Use the traditional method to test the given hypothesis. Assume that the samples

Question

Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected

24) A researcher finds that of 1000 people who said that they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.

Please show work and I am using TI-84.

Thank you very much

Explanation / Answer

p1 = 31/1000 = 0.031
n1 = 1000

p2 = 22/1200 = 0.018
n2 = 1200

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 = (p1 * n1 + p2 * n2) / (n1 + n2)
(0.031*1000 + 0.018*1200)/(1000+1200)
= 0.0239

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( 0.0239 * ( 1 - 0.0239 ) * [ (1/1000) + (1/1200) ] )
= 0.006

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 = (0.031 - 0.018) / 0.006
= 2.16

so we check the p value as
0.9846

as the p value is not less than 0.05 , hence we fail to reject the null hypothesis in favor of alternate hypothesis

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.