Question

Suppose you carry out a significance test of population mean = 7 versus the alternating hypotheses not equal to 7 based on a sample size n = 28 and obtain t = 1.45. Find the p-value for this test. What conclusion can you draw at the 5% significance level? Explain.

a) The p-value is 0.0793. We reject H0 at the 5% significance level because the p-value 0.0793 is greater than 0.05.
b) The p-value is 0.0793. We fail to reject H0 at the 5% significance level because the p-value 0.0793 is greater than 0.05.
c) The p-value is 0.4207. We fail to reject H0 at the 5% significance level because the p-value 0.4207 is greater than 0.05.
d) The p-value is 0.1586. We fail to reject H0 at the 5% significance level because the p-value 0.1586 is greater than 0.05.

Answer 1

The p-value for the significance test is 0.2150. We fail to reject the null hypothesis at the 5% significance level because the p-value is greater than 0.05.

Step-by-step explanation:

The p-value is 0.2150, which means that there is a 21.5% probability of obtaining a t-value of 1.45 or more extreme if the null hypothesis is true. Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the population mean is different from 7 at the 5% significance level.