Question

Assume a significance level of alpha = 0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm. The hypothesis test results in a​P-value of 0.2761.a. State a conclusion about the null hypothesis.​(Reject H0 or fail to reject H0​.) Choose the correct answer below.A. Fail to reject H0​ because the​ P-value is less than or equal to alphaα.B. Reject H0​ because the​ P-value is less than or equal to alphaα.C.Fail to reject H0​ because the​ P-value is greater than alphaα.D. Reject H0​ because the​ P-value is greater than alphaα.b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?A. The standard deviation of pulse rates of the group of adult males is more than 11 bpm.B. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.C. The standard deviation of pulse rates of the group of adult males is less than or equal to 11 bpm.D. There is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 11 bpm.

Answer 1

The correct decision is to fail to reject the null hypothesis since the p-value is greater than alpha. Consequently, there is not enough evidence to support the claim that the standard deviation of pulse rates is more than 11 bpm.

Step-by-step explanation:

Given an alpha level of 0.05 and a p-value of 0.2761:

(a) Since the p-value is greater than alpha (0.2761 > 0.05), we fail to reject the null hypothesis (H0). This corresponds to choice C of the provided options.

(b) The final conclusion regarding the original claim that the standard deviation of pulse rates of a group of adult males is more than 11 bpm would be there is not sufficient evidence to support the original claim. This corresponds to choice B of the provided options.

Answer 2

a

The correct option is B

b

The correct option is D

Step-by-step explanation:

From the question we are told that

The level of significance is
`\alpha = 0.05`

The p-value is
`p = 0.2761`

Considering question b

Given that the
`p< \alpha` then the null hypothesis is rejected

Considering question b

Given that the original claim is The standard deviation of pulse rates of a certain group of adult males is more than 11 bpm

Then the null hypothesis is
`H_o : \sigma = 11`

The reason why the null hypothesis is write like this above is because a null hypothesis expression can not contain only a > or a < but only allows =
`\le , \ and \ \ge`

and the alternative hypothesis is
`H_a : \sigma > 11`

Now given that the null hypothesis is rejected, it mean that there is sufficient evidence to support original claim