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):n1=84,n2=89,x1=57x2=64First-Years (Pop. 1):n1=84,x1=57Fourth-Years (Pop. 2):n2=89,x2=64

Is there evidence, at an α=0.1, 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

Answer 1

(A)

H0: Null Hypothesis: p1 = p2 ( There is no difference in proportions between first-years and fourth-years)

HA: Alternative Hypothesis: p1 p2 ( There is a difference in proportions between first-years and fourth-years) (Claim)

n1 = 84

1 = 57/84 = 0.6786

n2 = 89

2 = 64/89 = 0.7191

Pooled Proportion is given by:

Test Statistic is given by:

So,

The value of the standardized test statistic= - 0.581

(B)

= 0.10

From Table, critical values of Z = 1.64

The rejection region for the standardized test statistic:

(-infty, - 1.64)U(1.64, infty).

(C)

By Technology:

The p-value is 0.5612