[Objective: Understand the hypothesis test of proportions from two populations] Two movie reviewers give movies "thumbs Up" and "thumbs down" ratings. You sample 100 movies that they both have rated and find that they both gave "thumbs up" to 25 movies, both gave "thumbs down" to 30 movies, Sarah gave "thumbs up" and Jessica "thumb down" to 28 movies, and the remaining movies Sarah gave "thumbs down" and Jessica "thumbs up". Test whether there is a tendency for one reviewer to give more movies "thumbs up" (proportion 1) than the other (proportion 2).
A) z=1.56 For a two-sided test at \alpha=0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.
B) z=-1.56 For a two-sided test at \alpha=0.05 level, there is insufficient evidence to reject the null hypothesis because the cutoff z-value is at 1.96.
C) z=1.96 There is sufficient evidence to accept the null hypothesis.
D) z=-1.96 There is sufficient evidence to reject the null hypothesis.

Question

Quizplus · Accepted Answer

The calculation of the z-score in hypothesis testing for proportions involves comparing the observed difference in proportions to the expected difference under the null hypothesis, which assumes no difference between the two proportions. The z-score of 1.56 indicates the observed difference is 1.56 standard deviations away from the expected difference of zero. Since the absolute value of 1.56 is less than the critical value of 1.96 for a two-sided test at the 0.05 significance level, there is insufficient evidence to reject the null hypothesis, suggesting that the difference in proportions of "thumbs up" ratings between the two reviewers is not statistically significant.

[Objective: Understand the Hypothesis Test of Proportions from Two Populations]