1) Independent random samples, each containing 90 observations, were selected fr
ID: 2949039 • Letter: 1
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.
Explanation / Answer
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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