Question

WILL MARK BRAINLIEST IF YOU ARE CORRECT!
You are testing a claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds. You find the initial conclusion of your test fails to reject the null hypothesis. State the final conclusion.


There is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.


There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is not 15 seconds.


There is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds.


There is not sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds.

Answer 1

Answer: Choice C

There is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds

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Explanation:

First focus on "You find the initial conclusion of your test fails to reject the null hypothesis"

The key thing to pull out from that is "fail to reject the null hypothesis". Failing to reject means we basically "accept", more or less, the null. We have no other choice until more data comes along to reject the null.

The claim is " the standard deviation of time all women spend washing their hair in the morning is 15 seconds." which is where the null hypothesis is made. In terms of symbols, we would write $\sigma = 15$. The alternate hypothesis is $\sigma \ne 15$. The symbol $\sigma$ is the greek letter sigma that represents the population standard deviation.