Suppose there is a claim that a certain population has a mean,u , that is less than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05 level of significance. To start this test, you write the null hypothesis, Hv0 , and the alternative hypothesis, Hv1, as follows.

Question

Suppose there is a claim that a certain population has a mean,u , that is less than 9. You want to test this claim. To do so, you collect a large random sample from the population and perform a hypothesis test at the 0.05  level of significance. To start this test, you write the null hypothesis, Hv0 , and the alternative hypothesis, Hv1, as follows.

Hv0:  u=9
Hv1: u < 9
Suppose you also know the following information.

The value of the test statistic based on the sample is -2.144 (rounded to 3 decimal places).
The p-value is 0.016 (rounded to 3 decimal places).

Is this one or two-tailed?
what is the test statistic? what is the-p value?

GPT-4o mini · Answer

The hypothesis test you described is a one-tailed test. This is because the alternative hypothesis (Hv1: \( u < 9 \)) specifically looks for evidence that the mean is less than 9, rather than just any deviation from 9.

You've provided both the test statistic and the p-value:

The test statistic is \(-2.144\) (rounded to three decimal places).
The p-value is \(0.016\) (rounded to three decimal places).

To summarize:

Type of test: One-tailed
Test statistic: \(-2.144\)
p-value: \(0.016\)

At a significance level of \(0.05\), you would reject the null hypothesis (Hv0: \(u = 9\)) because the p-value \(0.016 < 0.05\), providing evidence that the population mean is less than 9.

Answer

(b)Based on your answer to part (a), which statement below is true?

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected.

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected.

Since the p-value is greater than the level of significance, the null hypothesis is rejected.

Since the p-value is greater than the level of significance, the null hypothesis is not rejected.

GPT-4o mini · Answer

Based on the information provided in part (a), where the p-value is \(0.016\) and the level of significance is \(0.05\), we can conclude the following:

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected.

Therefore, the correct statement is:

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected.