Let n1=80, X1=30, n2=80, and X2=40. Complete parts (a) and (b) below. a. At the
ID: 3180614 • Letter: L
Question
Let n1=80, X1=30, n2=80, and X2=40. Complete parts (a) and (b) below.
a. At the 0.05 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: 12
H1: 1>2
B.
H0: 12
H1: 1=2
C.
H0: 12
H1: 1<2
D.
H0: 1=2
H1: 12
Calculate the test statistic based on the difference p1p2.
ZSTAT=
(Round to two decimal places as needed.)
Determine the rejection region. Choose the correct answer below and fill in any answer box(es) in your choice. (Round to two decimal places as needed.)
A.
ZSTAT< - ___ or ZSTAT> +____
B.
ZSTAT< ____
C.
ZSTAT> + ____
Determine a conclusion. Choose the correct answer below.
A.
Since ZSTAT is in the rejection region, there is sufficient evidence to conclude that there is a significant difference between the two proportions.
B.
Since ZSTAT is in the nonrejection region, there is insufficient evidence to conclude that there is a significant difference between the two proportions.
C.
Since ZSTAT is in the nonrejection region, there is sufficient evidence to conclude that there is a significant difference between the two proportions.
D.
Since ZSTAT is in the rejection region, there is insufficient evidence to conclude that there is a significant difference between the two proportions.
b. Construct a 99% confidence interval estimate of the difference between the two population proportions.
____ 1 - 2 ____
(Round to four decimal places as needed.)
Explanation / Answer
D.
H0: 1=2
H1: 12
p1=30/80 =0.375 ; n1=80
p2=40/80 =0.5 ; n2=80
std error of difference =(p1(1-p1)/n1+p2(1-p2)/n2)1/2 =0.0778
test stat z=(p1-p2)/std errror =(0.375-0.5)/0.0778=-1.6064
Determine the rejection region :
A.
ZSTAT< - _1.96__ or ZSTAT> +_1.96___
B.
Since ZSTAT is in the nonrejection region, there is insufficient evidence to conclude that there is a significant difference between the two proportions.
b) fro 99% CI, z=2.5758
hence confidence interval =(p1-p2) +/- z*std error =-0.3254 ; 0.0754
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