assume a significance level of $ \alpha = 0.1 $ 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 17 bpm. the hypothesis test results in a p - value of 0.3167

a. state a conclusion about the null hypothesis. (reject $ h _ { 0 } $ or fail to reject $ h _ { 0 } $.) choose the correct answer below.
$ \bigcirc $ a. reject $ h _ { 0 } $ because the p - value is less than or equal to $ \alpha $.
$ \bigcirc $ b. fail to reject $ h _ { 0 } $ because the p - value is less than or equal to $ \alpha $.
$ \bigcirc $ c. reject $ h _ { 0 } $ because the p - value is greater than $ \alpha $.
$ \bigcirc $ d. fail to reject $ h _ { 0 } $ because the p - value is greater than $ \alpha $.

b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion?
$ \bigcirc $ a. 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 17 bpm.
$ \bigcirc $ b. there is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 17 bpm.
$ \bigcirc $ c. the standard deviation of pulse rates of the group of adult males is more than 17 bpm
$ \bigcirc $ d. the standard deviation of pulse rates of the group of adult males is less than or equal to 17 bpm.

Question

assume a significance level of $ \alpha = 0.1 $ 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 17 bpm. the hypothesis test results in a p - value of 0.3167

a. state a conclusion about the null hypothesis. (reject $ h _ { 0 } $ or fail to reject $ h _ { 0 } $.) choose the correct answer below.
$ \bigcirc $ a. reject $ h _ { 0 } $ because the p - value is less than or equal to $ \alpha $.
$ \bigcirc $ b. fail to reject $ h _ { 0 } $ because the p - value is less than or equal to $ \alpha $.
$ \bigcirc $ c. reject $ h _ { 0 } $ because the p - value is greater than $ \alpha $.
$ \bigcirc $ d. fail to reject $ h _ { 0 } $ because the p - value is greater than $ \alpha $.

b. without using technical terms, state a final conclusion that addresses the original claim. which of the following is the correct conclusion?
$ \bigcirc $ a. 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 17 bpm.
$ \bigcirc $ b. there is sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 17 bpm.
$ \bigcirc $ c. the standard deviation of pulse rates of the group of adult males is more than 17 bpm
$ \bigcirc $ d. the standard deviation of pulse rates of the group of adult males is less than or equal to 17 bpm.

Accepted Answer

# Explanation:
## Step1: Compare P - value and significance level
Given $ \alpha=0.1$ and $P - value = 0.3167$. Since $0.3167>0.1$ (i.e., $P - value>\alpha$).
## Step2: Make conclusion about null hypothesis
When $P - value>\alpha$, we fail to reject the null hypothesis $H_0$.
## Step3: Relate to original claim
The original claim is $H_1:\sigma > 17$ (where $\sigma$ is the standard deviation). Failing to reject $H_0$ (the opposite of the claim in a one - tailed test where $H_0:\sigma\leq17$) means there is not enough evidence to support the claim.

# Answer:
a. D. Fail to reject $H_0$ because the P - value is greater than $\alpha$
b. A. 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 17 bpm.

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QUESTION IMAGE

Question

Explanation:

Step1: Compare P - value and significance level

Step2: Make conclusion about null hypothesis

Step3: Relate to original claim

Answer: