Question

A sample of 41 observations is selected from a normal population. The sample mean is 43, and the population standard deviation is 5. Conduct the following test of hypothesis using the 0.10 significance level. What is the p-value?

Answer 1

The test statistic for the hypothesis test is -0.3162 and the p-value is 0.7571.

Step-by-step explanation:

The test statistic for the hypothesis test can be calculated using the formula:

t = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Substituting the given values into the formula, we get:

t = (43 - 44) / (5 / sqrt(41)) = -0.3162

The degrees of freedom for this test are (n - 1), which is 40. We can use a t-table or a t-distribution calculator to find the p-value associated with the test statistic. In this case, the p-value is 0.7571.