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 = 900 n2 = 400 number making claims = 171 number making claims = 40 (a) Use α = 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.) H0: p1 − p2 ≠ 0 Ha: p1 − p2 = 0 H0: p1 − p2 = 0 Ha: p1 − p2 ≠ 0 H0: p1 − p2 > 0 Ha: p1 − p2 ≤ 0 H0: p1 − p2 ≤ 0 Ha: p1 − p2 > 0 H0: p1 − p2 ≥ 0 Ha: 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. Reject H0. We can conclude that there is a difference between claim rates. Do not reject H0. We can conclude that there is a difference between claim rates. Reject H0. We can not conclude that there is a difference between claim rates. Do not reject H0. We can not 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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 = 900	n₂ = 400
number making claims = 171	number making claims = 40

(a) Use α = 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.)

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

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.

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

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

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

Do not reject H₀. We can not 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 ____

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