Question

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.

A) Check the two possible decisions that the graduate student can make given his choices of H₀ and H₁. Check all that apply.

1) 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) 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.

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

4) 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.

B) What decision should the graduate student make if the test statistic is not inside the critical region?

1) The graduate student should reject the alternative hypothesis.

2) The graduate student cannot reject the null hypothesis.

3)The graduate student should reject the null hypothesis.

C) Suppose that the test statistic is 2.59 and the boundary to the critical region is 1.96. The test statistic is (in/not in) the critical region????

Therefore, the graduate student (cannot/can) reject the null hypothesis???

and he (can/cannot) conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered????

Answer 1

Answer)

There are two possible conditions

First one

We reject the null hypothesis, in this case we have enough evidence to support the alternative hypothesis

Second one

We fail to reject the null hypothesis, in this case we do not have enough evidence to support the alternative hypothesis

So answers are

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 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.

B)

Critical region means rejection region

And if the test statistics is inside the critical region

Then we reject the null hypothesis

So as here test statistics is not in critical region

The graduate student cannot reject the null hypothesis or should reject the alternate hypothesis

C)

Critical region is

If test statistics is greater than 1.96

Aa 2.59 is > 1.96

The test statistics is in the critical region, therefore the graduate student can reject the null hypothesis

and he he can conclude that the level of contrast between lip color and skin tone affects how feminine a face is considered