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. Anderson, David R.. Essentials of Statistics for Business and Economics (p. 377). South-Western College Pub. Kindle Edition.

Answer 1

Answer: 37

Step-by-step explanation:

Given : Significance level : $\alpha:1-0.98=0.02$

Critical value : $z_{\alpha/2}=z_{0.01}=2.33$

margin of error : E= 1 mile per gallon

Population standard deviation: $\sigma=2.6$ miles per gallon.

We know that when the population standard deviation is known then the formula to find the sample size is given by  :

$n=(\dfrac{z_{\alpha/2}\times \sigma}{E})^2$

$n=(\dfrac{(2.33)\times 2.6}{1})^2=36.699364\approx37$  [Round to the next whole number.]

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