Question

The manager of the Public Broadcasting System for Tennessee is considering changing from the traditional week long contribution campaign to an intensive one day campaign. In an effort to better understand current donation patterns, she is studying past data. She is interested in investigating if male viewer’s donations have a significant different variability in amount from those of female viewers. To test this, random samples of 18 men and 16 women were selected from people who donated during last year’s telethon and the sample standard deviations of males and females were $2.5 and $3.2 respectively. Based on these sample data, is there sufficient evidence to conclude that male viewer’s donations have a significant different variability in amount from those of female viewers ? Use a significant level of 0.05.

I. The type of hypothesis test (lower-tailed, upper-tailed, two-tailed) to conduct for this study is:

II. The value of the test statistics to conduct the test is:

III. The critical value obtained from the table is:

V. The conclusion for this test is (Reject Ho, Fail to Reject Ho):

VI. Can we conclude that male viewer’s donations have a significant different variability in amount from those of female viewers (Yes, Insufficient evidence )? :

Answer 1

Answer: She is interested in investigating if male viewer’s donations have a significant different variability in amount from those of female viewers. To test this, random samples of 18 men and 16 women were selected from people who donated during last year’s telethon and the sample standard deviations of males and females were $2.5 and $3.2 respectively.

Solution:

Let σ1^2 be the variability of men and σ1^2 be the variability of female.

I) The type of hypothesis test is two tailed test.