A graduate student believes that people consider faces with more contrast between eye color and skin tone as more feminine. She identifies the null and alternative hypotheses as:
H₀: The level of contrast between eye color and skin tone does not affect how feminine a face is considered.
H₁: The level of contrast between eye color and skin tone affects how feminine a face is considered.

She chooses a significance level of 0.01. 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 eye color and skin tone affects how feminine a face is considered.
There is not enough evidence to reject the hypothesis that the contrast between eye 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 eye color and skin tone affects how feminine a face is considered.
There is enough evidence to reject the hypothesis that the contrast between eye 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 not inside the critical region?

A. The graduate student should reject the alternative hypothesis.
B. The graduate student should reject the null hypothesis.
C. The graduate student cannot reject the null hypothesis.


Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is ____ the critical region. Therefore, the graduate student _____ reject the null hypothesis, and she _____ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.

Respuesta :

The  two possible decisions that the graduate student  is that:

  • 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.

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

If the test is not inside the critical region, the graduate student cannot reject the null hypothesis.

Suppose that the test statistic is 3.29 and the boundary to the critical region is 2.576. The test statistic is outside the critical region. So:

The test statistic is not in the critical region.

2. Therefore, the graduate student cannot reject the null hyopthesis,

3. and she cannot conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered.

Note that a failure to reject the null hypothesis in any kind of significance test does not imply that the null hypothesis holds true. It only imply that the person was not able to give enough evidence for the alternative hypothesis.

See options for the last question

Options for the last section...

1. The test statistic is ____not in/in_____ the critical region.

2. Therefore, the graduate student _____can/cannot_____ reject the null hyopthesis,

3. and she ______can/cannot_______ conclude that the level of contrast between eye color and skin tone affects how feminine a face is considered

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