Question

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 92 politically conservative voters, r₁ = 20 responded yes. Another random sample of n₂ = 79 politically moderate voters showed that r₂ = 21 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 0.05.

What is the value of the sample test statistic? ______

Find (or estimate) the P-value: ______

Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of a national arts organization. A random sample of n₁ = 56 people who are conservative voters showed that r₁ = 40 said yes. Another random sample of n₂ = 65 people who are liberal voters showed that r₂ = 35 said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use α = 0.05.

Find (or estimate) the P-value: _____

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 214 women, r₁ = 68 responded yes. Another random sample of n₂ = 199 men showed that r₂ = 58 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference p₁ − p₂. Round the test statistic and critical value to two decimal places. Round the P-value to four decimal places.)

Critical value: _____

P-value: _______

In the Focus Problem at the beginning of this chapter, a study was described comparing the hatch ratios of wood duck nesting boxes. Group I nesting boxes were well separated from each other and well hidden by available brush. There were a total of 477 eggs in group I boxes, of which a field count showed about 278 hatched. Group II nesting boxes were placed in highly visible locations and grouped closely together. There were a total of 784 eggs in group II boxes, of which a field count showed about 260 hatched.

Find a 90% confidence interval for p₁.

Lower limit: ___

Upper limit: ____

Find a 90% confidence interval for p₁ − p₂.

Lower limit: _____

Upper limit: _____

Answer 1