A report summarized the results of a survey of 318 U.S. businesses. Of these com
ID: 3151891 • Letter: A
Question
A report summarized the results of a survey of 318 U.S. businesses. Of these companies, 209 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.)
State your conclusion.
a.Do not reject H0. We do not have convincing evidence that more than 60% of U.S. businesses monitor employees' web site visits.
b.Do not reject H0. We have convincing evidence that more than 60% of U.S. businesses monitor employees' web site visits.
c. Reject H0. We do not have convincing evidence that more than 60% of U.S. businesses monitor employees' web site visits.
d.Reject H0. We have convincing evidence that more than 60% 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. (Round your test statistic to two decimal places and your P-value to four decimal places.)
State your conclusion.
a. Reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits
b. .Do not reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.
c.Do not reject H0. We do not have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.Reject H0.
d,We do not have convincing evidence that a majority of U.S. businesses monitor employees' web site visits.
z = P-value =Explanation / Answer
A)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.6
Ha: p > 0.6
As we see, the hypothesized po = 0.6
Getting the point estimate of p, p^,
p^ = x / n = 0.657232704
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.027472113
Getting the z statistic,
z = (p^ - po)/sp = 2.083301887 [ANSWER, Z]
As this is a 1 tailed test, then, getting the p value,
p = 0.018611857 [ANSWER, P VALUE]
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As P > 0.01,
OPTION A: Do not reject H0. We do not have convincing evidence that more than 60% of U.S. businesses monitor employees' web site visits. [ANSWER]
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b)
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.5
Ha: p > 0.5
As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.657232704
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.028038608
Getting the z statistic,
z = (p^ - po)/sp = 5.607721541 [ANSWER, Z]
As this is a 1 tailed test, then, getting the p value,
p = 1.02504*10^-8 [ANSWER, P VALUE]
************************************
As P < 0.01,
OPTION A: a. Reject H0. We have convincing evidence that a majority of U.S. businesses monitor employees' web site visits [ANSWER]
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