Question

A filmmaker is considering two possible endings to her film. She shows both versions of her film to 50 young adults (aged 18-30) and 60 older adults (aged 30-50). Of the young adults, 39 preferred the first ending. Of the older adults, 43 preferred the first ending. She is interested in whether the proportions of individuals who prefer the first ending differ between the two age groups.

a. Which assumption is required for the filmmaker to be able to address her question of interest?

b. What are the null and alternative hypotheses?

c. What is the value of the test statistic?

d. What is the p-value? Give an expression involving a probability, not just a final answer.

e. State your conclusions in the language of the problem. Use a significance level of 5%.

f. Give a 95% confidence interval for the difference between the proportion of younger adults who prefer the first ending and the proportion of older adults who prefer the first ending.

Answer 1

a) It is assumed as the proportions of both young and older adults who preferred the first ending are different. It is also taken as Claim of this context.

b) H0 : the proporitons of both young and older adults who preferred the first ending are not different.

i.e P1 = P2

H1 :

the proporitons of both young and older adults who preferred the first ending are different.

i.e P1 P2

c) sample proportions 'p1' = 39/50 = 0.78

'p2' = 43/60 = 0.7167

n1 = 50

n2 = 60

Z test statistic = p1 - p2 / ?[p1q1/n1 + p2q2/n2]

= 0.78 - 0.7167 / ?[0.78 * 1 - 0.78 / 50 + 0.7167 * 1 - 0.7167 / 60]

= 0.759

d) This is two tailed test

so p value = 2 * p(Z > 0.759) = 2 * 0.2239 = 0.4479

e) Here

p value = 0.4479 > 0.05, then do not reject H0

Conclude that the proportions of both young and older adults who preferred the first ending are not different.