Question

1) Independent random samples, each containing 90 observations, were selected from two populations. The samples from populations 1 and 2 produced 21 and 14 successes, respectively.
Test H0:(p1?p2)=0 against Ha:(p1?p2)?0. Use ?=0.07.

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. We can reject the null hypothesis that (p1?p2)=0 and accept that (p1?p2)?0.
B. There is not sufficient evidence to reject the null hypothesis that (p1?p2)=0.

2)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=88,x1=43x2=38

Is there evidence, at an ?=0.08 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) is expressed (-infty, a), an answer of the form (b,?) is expressed (b, infty), and an answer of the form (??,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. Do Not Reject H0.
B. Reject H1.
C. Reject H0.
D. Do Not Reject H1.

Answer 1

Solution1:

H0:(p1?p2)=0

Ha:(p1?p2)?0

alpha=0.07

(a) The test statistic i

Z=p1^-p2^/sqrt(p1^(1-p1^)/n1+p2^(1-p2^)n2)

p1^=x1/n1=21/90=0.2333333

p2^=x2/n2=14/90=0.1555556

z=0.2333333-0.1555556/sqrt(0.2333333(1-0.2333333)/90+0.1555556(1-0.1555556)/90

z=1.318

Solutionb:

p value=0.1874

Solutionc:

p value=0.1874

p>0.07

Do not Reject Null Hypothesis.

Accept Null Hypothesis.

(c) The final conclusion is

There is not sufficient evidence to reject the null hypothesis that (p1?p2)=0.