Question

Minnesota had the highest turnout rate of any state for the 2016 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 630 of 840 registered voters from rural Minnesota voted in the 2016 presidential election, while 396 out of 550registered 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 2016 presidential election. (Let p₁ = the population proportion of voters in rural Minnesota who voted in the 2016 election and p₂ = the population proportion of voters in urban Minnesota who voted in the 2016 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 2016 presidential election?

(c)

What is the proportion of sampled registered voters in urban Minnesota that voted in the 2016 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 =

What conclusion do you draw from your results?

Reject H₀. We cannot conclude that voters from rural Minnesota voted more frequently than voters from urban Minnesota in the 2016 Presidential election. Do not reject H₀. We cannot conclude that voters from rural Minnesota voted more frequently than voters from urban Minnesota in the 2016 Presidential election.     Do not reject H₀. We can conclude that voters from rural Minnesota voted more frequently than voters from urban Minnesota in the 2016 Presidential election.Reject H₀. We can conclude that voters from rural Minnesota voted more frequently than voters from urban Minnesota in the 2016 Presidential election.

Answer 1

a)

H₀: p₁ − p₂ ≤ 0

H_a: p₁ − p₂ > 0

b)

p1cap = X1/N1 = 630/840 = 0.75

c)

p2cap = X2/N2 = 396/550 = 0.72

d)

pcap = (X1 + X2)/(N1 + N2) = (630+396)/(840+550) = 0.7381

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.75-0.72)/sqrt(0.7381*(1-0.7381)*(1/840 + 1/550))
z = 1.24

P-value Approach
P-value = 0.1067
As P-value >= 0.05, fail to reject null hypothesis.

e)

Do not reject H₀. We cannot conclude that voters from rural Minnesota voted more frequently than voters from urban Minnesota in the 2016 Presidential election.