Question

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:

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

Step-by-step explanation:

We shall need to formulate the hypotheses but first we need to understand the claim in context of this question. The claim is that  the standard deviation of time all women spend washing their hair in the morning is 15 seconds. In mathematical notation, this claim can be written as follows;

σ = 15

Clearly the claim contains an equality sign and thus it qualifies to be our null hypothesis;

H0: σ = 15

The complement of the above hypothesis will be our alternative hypothesis;

Ha: σ ≠ 15

We are then informed that the initial conclusion of the test fails to reject the null hypothesis. In short this implies that we fail to reject the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds since this claim is our null hypothesis. If we fail to reject a claim in hypothesis testing, this implies that there is sufficient evidence to support the claim. Therefore, 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