Question

An automotive engineer wants to estimate the cost of repairing a car that experiences a 40 kph head-on collision. He tests 24 crashed cars in a crash-test experiment, and the average repair is $11,000. The standard deviation of the 24-car sample is 2.9 THOUSAND dollars. Determine the margin of error for a 95% Confidence interval for the true mean repair cost. (NB WE ARE LOOKING FOR A 4-DIGIT WHOLE DOLLAR AMOUNT.)  

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 11000

sample standard deviation = s = 2900

sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,24 = 2.067

Margin of error = E = t_/2,df * (s /n)

= 2.067 * (2900 / 24)

= 1224

The margin of error for a 95% Confidence interval for the true mean repair cost is $1224 .