Question

A sample of 34 observations is selected from a normal population. The sample mean is 28, and the population standard deviation is 4. Conduct the following test of hypothesis using the 0.05 significance level.

H0: μ ≤ 26
H1: μ > 26

Is this a one- or two-tailed test?

A. One-tailed test
B. Two-tailed test

Answer 1

This is a one-tailed test. The correct option is A.

Step-by-step explanation:

This is a one-tailed test. A one-tailed test is used when the alternative hypothesis suggests a specific direction (in this case, that the population mean is greater than 26). In a one-tailed test, all of the rejection region is on one side of the distribution curve.

To conduct the hypothesis test, we can use the standard normal distribution since the sample size is large (n > 30). We can calculate the test statistic using the formula:

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

Once we obtain the test statistic, we compare it with the critical value from the standard normal distribution at the 0.05 significance level. If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.