A large automobile insurance company selected samples of single and married male policyholders and recorded the number who made an insurance claim over the preceding three-year period.

Single Policyholders	Married Policyholders
n1 = 400	n2 = 900
number making claims = 68	number making claims = 72

(a)Use = 0.05. Test to determine whether the claim rates differ between single and married male policyholders. State the null and alternative hypotheses. (Let p₁ = claim rate for single male policyholders and p₂ = claim rate for married male policy holders.)

a.H₀: p₁ p₂ 0

H_a: p₁ p₂ = 0

b.H₀: p₁ p₂ 0

H_a: p₁ p₂ > 0

c.H₀: p₁ p₂ 0

H_a: p₁ p₂ < 0

d.H₀: p₁ p₂ > 0

H_a: p₁ p₂ 0

e.H₀: p₁ p₂ = 0

H_a: p₁ p₂ 0

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to four decimal places.)p-value =

State your conclusion.

a .Do not reject H₀. We can not conclude that there is a difference between claim rates.

b. Reject H₀. We can not conclude that there is a difference between claim rates.

c.Reject H₀. We can conclude that there is a difference between claim rates.

d .Do not reject H₀. We can conclude that there is a difference between claim rates

(b)Provide a 95% confidence interval for the difference between the proportions for the two populations. (Round your answers to four decimal places.) ___________to ___________