Question

Minnesota had the highest turnout rate of any state for the 2012 presidential election.† Political analysts wonder if turnout in rural Minnesota was higher than turnout in the urban areas of the state. A sample shows that 663 of 884 registered voters from rural Minnesota voted in the 2012 presidential election, while 396 out of 550 registered voters from urban Minnesota voted.

(a) Formulate the null and alternative hypotheses that can be used to test whether registered voters in rural Minnesota were more likely than registered voters in urban Minnesota to vote in the 2012 presidential election. (Let p₁ = the population proportion of voters in rural Minnesota who voted in the 2012 election and p₂ = the populationproportion of voters in urban Minnesota who voted in the 2012 election.)

H₀: p₁ − p₂ < 0

H_a: p₁ − p₂ = 0

H₀: p₁ − p₂ ≠ 0

H_a: p₁ − p₂ = 0

    

H₀: p₁ − p₂ = 0

H_a: p₁ − p₂ ≠ 0

H₀: p₁ − p₂ ≤ 0

H_a: p₁ − p₂ > 0

H₀: p₁ − p₂ ≥ 0

H_a: p₁ − p₂ < 0

(b) What is the proportion of sampled registered voters in rural Minnesota that voted in the 2012 presidential election?

(c) What is the proportion of sampled registered voters in urban Minnesota that voted in the 2012 presidential election?

(d) At α = 0.05, test the political analysts' hypothesis.

Calculate the test statistic. (Round your answer to two decimal places.)

What is the p-value? (Round your answer to four decimal places.)

p-value =

Answer 1

H₀: p₁ − p₂ ≤ 0

H_a: p₁ − p₂ > 0

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 663 + 396 ) / ( 884 + 550 )
= 0.7385


Z = 1.26

Test Criteria :-
Reject null hypothesis if

= 1.257 < 1.6449, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z > 1.257 )
P value = 0.1044
Reject null hypothesis if P value <
Since P value = 0.1044 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0