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): n1=96, x1=49

Fourth-Years (Pop. 2):n2=88, x2=54

Is there evidence, at an α=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.

A. The value of the standardized test statistic: Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a) ( − ∞ , a ) is expressed (-infty, a), an answer of the form (b,∞) ( b , ∞ ) is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞) ( − ∞ , a ) ∪ ( b , ∞ ) is expressed (-infty, a)U(b, infty).

B. The rejection region for the standardized test statistic:

C. The p-value is

D. Your decision for the hypothesis test:

A. Reject H0

B. Do Not Reject H0

C. Do Not Reject H1

D. Reject H1

Answer 1

The statistical software output for this problem is:

From above output:

a) Test statistic = -1.4089

b) Rejection region: (-infty, -2.3263) U (2.3263, infty)

c) p - Value = 0.1589

d) Do not reject Ho