Question

A report summarized the results of a survey of 304 U.S.businesses. Of these companies, 207 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.

a. H₀: p= 0.75 versus H_a: p< 0.75

b. H₀: p< 0.75 versus H_a: p> 0.75

c.  H₀: p≠0.75 versus H_a: p= 0.75

d. H₀: p= 0.75 versus H_a: p≠0.75

e. H₀: p= 0.75 versus H_a: p> 0.75

Find the test statistic and P-value. (Use a tableor technology. Round your test statistic to two decimal places and your P-valueto four decimal places.)

z =

P-value =

State your conclusion.

Reject H₀. We do not have convincing evidence that more than 75% of U.S. businesses monitor employees' web site visits.

Fail to reject H₀. We do not 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.

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.

a.H₀: p= 0.5 versus H_a: p≠0.5

b.H₀: p< 0.5 versus H_a: p> 0.5

c.H₀: p= 0.5 versus H_a: p< 0.5

d.H₀: p= 0.5 versus H_a: p> 0.5

e.H₀: p≠0.5 versus H_a: p= 0.5

Find the test statistic and P-value. (Use a tableor technology. Round your test statistic to two decimal places and your P-valueto four decimal places.)

z=

P-value =

State your conclusion.

Fail to reject H₀.We do not have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.

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.

Answer 1

a) The statistical software output for this problem is:

Hence,

Hypotheses: Option E is correct.

z = -2.78

P - value = 0.9973

Conclusion: Option B is correct.

b) The statistical software output for this problem is:

Hence,

Hypotheses: Option D is correct.

z = 6.31

P - value = 0.0000

Conclusion: Option C is correct.