Question

Consider the hypothesis test given by Ho:u=530, H1:u does not equal 530. In a random sample of 85 subjects, the sample mean is found to be 522.3. Also, the population standard deviation is 29.

Determine the P-value for this test. Is there sufficient evidence to justify the rejection of Ho at the a=0.01 level? Explain and show work.

Answer 1

Use a one-sample z-test.

z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With your data:
z = (522.3 - 530)/(29/√85) = ?

Finish the calculation.

Check a z-table at .01 level of significance for a two-tailed test (H1 does not show a specific direction; therefore, the test is two-tailed.)
If the z-test statistic exceeds the critical value from the z-table, reject the null and conclude H1 ≠ 530. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null. If you determine the P-value, check the table using the z-test statistic. The P-value is the actual level of the test statistic.

I hope this will help get you started.