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 45 of those 200 who were contacted by telephone actually made contributions compared to only 35 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 each answer to 4 places after the decimal):

lower end =

higher end =

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?

This interval contains all positive numbers, indicating that there is sufficient evidence to conclude that the percent of people who made a contribution after being contacted by telephone is greater than the percent of people who made a contribution after receiving first class mail requests.

This interval contains all negative numbers, indicating that there is sufficient evidence to conclude that the percent of people who made a contribution after receiving first class mail requests is greater than the percent of people who made a request after being contacted by telephone.  

  This interval contains zero, indicating that there is not sufficient evidence to conclude that the percent of people who made a contribution after being contacted by telephone is greater than the percent of people who made a contribution after receiving first class mail requests.

Answer 1

We can find the required confidence interval using TI-84 calculator ,

Press STAT key ---> Scroll to TESTS ---> Scroll down to 2-Prop z Interval and hit enter.

Then plug the given values accordingly,

Lower end = -0.0282  

Upper end = 0.1282

Since 0 lies in the interval ( -0.0282 , 0.1282 )

This interval contains zero, indicating that there is not sufficient evidence to conclude that the percent of people who made a contribution after being contacted by telephone is greater than the percent of people who made a contribution after receiving first class mail requests.