Question

# 1) Independent random samples, each containing 90 observations, were selected from two populations. The samples from...

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.

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.

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