Question

Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 94 politically conservative voters, r₁ = 17 responded yes. Another random sample of n₂ = 84 politically moderate voters showed that r₂ = 22 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?

state null and alternate hypothesis

What sampling distribution will you use? What assumptions are you making?

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Sketch the sampling distribution and show the area corresponding to the P-value.

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?

(e) Interpret your conclusion in the context of the application.

Answer 1

P1 :- Population proportion of conservative voters inclined to spend more federal tax

P2 :-  Population proportion of moderate voters inclined to spend more federal tax

To Test :-

H0 :- P1 = P2

H1 :- P1 < P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 17 + 22 ) / ( 94 + 84 )
= 0.2191

Z = -1.30

Test Criteria :-
Reject null hypothesis if

= -1.3 > -1.64, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z < -1.3 )
P value = 0.0968
Reject null hypothesis if P value <
Since P value = 0.0968 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is insufficient evidence to 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