Question

QUESTION 7

1. Question 7-9 are based on the following information:

   The mean annual premium for automobile insurance in the United States is $1503 (Insure.com website, March 6, 2014). Being from Pennsylvania, you believe automobile insurance is cheaper there and wish 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 $1440 with a standard deviation of s = $165.

   If required, enter negative values as negative numbers.

   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 less than 1503 H a: μ greater than or equal to 1503
   		H 0: μ greater than or equal to 1503 H a: μ less than 1503
   		H 0: μ equal 1503 H a: μ greater than 1503
   		H 0: μ less than 1503 H a: μ equal 1503

0.075 points   

QUESTION 8

1. What is a point estimate of the difference between the mean annual premium in Pennsylvania and the national mean (to the nearest dollar)?

0.075 points   

QUESTION 9

1. t α = .05, test for a significant difference by completing the following 3 parts.

   Calculate the value of the test statistic (to 2 decimals).

   The p-value is _____

   What is your conclusion?

   		-2.03; between 0.025 and 0.05; The population mean automobile premium is higher in Pennsylvania than the national mean.
   		1.91; greater than 0.05; The population mean automobile premium is higher in Pennsylvania than the national mean.
   		-1.91; between 0.025 and 0.05; The population mean automobile premium is lower in Pennsylvania than the national mean.
   		2.03; less than 0.05; The population mean automobile premium is lower in Pennsylvania than the national mean.

Answer 1

Q7 Let's consider X be the annual premium for automobile insurance.

Given:

μ 1503

n=25

X 1440

s=$165

WE want to test whether the mean annual premium in Pennsylvania is lower than the national mean annual premium.

The hypothesis testing problem is:

H0 : μ > 1503 2
       Vs
H1 : μ < 1503

Q8.The point estimate of the difference between the mean annual premium in Pennsylvania and the national mean is

μ 1440-1503

$\bar{X}-\mu=-63$

The point estimate of the difference between the mean annual premium in Pennsylvania and the national mean is -63 dollars.

Q9. The test statistic is given by:

By assuming normality

Vn

$t=\frac{-63}{\frac{165}{\sqrt{25}}}$

0 63

ー63

t =-1.909

tー-1.91

The p value for the test statistic with 24 degrees of freedom for left tail test is:

$p=P(t\geq \left |-1.91 \right |)$

$p=P(t\geq 1.91)$

i.e 0.025<p value <0.05            ### using t distribution table:

since p value <0.05, we reject the null hypothesis at 5% level of significance.

Conclusion:

The population mean automobile premium is lower in Pennsylvania than the national mean.