Question

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 = 144	number making claims = 28

(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.

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

Answer 1

Solution :

The statistic software output for this problem is:

p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Hypothesis test results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	Z-Stat	P-value
p1 - p2	144	900	28	400	0.09	0.020360847	4.4202483	<0.0001

H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Test statistic = 4.42

P-value = 0.0001

(b)

Two sample proportion summary confidence interval:
p₁ : proportion of successes for population 1
p₂ : proportion of successes for population 2
p₁ - p₂ : Difference in proportions

95% confidence interval results:

Difference	Count1	Total1	Count2	Total2	Sample Diff.	Std. Err.	L. Limit	U. Limit
p1 - p2	144	900	28	400	0.09	0.01766588	0.055375511	0.12462449

0.0554 to 0.1246