Question

The test statistic of z = 2.27 is obtained when testing the claim that p > 0.52. This is a right-tailed test. Using a 0.10 significance level, complete parts (a) and (b).

a. Find the critical value(s). Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.)

A. There is one critical value; the critical value is [Enter the critical value]
B. There are two critical values; the lower critical value is [Enter the lower critical value], and the upper critical value is [Enter the upper critical value]

b. Should we reject H0 or should we fail to reject H0?

A. H0 should not be rejected since the test statistic is in the critical region.
B. H0 should not be rejected since the test statistic is not in the critical region.
C. H0 should be rejected since the test statistic is not in the critical region.
D. H0 should be rejected since the test statistic is in the critical region.

Answer 1

To find the critical value, subtract the significance level from 1 and then find the corresponding z-score in the standard normal distribution table. Compare the test statistic with the critical value to determine whether to reject or fail to reject the null hypothesis.

Step-by-step explanation:

a. To find the critical value(s), we need to determine the cutoff point that separates the critical region from the non-critical region. Since this is a right-tailed test, the critical value will be on the right side of the distribution. Using a 0.10 significance level, we can find the critical value by subtracting the significance level from 1 and then finding the corresponding z-score in the standard normal distribution table.

b. To determine whether to reject or fail to reject the null hypothesis (H0), we compare the test statistic (z = 2.27) with the critical value(s) we found in part (a). If the test statistic is in the critical region (greater than the critical value), we reject H0. If the test statistic is not in the critical region (less than or equal to the critical value), we fail to reject H0.