Question

You work at an auto insurance company. The national office sends your office a report that states that the average auto accident insurance claim is $1,200, and the population stan- dard deviation is $250. You take a sample of 20 claims filed through your office and find a mean of $1,450. Use the 0.1 level of significance and determine if your claims are higher than the national average. Use the five-step procedure to answer the question and include the p-value.

Answer 1

Solution :

Given that,

Population mean = = 1200

Sample mean = = 1450

Population standard deviation = = 250

Sample size = n = 20

Level of significance = = 0.1

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 1200

Ha: 1200

The test statistics,

Z =( - )/ (/n)

= ( 1450 - 1200 ) / ( 250 / 20 )

= 4.472

Critical value of  the significance level is α = 0.1, and the critical value for a two-tailed test is

= 1.64

Since it is observed that |Z| = 4.472 > = 1.64 it is then concluded that the null hypothesis is rejected.

P- Value = 2*P(Z > z )

= 2*(1 - P(Z< 4.472))

= 2* ( 1 - 1)

= 0

The p-value is p = 0, and since p = 0 < 0.1 , it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is different than 1200, at the 0.1 significance level.