Question

Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering yes'' are given below: First-Years (Pop. 1):Fourth-Years (Pop. 2):?1=88,?2=98,?1=46?2=53 Is there evidence, at an ?=0.04 level of significance, to conclude that there is a difference in proportions between first-years and fourth-years?

Carry out an appropriate hypothesis test, filling in the information requested (to at least three decimal places, without rounding in intermediate steps). Remember that for the test of equality of two proportions, the SE requires the use of the pooled proportion.

A. The value of the standardized test statistic _______:

B. The p-value is ______.

Your decision for the hypothesis test:

A. Do Not Reject ?1.

B. Do Not Reject ?0.

C. Reject ?0.

D. Reject ?1.

Answer 1

Here we have 46, n-88, Pi-0.522727 253,n2 -98, P2 -0.540816 Hypotheses are Ho:P1-P20 Level of significance a-0.04 Test is two tailed The pooled proportion is -(46+53)/(88+98)-0.532258 The standard error is: P(l-p)0.073277 1 ni Test Statistics: P P-(P-P)-0.25 SE Critical value: CV 2.05 Rejection Region: If I zl > 2.05, Reject H0 Decision: Since test statistics does not lie in rejection region so we fail to reject the null P-value =0.8026 Decision: Since p-value is not less than level of significance so we fail to reject the null Excel function for critical value Excel function for p-value: NORMSINV(1-(0.04/2)) =2*(1-NORMSDIST(0.25))

Answers:

A:

The test statistics is:

z = -0.25

B:

The p-value is

p-value = 0.8026

C:

B. Do Not Reject ?0.