A survey reported that 69.6% of users over age 70 believe that e-mail messages s

Question

A survey reported that 69.6% of users over age 70 believe that e-mail messages should be answered quickly, as compared to 57.9% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over age 70 and 1,000 users 12 to 50 years old Complete (a) and (b) below. a. At the 0 01 level of significance, is there evidence of a significant difference between the two age groups in their belief that e mail messages should be answered quickly? Let pi_1, represent the proportion of users over age 70 who believe that e-mail messages should he answered quickly, and let x_2 represent the proportion of users 12 to 50 years old who believe that e-mail messages should he answered quickly Set up the null and alternative hypotheses to test. H_0: X_1 = x_2 H_1:x_1 notequalto x_2 Calculate the lest statistic. x^2_0.01 = (Round to two decimal places as needed.) State the conclusion. Since the test statistic is the critical value, the null hypothesis. There is evidence to conclude there is a significant difference between the proportions. B. Determine the p-value in (a) and interpret its meaning. P value = (Round to three decimal places as needed.)

Explanation / Answer

proprotion P1 is 69.6% or 0.696

and P2 is 57.9% or 0.579

1) test statistic is 5.44

2) Crtitical value at 0.01 is 2.58

Since test statistics is greater than the crtical value, reject null hypothesis , There is sufficient evidence to conclude that there is a significant difference between the proportions.

P-value =0.00

Null hypothesis: P1 = P2 Alternative hypothesis: P1 P2 n1   = 1000 n2 = 1000 P1 = 0.696 P2 = 0.579 P = ( P1*n1 + P2*n2) / (n1 + n2)= 0.64 Standard Error (S.E) = SQRT(P*(1-P)*((1/n1)(1/n2))) S.E = 0.02 Z = ( P1 - P2) / SE Z = 5.44

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