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

Step-by-step 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 :

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

i.e. $n=(\dfrac{(2.33)\cdot(2.6)}{1})^2$

$\Rightarrow\ n=36.699364\approx37$

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