Let n1 equals 100, X 1 equals 60, n2 equals 100, and X 2 equals 40. complete par
ID: 3180943 • Letter: L
Question
Let n1 equals 100, X 1 equals 60, n2 equals 100, and X 2 equals 40. complete parts (a) and (b) below.
a. At the 0.10 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.
H 0 : pi 1 not equals pi 2
H 1 : pi 1 equals pi 2
B.
H 0 : pi 1 greater than or equals pi 2
H 1 : pi 1 less than pi 2
C.
H 0 : pi 1 less than or equals pi 2
H 1 : pi 1 greater than pi 2
D.
H 0 : pi 1 equals pi 2
H 1 : pi 1 not equals pi 2
Calculate the test statistic based on the difference p1 minus p2.
ZSTAT equals ____
(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 three decimal places as needed.)
A.
ZSTAT greater than +____
B.
ZSTAT less than -____ or ZSTAT greater than +____
C.
ZSTATless than -____
Determine a conclusion. Choose the correct answer below.
A. Since ZSTAT is in the rejection region, there is insufficient evidence to conclude that there is a significant difference between the two proportions.
B. Since ZSTAT is in the nonrejection region, there is sufficient evidence to conclude that there is a significant difference between the two proportions.
C. Since ZSTAT is in the rejection region, there is sufficient evidence to conclude that there is a significant difference between the two proportions.
D. Since ZSTAT is in the nonrejection region, there is insufficient evidence to conclude that there is a significant difference between the two proportions.
b. Construct a 90% confidence interval estimate of the difference between the two population proportions.
___ less than or equals pi1 minus pi2 less than or equals ___
(Round to four decimal places as needed.)
Explanation / Answer
here p1 =60/100=0.6 ; n1=100 ; p2 =40/100=0.4 ; n2=100
D.
H 0 : pi 1 equals pi 2
H 1 : pi 1 not equals pi 2
std error =(p1(1-p1)/n1 +p2(1-p2)/n2)1/2 =0.0693
hence zstat =(p1-p2)/std error =2.8867
B.
ZSTAT less than -1.6449____ or ZSTAT greater than +1.6449____
C. Since ZSTAT is in the rejection region, there is sufficient evidence to conclude that there is a significant difference between the two proportions.
for confidence interval =(proportion differnce -/+ z*std error =0.0860 ; 0.3140
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