Question

A report summarized the results of a survey of 301 U.S. businesses. Of these companies, 205 indicated that they monitor employees' web site visits. Assume that it is reasonable to regard this sample as representative of businesses in the United States. (a) Is there sufficient evidence to conclude that more than 75% of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. H0: p = 0.75 versus Ha: p < 0.75 H0: p = 0.75 versus Ha: p > 0.75 H0: p ≠ 0.75 versus Ha: p = 0.75 H0: p = 0.75 versus Ha: p ≠ 0.75 H0: p < 0.75 versus Ha: p > 0.75 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State your conclusion. Fail to reject H0. We do not have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits. Reject H0. We do not have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits. Reject H0. We have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits. Fail to reject H0. We have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits. (b) Is there sufficient evidence to conclude that a majority of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. State the appropriate null and alternative hypotheses. H0: p = 0.5 versus Ha: p > 0.5 H0: p < 0.5 versus Ha: p > 0.5 H0: p = 0.5 versus Ha: p < 0.5 H0: p ≠ 0.5 versus Ha: p = 0.5 H0: p = 0.5 versus Ha: p ≠ 0.5 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State your conclusion. Reject H0. We do not have convincing evidence that a majority of U.S. businesses monitor employees' web site visits. Reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits. Fail to reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits. Fail to reject H0. We do not have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.

Answer 1

H0: p = 0.75
Ha: p > 0.75

pcap = 205/301 = 0.6811

test statistic,
z = (0.6811 - 0.75)/sqrt(0.75*0.25/301)
z = -2.7606

p-value = 0.9971
Fail to reject H0. We do not have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits.

H0: p = 0.5 versus Ha: p > 0.5
test statistic,
z = (0.6811 - 0.5)/sqrt(0.5*0.5/301)
z = 6.2839

p-value = 0.0000
Reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.