Question

12. A survey of 61 comma 648 people included several questions about office relationships. Of the​ respondents, 26.7​% reported that bosses scream at employees. Use a 0.01 significance level to test the claim that more than 1 divided by 4 of people say that bosses scream at employees. How is the conclusion affected after learning that the survey is an online survey in which Internet users chose whether to​ respond? Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

Identify the null and alternative hypotheses. Choose the correct answer below.

A.H0​: p = 0.25

H1​: p > 0.25

B.H0​: p = 0.75

H1​: p > 0.75

C.H0​: p = 0.75

H1​: p ≠ 0.75

D.H0​: p = 0.75

H1​: p < 0.75

E.H0​: p = 0.25

H1​: p ≠ 0.25

F.H0​: p = 0.25

H1​: p < 0.25

The test statistic is z=____

​(Round to two decimal places as​ needed.)

The​ P-value is_____

​(Round to four decimal places as​ needed.)

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

(Reject/Fail to reject) H0. There (is not/is) sufficient evidence to support the claim that more than 1 divided by 4 of people say that bosses scream at employees. If the sample is a voluntary response​ sample, the conclusion (might not be/is) valid.

Answer 1

The null and alternative hypothesis are

H0: p = 0.25

Ha: p > 0.25

Test statistics

z = - p / sqrt( p( 1 - p) / n)

= 0.267 - 0.25 / sqrt( 0.25 * 0.75 / 61648)

= 9.75

This is test statistics value.

p-value = P( Z > z)

= P( Z > 9.75)

= 0 (From Z table)

Since p-value < 0.01 level, we have sufficient evidence to reject H0.

We conclude that,

Reject H0, There is sufficient evidence to support the claim that more than 1/4 of people says that

bosses scream at employees. If sample is voluntary response sample, the conclusion might not be valid.