Question

In a study of automobile collision insurance costs, a random sample of n = 35 repair costs of front-end damage caused by hitting a wall at a specified speed had a mean of $1,438. (a) Given that σ = $269 for such data, what can be said with 98% confidence about the maximum error if x = $1, 438 is used as an estimate of the average cost of such repairs.

Answer 1

Answer: The maximum error = $105.76.

Explanation:

Formula to find the maximum error:

`E= z^*(\sigma)/(√(n))`

, where n= sample size.

`\sigma` = Population standard deviation

z*= Critical value(two-tailed).

As per given , we have

`\overline{x}=1438`

n= 35

`\sigma=269`

For 98% confidence , the significance level =
`1-0.98=0.02`

By z-table , the critical value (two -tailed) =
`z^* = z_(\alpha/2)=z_(0.01)=2.326`

Now , the maximum error =
`E= (2.326)(269)/(√(35))`

`E= (2.326)(269)/(5.9160797831)`

`E= (2.326)*45.4692989044=105.761589252\pprox105.76`

Hence, With 98% confidence level , the maximum error = $105.76.