Let n1 = 100, X1 = 90, n2 = 100, and X2 = 70. Complete parts (a) and (b) below.
ID: 3245758 • Letter: L
Question
Let n1 = 100, X1 = 90, n2 = 100, and X2 = 70.
Complete parts (a) and (b) below.
a. At the 0.01 level of significance, is there evidence of a significant difference between the two population proportions?
Determine the null and alternative hypotheses. Choose the correct answer below.
A. H0: 1 2; H1: 1 < 2
B. H0: 1 = 2; H1: 1 2
C. H0: 1 2; H1: 1 > 2
D. H0: 1 2; H1: 1 = 2
Calculate the test statistic, ZSTAT, based on the difference p1 p2.
The test statistic, ZSTAT, is ____? (Type an integer or a decimal. Round to two decimal places as needed.)
Calculate the p-value.
The p-value is ____? (Type an integer or a decimal. Round to three decimal places as needed.)
Determine a conclusion. Choose the correct answer below.
(Do not reject, Reject) the null hypothesis. There is (insufficient, sufficient) evidence to support the claim that there is a significant difference between the two population proportions.
b. Construct a 99% confidence interval estimate of the difference between the two population proportions.
____? 2 ____? (Type integers or decimals. Round to four decimal places as needed.)
Explanation / Answer
B. H0: 1 = 2; H1: 1 2
is correct
2) n1 = 100, X1 = 90, n2 = 100, and X2 = 70.
p1^ = 90/100 = 0.9 . p2^ = 70/100 = .0.7
test statistic = (p1^-p2^) /sqrt(p1q1/n1 + p2q2/n2)
= ( 0.9 -0.7)/(sqrt(0.9*0.1/100 + 0.7*0.3/100))
= 3.65148
c) p-value = 2P(Z >3.65148) = 0.0002
d) z-critical =1.96
3.65148 > 1.96
we reject the null hypothesis. There is (sufficient) evidence to support the claim that there is a significant difference between the two population proportions.
b) z- critical for 99 % = 2.576
p1^ - p2^ = 0.9-0.7 = 0.2
sd (p1^ - p2^) = (sqrt(0.9*0.1/100 + 0.7*0.3/100)) = 0.05477
hence confidence interval is
(0.2 - 2.576 *0.05477, (0.2 + 2.576 *0.05477, )
=(0.05891,0.3410875)
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