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 50 of those 200 who were contacted by telephone actually made contributions compared to only 25 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 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. 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 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.

Answer 1

Answer:

Lower End = 0.0495

Upper End = 0.2005

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.

Explanation:

From the data table,

Contacted via	Made a Contribution	Total
Telephone	50	200
Mail	25	200

The 95% Confidence Interval of the difference of two proportions is defined by,

where,

For a 95% confidence interval, z critical value is obtained using the standard normal distribution table,

Now,

Since the 95% confidence interval doesn't include zero and positive, the difference is significantly larger.