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 400 people shows that 28% of those 200 who were contacted by telephone actually made contributions compared to only 18% of the 200 who received first class mail requests.

The 95% confidence interval for the difference in the proportions of people who make donations if contacted by telephone or first class mail is (____,____) (round the answers to 4 decimal places. Do not include the 0 before the decimal point.)

Is 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 contribution? ____ Fill in the blank with one of these options: yes, no, not enough information

Explanation / Answer

Given n1=n2=200; p1=0.28; p2=0.18; q1=1-0.28=0.72;q2=1-0.18=0.8

SE=Sqrt[(p1*q1/n1) +(p2*q2/n2)]=0.0418

z value at 5% is 1.96, confidence interval is [(p1-p2)-SE,(p1-p2)+SE]

The 95%confidence interval is( .0181,.1819)

B) Yes.

There is 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 contribution

See the calculations below

Data Hypothesized Difference 0 Level of Significance 0.05 Group 1 Number of Items of Interest 56 Sample Size 200 Group 2 Number of Items of Interest 36 Sample Size 200 Intermediate Calculations Group 1 Proportion 0.28 Group 2 Proportion 0.18 Difference in Two Proportions 0.1 Average Proportion 0.23 Z Test Statistic 2.376242283 Upper-Tail Test Upper Critical Value 1.644853627 p-Value 0.008744987 Reject the null hypothesis

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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