Consider the following hypothesis test: H0:
≤ 50
Ha: > 50
A sample of 55 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05.
a. With = 52.5, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No
b. With = 51, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No
c. With = 51.8, what is the value of the test statistic (to 2 decimals)?
Can it be concluded that the population mean is greater than 50?
Yes or No

a. z=3.09. Yes, it can be concluded that the population mean is greater than 50.

b. z=1.24. No, it can not be concluded that the population mean is greater than 50.

c. z=2.22. Yes, it can be concluded that the population mean is greater than 50.

Step-by-step explanation:

We have a hypothesis test for the mean, with the hypothesis:

The sample size is n=55 and the population standard deviation is 6.

The significance level is 0.05.

We can calculate the standard error as:

For a significance level of 0.05, the critical value for z is zc=1.644. If the test statistic is bigger than 1.644, the null hypothesis is rejected.

a. If the sample mean is M=52.5, the test statistic is:

The null hypothesis is rejected, as z>zc and falls in the rejection region.

b. If the sample mean is M=51, the test statistic is:

The null hypothesis failed to be rejected, as z<zc and falls in the acceptance region.

c. If the sample mean is M=51.8, the test statistic is:

The null hypothesis is rejected, as z>zc and falls in the rejection region.