare to the distribution of sample means? c. What is the percentile rank for this sample? 7.39 Directional versus nondirectional hypotheses: For each of the following example, identify whether the research has expressed a directional or a nondirectional hypothesis: a. A researcher is interested in studying the relation between the use of antibacterial products and the dryness of people's skin. He thinks these products might alter the moisture in skin compared to other products that are not antibacterial. b. A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students? c. Cell phones are everywhere, and we are now available by phone almost all of the time. Does this translate into a change in the closeness of our long-distance relationships? 7.40 Null hypotheses and research hypotheses: For each of the following examples (the same as those in Exercise 7.39), state the null hypothesis and the research hypothesis, in both words and symbolic notation: a. A researcher is interested in studying the relation between the use of antibacterial products and the dryness of people's skin. He thinks these products might alter the moisture in skin compared to other products that are not antibacterial. b. A student wonders if grades in a class are in any way related to where a student sits in the classroom. In particular, do students who sit in the front row get better grades, on average, than the general population of students? 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. Part I: Concepts Questions 1-4 These questions are based on the Nolan and Heinzen reading and end-of-chapter questions. Part I: Questions 1-8 End-of-chapter problems: Answer the following Nolan and Heinzen end-of-chapter questions for Chapter 7: o 7.8, 7.18, 7.20, 7.22, 7.28 [sections (a) and (b)] o 7.32 [sections (a)-(d)], 7.34, 7.39 o 7.40 [sections (a) and (b)]. If applicable, remember to show work in your homework document for partial credit. 1) Exercise 7.8 (1 pt) (State the 6 steps) A) Identify the populations, comparison distribution, and assumptions. B) State the null and research hypotheses. C) Determine the characteristics of the comparison distribution. D) Determine critical values or cut-offs. E) Calculate the test statistic. F) Make a decision about the null hypothesis. 2) Exercise 7.18 (1 pt each) 2-a) Above this z score Work: 3.19% + 50% = 53.19%; Page 1 of 8 PSYC 354 2-b) Below this z score 2-c) At least as extreme as this z score Work: 50% - 3.19% = 46.81%; Work: Area beyond z score = 46.81%; 46.81(2) = 93.62% 3) Exercise 7.20 (1 pt each) 3-a) 0.05; 3-b) 0.83; 3-c) 0.51 4) Exercise 7.28 (a & b) (1 pt each) 4a) Fail to reject null; -.94 is not more extreme than -2.58; 4b) Fail to reject null; 2.12 is not more extreme than 2.58 5 Exercise 7.32 (a, b, c) (1 pt each) ) 5a) Calculate her z score. 5b) What percentage of girls are taller than Elena? 5c) What percentage of girls are shorter? 6 ) Work: -2.18; Work: 98.54%; Work: 1.46% inches; Exercise 7.34 (a & b) (note that this is a z statistic problem) (1 pt each) 6a) z statistic = -2.59; 6b) The sample of girls has a mean height well below average (2.59 standard deviations below the the expected mean). 7 ) Exercise 7.39 (1 pt each) 7a) Nondirectional (\"alter\" does not specify increase or decrease); 7b) Directional: better grades expected; Page 2 of 8 PSYC 354 7c) Nondirectionalinterested in any change in closeness in relationships 8 ) Exercise 7.40a: Symbolic notation must include the symbols \" \" and \" \" and a comparison operator (=, , <, >, , ), as described in Nolan and Heinzen (2014) (4 pts) Null Hypothesis (H0): Symbolic Notation H0: 1 = 2; there is no difference between groups; H1: 1 /= 2; there is some difference between groups (nondirectional); Null Hypothesis: Written Statement Research Hypothesis (H1): Symbolic Notation Research Hypothesis: Answer Answer Written Statement 8b) Exercise 7.40b: Symbolic notation must include the symbols \" \" and \" \" and a comparison operator (=, , <, >, , ), as described in Nolan and Heinzen (2014) (4 pts) Null Hypothesis (H0): Symbolic Notation Null Hypothesis: Answer H0: 1 <= 2; students in front of class earn grades of equal or lesser value than general population; H1: : 1 > 2; students in front of class earn grades of higher value than general population Answer Written Statement Research Hypothesis (H1): Symbolic Notation Answer Research Hypothesis: Answer Written Statement Part I: Questions 9a-9f Fill in the highlighted blanks with the best word or words. (1 pt each) 9-a) Values of a test statistic beyond which you reject the null hypothesis are called critical values. 9-b) The rejection region is the area in the tails in which the null can be rejected. Page 3 of 8 PSYC 354 9-c) If your data differ from what you would expect if chance were the only thing operating, you would call your finding statistically significant. 9-d) A hypothesis test in which the research hypothesis is directional is a(n) onetailed test. 9-e) 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) twotailed test. 9-f) If your z-statistic exceeds the critical cutoff, you can reject the null hypothesis. Page 4 of 8 PSYC 354 Part I: Questions 10a-10c The police department of a major city has found that the average height of their 1,250 officers is 71 inches (in.) with = 2.3 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 73 inches tall? Based on the z score and 10a) the z table, what is the officer's percentile? (4 pts) Answer (z score): Answer (percentile): 10b ) Work (required): Work/reasoning using z table (required): What is the height (in inches) that marks the 80th percentile for this group of officers? (2 pts) Answer Work (required): 10c) What percent of officers are between 64 and 71 inches tall? (2 pts) Answer Work (required): Page 5 of 8 PSYC 354 Part I: Questions 11a-11c The verbal part of the Graduate Record Exam (GRE) has a of 500 and = 100. Use the normal distribution 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 523? 11a) What is the percentile rank of this z score? (4 pts) Answer (z Work (required): score): Answer Work (required): (percentile): 11b) What verbal GRE score corresponds to a percentile rank of 12%? (2 pts) Answer Work (required): If you wanted to select only students at or above the 85th percentile, what 11c) verbal GRE score would you use as a cutoff score (i.e. what GRE score corresponds to this percentile)? (2 pts) 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 6 of 8 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). (5 pts) Answer: Row 1: 86.39; Row 2: 80.72; Row 3: 50.15; Row 4: 99.10; Row 5: 59.26 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) (1 pt) raw IQ = 104 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 = 30 and s = 6: Page 7 of 8 PSYC 354 1) What is the z-score corresponding to a raw score of 20? (2 pts) Work: 20? z = (20-25)/4 = -1.25 2) What is the z-score corresponding to a raw score of 36? (2 pts) Work: 36? z = (36-25)/4 = 2.75 3) If a person has a z-score of 1.2, what is his/her raw score? (2 pts) Work: x = 1.2(4) + 25 = 29.8 4) If a person has a z-score of -.73, what is his/her raw score? (2 pts) x = -.73(4) + 25=22.08 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) (1 pt) Answer 6) One scale variable with frequencies (when you want to see the general shape of the distribution). (1 pt) Answer 7) One scale IV and one scale DV (1 pt) Answer 8) One nominal variable broken down into percentages (1 pt) Answer Submit Homework 6 by 11:59 p.m. (ET) on Monday of Module/Week 6. Remember to name file appropriately. Done! Page 8 of 8