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.

Step-by-step explanation:

Formula to find the maximum error:

$E= z^*\dfrac{\sigma}{\sqrt{n}}$

, 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 = $E= (2.326)\dfrac{269}{\sqrt{35}}$

$E= (2.326)\dfrac{269}{5.9160797831}$

$E= (2.326)\times45.4692989044=105.761589252\pprox105.76$

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