Question

In: Statistics and Probability

With economical concerns being so great, many people are no longer purchasing new vehicles, but are...

With economical concerns being so great, many people are no longer purchasing new vehicles, but are instead keeping their vehicles for a longer period of time, until they no longer work. The Amer-ican Automobile Association is interested in estimating the average age of vehicles for Americans. A random sample of thirty-five Americans was obtained. The average age of their vehicles was 6.2 years with standard deviation 1.2. Estimate with 99% confidence the average age of vehicles for Americans

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 6.2

Population standard deviation = = 1.2

Sample size = n =35

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 2.576* ( 1.2/ $\sqrt$ 35)

= 0.5225

At 99% confidence interval estimate of the population mean is,

- E < < + E

6.2 - 0.5225< <6.2 + 0.5225

5.6775< < 6.7225

(5.6775 , 6.7225)

orchestra answered 1 year ago

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