Question

The Insure.com website reports that the mean annual premium for automobile insurance in the United States was $1,503 in March 2014. Being from Pennsylvania at that time, you believed automobile insurance was cheaper there and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1,425 with a standard deviation of

s = $160.

(a)

Develop a hypothesis test that can be used to determine whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.

H₀: μ ≤ 1,503

H_a: μ > 1,503

H₀: μ > 1,503

H_a: μ ≤ 1,503

    

H₀: μ < 1,503

H_a: μ ≥ 1,503

H₀: μ ≥ 1,503

H_a: μ < 1,503

H₀: μ = 1,503

H_a: μ ≠ 1,503

(b)

What is a point estimate in dollars of the difference between the mean annual premium in Pennsylvania and the national mean? (Use the mean annual premium in Pennsylvania minus the national mean.)

$

(c)

At

α = 0.05,

test for a significant difference.

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

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

p-value =

State your conclusion.

Reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.Do not reject H₀. We cannot conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.    Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.Do not reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.

Answer 1

Solution:

a)

H₀: μ ≥ 1,503

H_a: μ < 1,503

b)

Sample mean is the point estimate of the population mean.

So , required point estimate is

$ 1425

c)

The test statistics t is given by ..

t =  

= (1425 - 1503)/(160/25)

= -2.438

Test statistic t = -2.428

Now ,

df = n - 1 = 25 - 1 = 24

Left tailed test(One tailed left sided)

So ,

p value = 0.0115

p value is less than α = 0.05

Reject H₀. We can conclude that the population mean automobile premium in Pennsylvania is lower than the national mean.