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In 1993 a typical American family spent 22% of its after-tax income on clothing, entertainment and other activities, while the remaining 78% was spent on essentials like housing, food, transportation, health care and insurance. It is suggested that because of the increase in the cost of essentials since 1993, the mean percentage income spent on the first three items has decreased. To test this proposition a random sample of 50 households is taken and the percentage spent on these three items is determined. Assume that this percentage varies across families according to a normal distribution with unknown mean u and know o = 5% . (a) State the null and alternative hypotheses for u. (b) If the average percentage for 50 families is 20.5%, what conclusion would you make about the null hypot- thesis? (c) Find the p-value of this test.

In 1993 a typical American family spent 22% of its after-tax income on clothing, entertainment and other activities, while the remaining 78% was spent on essentials like housing, food, transportation, health care and insurance. It is suggested that because of the increase in the cost of essentials since 1993, the mean percentage income spent on the first three items has decreased. To test this proposition a random sample of 50 households is taken and the percentage spent on these three items is determined. Assume that this percentage varies across families according to a normal distribution with unknown mean u and know o = 5% . (a) State the null and alternative hypotheses for u. (b) If the average percentage for 50 families is 20.5%, what conclusion would you make about the null hypot- thesis? (c) Find the p-value of this test.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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In 1993 a typical American family spent 22% of its after-tax income on clothing, entertainment and other activities, while the remaining 78% was spent on essentials like housing, food, transportation, health care and insurance. It is suggested that because of the increase in the cost of essentials since 1993, the mean percentage income spent on the first three items has decreased. To test this proposition a random sample of 50 households is taken and the percentage spent on these three items is determined. Assume that this percentage varies across families according to a normal distribution with unknown mean u and know o = 5% . (a) State the null and alternative hypotheses for u. (b) If the average percentage for 50 families is 20.5%, what conclusion would you make about the null hypot- thesis? (c) Find the p-value of this test.
Transcribed Image Text:In 1993 a typical American family spent 22% of its after-tax income on clothing, entertainment and other activities, while the remaining 78% was spent on essentials like housing, food, transportation, health care and insurance. It is suggested that because of the increase in the cost of essentials since 1993, the mean percentage income spent on the first three items has decreased. To test this proposition a random sample of 50 households is taken and the percentage spent on these three items is determined. Assume that this percentage varies across families according to a normal distribution with unknown mean u and know o = 5% . (a) State the null and alternative hypotheses for u. (b) If the average percentage for 50 families is 20.5%, what conclusion would you make about the null hypot- thesis? (c) Find the p-value of this test.
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