Question

# The ABC insurance INC. reports that the mean annual premium for automobile insurance in the United...

The ABC insurance INC. reports that the mean annual premium for automobile insurance in the United States was \$1608 in summer 2018. However, you believed automobile insurance was cheaper in North Carolina and decided to develop statistical support for your opinion. A sample of 25 automobile insurance policies from the state of North Carolina showed a mean annual premium of \$1560 with a standard deviation of s = \$165.

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

b. At a = .05, test for a significant difference. What is your conclusion?

Solution :

= 1608

=1560

S =165

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H0 :    = 1608

Ha : <1608

Test statistic = t

= ( - ) / S / n

= (1560-1608) / 165 / 25

= −1.455

Test statistic = t = −1.455

P-value =0.0794

= 0.05

P-value >

0.0794 > 0.05

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that