Grand Canyon University_PSY 520 Topic 7 Exercise:Chapter 19 and 20 COMPLETE SOLUTION;Graded A

Running head: TOPIC 7 EXERCISES 1 Topic 7 Exercises Meagan Brown Grand Canyon University: PSY-520 November 5, 2017 TOPIC 7 EXERCISES Topic 7 exercises 19.9 Randomly selected records of 140 convicted criminals rev ...

Running head: TOPIC 7 EXERCISES 1 Topic 7 Exercises Meagan Brown Grand Canyon University: PSY-520 November 5, 2017 TOPIC 7 EXERCISES Topic 7 exercises 19.9 Randomly selected records of 140 convicted criminals reveal that their crimes were committed on the following days of the week: (a) Using the .01 level of significance, test the null hypothesis that in the underlying population, crimes are equally likely to be committed on any day of the week. H0: μ m = μ t = μ w = μ th = μ f = μ sa = μ su =1/7 H1: H0 is false α=.01 df=6 X 2 crit= 16.81 X 2= 3.4 Days when crimes were committed fequency M T W TH F Sa Su total observed 17 21 22 18 23 24 15 140 expected 20 20 20 20 20 20 20 difference s -3 1 2 -2 3 4 -5 squared 9 1 4 4 9 16 25 div/fe 0.45 0.05 0.2 0.2 0.45 0.8 1.25 3.4 X^2= 3.4 Decision 2 TOPIC 7 EXERCISES Fail to reject the null hypothesis because X 2= 3.4 does not exceed the X 2 crit= 16.81 at the . 01 level of significance. (b) Specify the approximate p -value for this test result. p>.10 (c) How might this result be reported in the literature? There is no evidence that crimes are committed more often on any day of the week [X 2 (6, n=140) = 3.4, p > .10, Cramer’s phi = 0.004048]. 19.10 While playing a coin-tossing game in which you are to guess whether heads or tails will appear, you observe 30 heads in a string of 50 coin tosses. (a) Test the null hypothesis that this coin is unbiased, that is, that heads and tails are equally likely to appear in the long run. H T total fo 30 20 50 fe 25 25 differenc e 5 -5 square 25 25 div/fe 1 1 2 X^2= 2 α=.05 df=1 X 2 crit= 3.84 X 2= 2 H0: μ h = μ t = 1/2 H1: H0 is false 3 TOPIC 7 EXERCISES Fail to reject the null hypothesis at the .05 level of significance because X 2= 2 which is exceeded by X 2 crit= 3.84. (b) Specify the approximate p -value for this test result. p>.10 *19.13 In 1912, over 800 passengers perished after the ocean liner Titanic collided with an iceberg and sank. The table below compares the survival frequencies of cabin and steerage passengers. (a) Using the .05 level of significance, test the null hypothesis that survival rates are independent of the passengers’ accommodations (cabin or steerage). Chi-Square Test SUMMARY Alpha 0.05 Count Rows Cols df 1291 2 2 1 CHI-SQUARE chi-sq p-value x-crit si g Cramer V Odds Ratio Pearson's 88.6487963 9 4.71513E21 3.84145882 1 ye s 0.26204344 5 3.01985407 1 Max likelihood 89.1385542 4 3.68107E21 3.84145882 1 ye s 0.26276630 4 3.01985407 1 H0: The type of accommodation and the survival rate are independent. 4 TOPIC 7 EXERCISES H1: H0 is false Decision Rule: Reject the null hypothesis at the .05 level of significance if X 2 ≥ 3.84, given that df = 1. Decision Reject H0 at the .05 level of significance because X 2= 88.64879639 which exceeds 3.84. Interpretation Survival was lower among steerage passengers. (b) Assuming a significant X 2 , estimate the strength of the relationship. Cramer’s phi= 88.64879639/1291(2-1)= 0.068667 According to Cramer’s phi of 0.069 there is a small to medium effect size. (c) To more fully appreciate the importance of this relationship, calculate an odds ratio to determine how much more likely a cabin passenger is to have survived than a steerage passenger. OR 1.06785 7 0.35361 2 3.01985 4 Cabin passengers were 3.02 times more likely to survive the sinking of the Titanic than the steerage passengers. 19.14 In a classic study, Milgram et al . “lost” stamped envelopes with fictitious addresses (Medical Research Association, Personal Address, Friends of Communist Party, and Friends of Nazi Party).* One hundred letters with each address were distributed among four locations (shops, cars, streets, and phone booths) in New