Question

Would you favor spending more federal tax money on the arts? Of a random sample of n1 = 95 politically conservative voters, r1 = 15 responded yes. Another random sample of n2 = 84 politically moderate voters showed that r2 = 20 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. (a) What is the level of significance?

Answer 1

(a)

The level of significance = = 0.05

(b)

H0: Null Hypothesis: P1 P2

HA: Alternative Hypothesis: P1 < P2

n1 = 95

p1 = 15/95 = 0.1579

n2 = 84

p2 = 20/84 = 0.2381

Test Statistic is given by:

From Table, critical value of Z = - 1.64

Since calculated value of Z = - 1.35 is greater than critical value of Z = - 1.64, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim 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.