Question

Assume a significance level of alpha equals 0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: Less than 53​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.2831.

a. State a conclusion about the null hypothesis.​ (Reject Upper H 0 or fail to reject Upper H 0​.) Choose the correct answer below.
A. Reject Upper H 0 because the​ P-value is less than or equal toless than or equal to alphaα.
B. Reject Upper H 0 because the​ P-value is greater thangreater than alphaα.
C. Fail to reject Upper H 0 because the​ P-value is greater thangreater than alphaα.
D. Fail to reject Upper H 0because the​ P-value is less than or equal toless than or equal to alphaα.

Answer 1

Fail to reject Upper H 0 because the​ P-value is greater than alpha (α).

Explanation:

We are given the following hypothesis below;

Null Hypothesis,
`H_0` : p = 53% {means that 53​% of adults would erase all of their personal information online if they could}

Alternate Hypothesis,
`H_A` : p < 53% {means that less than 53​% of adults would erase all of their personal information online if they could}

Also, we are given the level of significance to be 0.05 and P-value = 0.2831.

Now, the decision rule about null hypothesis based on P-value is given by;

• If the P-value is less than the level of significance, then we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.

• If the P-value is more than the level of significance, then we have insufficient evidence to reject our null hypothesis as the test statistics will not fall in the rejection region.

So here, the P-value is more than the level of significance as 0.2831 > 0.05, so we will fail to reject our null hypothesis because the​ P-value is greater than alphaα.