Question

A researcher is testing the null hypothesis that the population mean is 50, at the .05 significance level. If the p-value associated with the t-test is .073, the researcher should conclude:

1) the population mean equals 50
2) the population mean may be 50
3) the population mean is different from 50
4) the sample mean is different from the population mean

Answer 1

The correct conclusion, given a p-value of .073 and a significance level of .05, is that the researcher does not reject the null hypothesis, suggesting that the population mean may be 50.

Step-by-step explanation:

The question is regarding the decision a researcher should make after conducting a t-test to compare a sample mean to a known population mean. The null hypothesis states that the population mean is 50.

Given that the p-value associated with the t-test is .073, and the significance level is at .05, the researcher should compare the p-value to the significance level. Since the p-value is higher than the significance level (0.073 > 0.05), the researcher does not reject the null hypothesis.

Therefore, based on the given data, the correct conclusion is that the population mean may be 50. It does not provide sufficient evidence to prove that the population mean is different from 50 (option 2).