Question

Last year, President Bush granted a tax-cut check to all income tax filers. In doing so, it was reported that he thought that at least 30% of the households would use the tax-cut check to increase spending. According to a report by the University of Michigan Research Center (Wall Street Journal, Feb. 26, 2002), 220 of the 1000 people surveyed said that the 2001 tax-cut check they received has led them to increase spending.

1. The alternate hypothesis for this test is:

A. p < 0.30

B. p > 0.22

C. p > 0.29

D. p > 0.30

2. A Type II error is to:

A. Conclude that the proportion of people that would use the tax-cut check to increase spending is at least 30% when in fact the proportion is less than 30%

B. Conclude that the proportion of people that would use the tax-cut check to increase spending is less than 30% when in fact the proportion is at least 30%

C. Conclude that the proportion of people that would use the tax-cut check to increase spending is less than 22% when in fact the proportion is at least 22%.

D. Conclude that the proportion of people that would use the tax-cut check to increase spending is at least 22% when in fact the proportion is less than 22%.

3. Which of the following is the correct decision to make for the test?

A. Reject the null hypothesis.

B. Do not reject the null hypothesis.

C. The test is inconclusive.

D. None of the answers

Answer 1

1)

Ho: p >= 0.3

Ha : p < 0.3

option A. p < 0.30   is correct

2)

type ii error - fail to reject the null hypothesis when it is false

A. Conclude that the proportion of people that would use the tax-cut check to increase spending is at least 30% when in fact the proportion is less than 30%

3)

X = 220 , n = 1000

p^ = 220/1000 = 0.22

TS = (p^ - p)/sqrt(pq/n) = (0.22 - 0.3)/sqrt(0.3*0.7/1000) = -5.5205

since TS lies in critical region

we reject the null hypothesis

A. Reject the null hypothesis.