Question

A report summarized the results of a survey of 311 U.S. businesses. Of these companies, 204 indicated that they monitor employees' web site visits. For purposes of this exercise, 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 60% of U.S. businesses monitor employees' web site visits? Test the appropriate hypotheses using a significance level of 0.01. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	= ____________
P-value	= __________

(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. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z	=
P-value	=

Answer 1

a.

The following null and alternative hypotheses need to be tested Ho:p 0.6 Ha : p0.6 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region Based on the information provided, the significance level is a0.01, and the critical value for a right-tailed tse2.33 The rejection region for this right-tailed test is R :2.33) The z-statistic is computed as follows Po 0.6559 0.6 = 2.014 Since it is observed that2.0142.33, it is then concluded that the null hypothesis is not rejected using the P-value approach: The p-value is p = 0.022, and since p concluded that the null hypothesis is not rejected 0.022 > 0.01, it is It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p is greater than po, at the a 0.01 significance level The 99% confidence interval for p is: 0.587 p < 0.725

b)

The following null and alternative hypotheses need to be tested Ho:p 0.5 на : p > 0.5 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used (2) Rejection Region Based on the information provided. the significance level is 0.017 and the critical value for a right-tailed tse2.33 The rejection region for this right-tailed test is R :2.33) The z-statistic is computed as follows Po 0.6559 0.5 -5.5 Since it is observed that z5.5e 2.33, it is then concluded that the null hypothesis is rejected Using the P-value approach: The p-value is p 0, and since p 00.01, it is concluded that the null hypothesis is rejected It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than po, at the a 0.01 significance level Confidence Interval The 99% confidence interval for p is: 0.587 p < 0.725