Question

Asked Dec 12, 2019

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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 $1,430 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.

H_{0}: μ > 1,503

H_{a}: μ ≤ 1,503

H_{0}: μ ≤ 1,503

H_{a}: μ > 1,503

H_{0}: μ = 1,503

H_{a}: μ ≠ 1,503

H_{0}: μ < 1,503

H_{a}: μ ≥ 1,503

H_{0}: 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.)

Step 1

Null hypothesis:

*µ=*1,503*.*

Alternative hypothesis:

*µ*<1,503.

This is a left tailed test.

Since the population standard deviation is unknown, the appropriate test is one sample *t*-test.

Here, the sample mean, *x*-bar is 1,430.

Population mean, *µ* is 1,503.

Sample standard deviation, *s *= 160.

Sample size, *n* is 25.

The test statistic value can be obtained as follows:

Step 2

*Computation of P-value:*

The *P*-value *t*-distribution at 24 degrees of freedom can be obtained using the exc...

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