Donations to tax-exempt organizations such as the Red Cross, the Salvation Army, the YMCA, and the American Cancer Society not only go to the stated charitable purpose, but are used to cover fundraising expenses and overhead. The CHARITY file (see table on p. 341) contains the charitable commitments (i.e., the percentage of expenses that goes toward the stated charitable purpose) for a sample of 30 charities.
Organization ............. Charitable Commitment (%)
American Cancer Society ........ 71
American National Red Cross ...... 89
Big Brothers Big Sisters of America .... 78
Boy Scouts of America .......... 87
Boys & Girls Clubs of America ...... 80
CARE USA .............. 90
Covenant House ............. 67
Disabled American Veterans ....... 69
Ducks Unlimited ........... 86
Feed The Children ............ 84
Girl Scouts of the USA .......... 82
Goodwill Industries International ..... 88
Habitat for Humanity International .... 83
Mayo Clinic ............. 97
March of Dimes Foundation ....... 77
Multiple Sclerosis Society ......... 78
Museum of Modern Art ......... 80
Nature Conservancy ............ 80
Paralyzed Veterans of America ....... 62
Planned Parenthood Federation ....... 82
Salvation Army .............. 82
Shriners Hospital for Children ....... 92
Smithsonian Institution ......... 82
Special Olympics .............. 74
Rust for Public Land ........... 89
United States Olympic Committee ...... 71
United Way ................ 86
WGBH Educational Foundation ....... 79
World Trade Center Memorial Foundation ... 79
YMCA of the USA .............. 81
a. Give a point estimate for the mean charitable commitment of tax-exempt organizations.
b. Construct a 95% confidence interval for the mean charitable commitment.
c. What assumption(s) must hold for the method of estimation used in part b to be appropriate?
d. Why is the confidence interval of part b a better estimator of the mean charitable commitment than the point estimator of part a?
e. Construct a 95% confidence interval for the variance in charitable commitments for all tax-exempt organizations.