Question

Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: More than 52​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.2504.

a. State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H 0​.) Choose the correct answer below.

A. Fail to reject H0 because the​ P-value is greater than alpha.
B. Fail to reject H0 because the​ P-value is less than or equal to alpha.
C. Reject H0 because the​ P-value is greater than alpha.
D. Reject H0 because the​ P-value is less than or equal to alpha.

b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?

A. The percentage of adults that would erase all of their personal information online if they could is less than or equal to 52​%.
B. There is sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is more than 52​%.
C. The percentage of adults that would erase all of their personal information online if they could is more than 52​%.

Answer 1

(a) Fail to reject
`H_0` because the​ P-value is greater than alpha.

(b) The percentage of adults that would erase all of their personal information online if they could is less than or equal to 52​%.

Explanation:

We are given that assume a significance level of alpha equals 0.05 and use the given information to complete parts​;

Original​ claim : More than 52​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.2504.

Let p = ​% of adults who would erase all of their personal information online if they could

So, Null Hypothesis,
`H_0` : p
`\leq` 52% {means that percentage of adults that would erase all of their personal information online if they could is less than or equal to 52​%}

Alternate Hypothesis,
`H_A` : p > 52% {means that percentage of adults that would erase all of their personal information online if they could is more than 52​%}

(a)The conclusion about the null hypothesis is that;

We fail to reject null hypothesis,
`H_0` because the​ P-value is greater than alpha as 0.2504 > 0.05.

(b) The correct conclusion based on the fact that null hypothesis has been rejected is;

The percentage of adults that would erase all of their personal information online if they could is less than or equal to 52​%.