Question

Mileage tests are conducted for a particular model of automobile. If a 98% confidence interval with a margin of error of 1 mile per gallon is desired, how many automobiles should be used in the test? Assume that preliminary mileage tests indicate the standard deviation is 2.6 miles per gallon.

Answer 1

Answer: 37

Explanation:

As per given description in the question, we have

Population standard deviation :
`\sigma=2.6\text{ miles per gallon}`

Critical value for 98% confidence interval =
`z_(\alpha/2)=2.33`

Margin of error : E= 1 mile per gallon

Formula we use to find the sample size :

`n=((z_(\alpha/2)\cdot \sigma)/(E))^2`

i.e.
`n=(((2.33)\cdot(2.6))/(1))^2`

`\Rightarrow\ n=36.699364\approx37`

Therefore , the number of automobiles should be used in the test =37