The following data is from A. Welsh (2010). “On the Perils of Living Dangerously
ID: 3154285 • Letter: T
Question
The following data is from A. Welsh (2010). “On the Perils of Living Dangerously in the Slasher Horror Film: Gender Differences in the Association Between Sexual Activity and Survival,” Sex Roles, Vol. 62 pp. 762-773. Below is a 2 × 2 contingency table summarizing data for 485 characters from 50 randomly selected horror films. The categorical variables are whether the character engaged in sexual activity during the film and whether they survived at the end of the film.
.......Survive
Sex | No Yes | Total
No ....261 67 ...328
Yes ..139 18 ....157
Total ..400 85 ...485
(a) State the null and alternative hypotheses of the 2test for independence.
(b) What are the assumptions for this test?
(c) Compute the 2 × 2 table of expected counts.
(d) Calculate the 2 test statistic and state your decision for this test at the = 0.05 significance
level. Show your work.
(e) Calculate the conditional probabilities of survival given sexual activity.
(f) Let p1 represent the proportion of characters who engaged in sexual activity and died, and let p2 represent the proportion of characters who did not engage in sexual activity and died. Without
conducting this test directly, what is the test statistic and p-value for the test
H0 : p1 p2 = 0 vs HA : p1 6= p2
Hint: Use your result from (c).
(g) Calculate the relative risk of dying for the characters who engaged in sexual activity to those
who did not. Interpret the result.
Explanation / Answer
answer a)
H0: sexual activity during the film are independent of they survived at the end of the film
HA: sexual activity during the film are not independent of they survived at the end of the film
answer b) relative risk=(a/(a+b))/(c/(c+d)) =(261/328)/(139/157)=0.8987
answer c)
answer d)
chi-square=sum(O-E)2/E=5.899 with 1 df
critical chi-squrar(0.05,1)=3.84
null hypothesis is rejected and we conclude that sexual activity during the film are not independent of they survived at the end of the film
answer e)
answer f) difficult to answer as the alternative hypothesis HA not clearly stated (please send proper information)
answer g)
survive sex NO Yes total No a=261 b=67 a+b=328 Yes c=139 d=18 c+d=157 400 85 485Related Questions
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