Question

5. The decision-making process

A graduate student believes that people consider faces with more contrast between lip color and skin tone as more feminine. He 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.

He chooses a significance level of 0.05. After he collects the data and computes the sample statistics, it is time for him to make a decision about H₀.

Check the two possible decisions that the graduate student can make given his 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 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.

There is enough evidence to reject the hypothesis that the contrast between lip color and skin tone affects how feminine a face is considered.

What decision should the graduate student make if the test statistic is not inside 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 2.59 and the boundary to the critical region is 1.96. The test statistic is   the critical region. Therefore, the graduate student   reject the null hypothesis, and he   conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered.

You may use the Distributions tool if you find it helpful.

Answer 1

(a)

Correct option:

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.

(b)

If the test statistic is not in the critical rgion:

Correct option:

The graduate student cannot reject the null hypothesis.

(c)

Suppose the test statistic is 2.58 and the boundary to the critical region is 1.96. The test statistic is inside the critical region. Therefore the graduate student must reject the null hypothesis and he must conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered.