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=86,n2=83,x1=50x2=58First-Years (Pop. 1):n1=86,x1=50Fourth-Years (Pop. 2):n2=83,x2=58

Is there evidence, at an α=0.065α=0.065 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 :

Answer 1

Ans:

A)

sample proportion 1=50/86=0.5814

sample proportion 2=58/83=0.6988

pooled proportion(50+58)/(86+83)=0.6391

Test statistic:

z=(0.5814-0.6988)/SQRT(0.6391*(1-0.6391)*((1/86)+(1/83)))

z=-1.589

B)critical z values=+/-1.845

Reject H0 if z<-1.845 or z>1.845

(−∞,-1.845)∪(1.845,∞)

c)p-value=2*P(z<-1.589)=0.1121

d)Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that there is a difference in proportions between first-years and fourth-years