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 ofs = $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 ≥ 1,503Ha: μ < 1,503H0: μ ≤ 1,503Ha: μ > 1,503 H0: μ > 1,503Ha: μ ≤ 1,503H0: μ < 1,503Ha: μ ≥ 1,503H0: μ = 1,503Ha: 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.)

Answer 1

a) Option A)

`H_(0): \mu \geq 1503\\H_A: \mu < 1503`

b) Point estimate of difference = -78

Explanation:

We are given the following in the question:

Population mean, μ = $1,503

Sample mean,
`\bar{x}` = $1,425

Sample size, n = 25

Sample standard deviation, s = $160

We have to carry a hypothesis test that the mean annual premium in Pennsylvania is lower than the national mean annual premium.

a) First, we design the null and the alternate hypothesis

`H_(0): \mu \geq 1503\text{ dollars}\\H_A: \mu < 1503\text{ dollars}`

b) Point estimate of the difference between the mean annual premium in Pennsylvania and the national mean

Point estimate of difference =

Mean annual premium in Pennsylvania - National mean

`\text{Point estimate} = \bar{x} - \mu = 1425 - 1503 = -78`

Thus,

Point estimate of difference = -78