Question

A graduate student believes that people consider faces with more contrast between lip color and skin tone as more feminine. She identifies the null and alternative hypotheses as: H₀: The level of contrast between lip color and skin tone does not affect how feminine a face is considered. H₁: The level of contrast between lip color and skin tone affects how feminine a face is considered. She chooses a significance level of 0.05. After she collects the data and computes the sample statistics, it is time for her to make a decision about H₀. Check the two possible decisions that the graduate student can make given her choices of H₀ and H₁.

Check all that apply.

*There is not enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.

*There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone affects how feminine a face is considered. There is not enough evidence to reject the hypothesis that the contrast between lip color and skin tone affects how feminine a face is considered.

*There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.

What decision should the graduate student make if the test statistic is in the critical region?

*The graduate student should reject the alternative hypothesis.

*The graduate student cannot reject the null hypothesis.

*The graduate student should reject the null hypothesis.

Suppose that the test statistic is 2.62 and the boundary to the critical region is 1.96. The test statistic is ( in or not in ) the critical region. Therefore, the graduate student ( can or cannot ) reject the null hypothesis, and she ( can or cannot ) conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered.

Answer 1

1.

*There is not enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.

There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone does not affect how feminine a face is considered.

2.

*The graduate student cannot reject the null hypothesis.

Suppose that the test statistic is 2.62 and the boundary to the critical region is 1.96. The test statistic is not in the critical region. Therefore, the graduate student can reject the null hypothesis, and she can conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered.