Question

In testing the hypotheses H0: p = 0.40 versus Ha: p > 0.40, at the 5% significance level, if the sample proportion is .45, and the standard error of the sample proportion is .035, the appropriate conclusion would be:

a. Reject the null hypothesis.
b. Fail to reject the null hypothesis.
c. Accept the alternative hypothesis.
d. The conclusion cannot be determined from the information provided.

Answer 1

In testing the hypotheses H0: p = 0.40 versus Ha: p > 0.40, with a sample proportion of .45 and a standard error of .035, the appropriate conclusion would be to fail to reject the null hypothesis.

Step-by-step explanation:

In testing the hypotheses H0: p = 0.40 versus Ha: p > 0.40, we can use the sample proportion and the standard error of the sample proportion to calculate the test statistic and the p-value. The test statistic is calculated as (sample proportion - null hypothesis value) / standard error of the sample proportion. In this case, the test statistic is (0.45 - 0.40) / 0.035 = 1.43.

Since the alternative hypothesis is one-tailed (p > 0.40), we need to compare the test statistic to the critical value for a one-tailed test at 5% significance level. The critical value can be found in a Z-table and for a one-tailed test at 5% significance level, it is approximately 1.645.

Since the test statistic (1.43) is less than the critical value (1.645), we fail to reject the null hypothesis. Therefore, the appropriate conclusion is b. Fail to reject the null hypothesis.