Question

A student claims that statistics students at her school spend, on average, an hour doing statistics homework each night. In an attempt to substantiate this claim, she selects a random sample of 6 of the 62 students who are taking statistics currently and asks them how much time they spend completing statistics homework each night. Here are the data (in hours): 0.75, 0.75, 0.75, 0.5, 1, 1.25. She would like to know if the data provide convincing statistical evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour. The student plans to test the hypotheses, H0: μ = 1 versus Ha: μ < 1, where μ = the true mean amount of time that statistics students spend doing statistics homework each night. The conditions for inference are met. The test statistic is t = –1.58 and the P-value is between 0.05 and 0.10. What conclusion should be made at the significance level, Alpha = 0.10?

Reject H0. There is convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.
Reject H0. There is not convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.
Fail to reject H0. There is convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.
Fail to reject H0. There is not convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.

Answer 1

Answer: Choice A

Reject the null H0

There's convincing evidence that the average amount time spent studying is less than one hour.

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Explanation:

There's a lot of info to sort through here. However, the only things we care about really are alpha and the p-value. While we don't know what the p-value is exactly, we know that it's between 0.05 and 0.10, which would make it smaller than alpha = 0.10

Any time the p-value is smaller than alpha we reject the null. We side with the alternative hypothesis and conclude that mu < 1. There's convincing evidence that the average amount of time studied is less than an hour.

One way to help remember whether to accept or reject the null is the phrase "if the p-value is low, then the null must go". By "low", it means "p-value smaller than alpha". We can think of the p-value as the probability of selecting that test statistic or more extreme. With a small p-value, it's fairly unlikely that will happen so that could mean that the null distribution isn't what we think it is (ie the true mean is likely smaller than 1).

Answer 2

The conclusion that can be made at the significance level, Alpha = 0.10 is to reject the null hypothesis.

What is a null hypothesis?

It should be noted that a null hypothesis simply means there's no significant relationship between the variables.

In this case, the conclusion that can be made at the significance level, Alpha = 0.10 is to reject the null hypothesis.

Therefore, there is convincing evidence that the true mean amount of time that statistics students spend doing statistics homework each night is less than one hour.

Learn more about null hypothesis on:

https://brainly.com/question/15980493