A relief fund is set up to collect donations for the families affected by recent

Question

A relief fund is set up to collect donations for the families affected by recent storms. A random sample of 800 people shows that 28% of those 400 who were contacted by telephone actually made contributions compared to only 18% of the 400 who received first class mail requests The 95% confidence interval for the difference in the proportions of people who make donations if contacted (round the by telephone or first class mail is answers to 4 decimal places. Do not include the 0 before the decimal point.) ls there significant statistical evidence that the percent of people who were contacted by telephone and made a contribution is larger than the percent of people who received first class mail requests and made a Fill in the blank with one of these options: yes, no, not enough contribution? information

Explanation / Answer

p1 = 0.28; p2 = 0.18

SE = p(1-p) / n

SE1 = 0.28(1-0.28) / 400 = 0.022

SE2 = 0.18(1-0.18) / 400 = 0.0192

SE of (p1-p2) = SE21 + SE22 = 0.0292

CI = ((p1-p2) ± z/2 * SE) = 0.1 ± 1.96*0.0292 = [0.0427, 0.1572]

H0: P1 = P2
Ha: P1 P2

p = (p1 * n1 + p2 * n2) / (n1 + n2) = 0.23

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = 0.02972

z = (p1 - p2) / SE = 3.36

p-value = 0.9961

1 - = 0.05

= 1 - 0.05

= 0.95

p value > . Hence we cannot reject the null hypothesis.

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