Question

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?

Answer 1

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