Final answer:
To test the hypothesis H0: p = 0.75 versus Ha: p > 0.75, use a one-sample proportion test with a sample size of 20, proportion of 0.78, and standard error of 0.015. Calculate the test statistic and compare it to the critical value or use the p-value to determine whether to reject or fail to reject the null hypothesis.
Step-by-step explanation:
To test the hypothesis H0: p = 0.75 versus Ha: p > 0.75, we can use a one-sample proportion test. Given a sample size (n) of 20, a proportion (p) of 0.78, and a standard error (se) of 0.015, we can calculate the test statistic using the formula:
test statistic = (p - p0) / se
where p0 is the hypothesized proportion. In this case, p0 = 0.75.
Plugging in the values, we get the test statistic: (0.78 - 0.75) / 0.015 = 2.00.
Considering a right-tailed test, we can find the p-value by comparing the test statistic to the critical value from the standard normal distribution or by using a statistical software or calculator. If the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.