Question

An increased number of colleges have been using online resources to research applicants. According to a study from last​ year, 31​% of admissions officers indicated that they visited an applying​ student's social networking page. A random sample of 200 admissions officers was recently selected and it was found that 65 of them visit the social networking sites of students applying to their college. Using α = 0.01​, complete parts a and b below.

a. Does this sample provide support for the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past​ year?

Determine the null and alternative hypotheses.

Choose the correct answer below.

A. H0​:p ≤ 0.31

H1​:p >0.31

B.H0​: p= 0.31

H1​:p ≠ 0.31

C. H0​: p > 0.31

H1​: p ≤ 0.31

D.H0≥ 0.31 0

H1​: p l < 0.31

Determine the critical​ value(s) of the test statistic.

zα= ​(Use a comma to separate answers as needed. Round to two two decimal places as​ needed.)

Calculate the test statistic.

zp = ​(Round to two decimal places as​ needed.)

Determine the conclusion. Choose the correct answer below.

A. Reject Reject Upper H 0 H0. There is not is not sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

B. Reject Reject Upper H 0 H0. There is is sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

C. Do not reject Do not reject Upper H 0 H0. There is not is not sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

D. Do not reject Do not reject Upper H 0 H0. There is is sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

b. Determine the​ p-value for this test. ​

p-value equals =

​(Round to three decimal places as​ needed.)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p <= 0.31
Alternative Hypothesis, Ha: p > 0.31

Rejection Region
This is right tailed test, for α = 0.01
Critical value of z is 2.33.
Hence reject H0 if z > 2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.325 - 0.31)/sqrt(0.31*(1-0.31)/200)
z = 0.46

C. Do not reject Do not reject Upper H 0 H0. There is not is not sufficient evidence to support the hypothesis that the proportion of admissions officers who visit an applying​ students' social networking page has increased in the past year

b)

P-value Approach
P-value = 0.323
As P-value >= 0.01, fail to reject null hypothesis.