Find the values of the two sample proportions, p^1= ? and p^2 = ?. Round your an
ID: 3324207 • Letter: F
Question
Find the values of the two sample proportions,
p^1= ? and p^2 = ?. Round your answers to three decimal places.
Compute the weighted estimate of p, p— . Round your answer to three decimal places.
Compute the value of the test statistic. Round your answer to two decimal places.
Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to two decimal places.
Reject H0 if … … …
Given two independent random samples with the following results n1 658 n2 550 x1 = 362 x2-194 Can it be concluded that there is a difference between the two population proportions? Use a significance level of = 0.01 for the test.Explanation / Answer
n1 = 658
n2 = 550
x1 = 362
x2 = 194
p1 = x1/n1 = 362/658 = 0.55
p2 = x2/n2 = 194/550 = 0.35
Pooled sample proportion. Since the null hypothesis states that P1=P2, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.
p = (p1 * n1 + p2 * n2) / (n1 + n2)
where p1 is the sample proportion from population 1, p2 is the sample proportion from population 2, n1 is the size of sample 1, and n2 is the size of sample 2.
p = (0.55*658 + 0.35*550)/(658 +550) = 0.458
Standard error. Compute the standard error (SE) of the sampling distribution difference between two proportions.
SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
where p is the pooled sample proportion, n1 is the size of sample 1, and n2 is the size of sample 2.
SE = sqrt( 0.458 * ( 1 - 0.458 ) * [ (1/550) + (1/658) ] ) = 0.028
Test statistic. The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
where p1 is the proportion from sample 1, p2 is the proportion from sample 2, and SE is the standard error of the sampling distribution.
z = (0.55 - 0.35) / 0.028 = 7.14
as the p value is almost close to 1 , from the z table
hence we fail to reject the null hypothesis
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.