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

question 52

Multiple Choice

[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.

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Definitions:

P-value

The probability of obtaining a statistical summary (e.g., the difference in means) at least as extreme as the one observed in a study assuming the null hypothesis is true.

Two-sided Significance Tests

Statistical tests that assess the significance of an effect in either direction, allowing for the evaluation of both positive and negative differences.

Null Hypothesis

A statistical hypothesis that assumes no significant difference or relationship exists between certain parameters or distributions.

SRS

Simple Random Sample, a basic sampling technique in which each member of the population has an equal chance of being included in the sample.