Question

A simple random sample of 20 new automobile models yielded the data shown to the right on fuel tank capacity, in gallons 19.8 18.6 14.1 19.4 21.8 15.7 21.6 21.8 16.7 19.4 14.3 20.7 17.2 15.5 21.8 13.8 15.6 19.3 17.4 16.9 a. Find a point estimate for the mean fuel tank capacity for all new automobile models. (Note: 361.4 A point estimate is 18.07 gallons (Type an integer or a decimal. Do not round.) b. Determine a 95.44% confidence interval for the mean fuel tank capacity of all new automobile models. Assume σ= 3.30 gallons The 95.44% confidence interval is from gallons to gallons (Do not round until the final answer. Then round to two decimal places as needed.)

Answer 1

Part a) is correct .

Part b) Here we need to find the 95.44% confidence interval for the mean fuel tank capacity of all new automobile models.

We are given population standard deviation $\sigma$ = 3.30 ,

So using z score we have to find confidence interval for $\mu$

X^​​​ bar - Z_{​​​​​​a/2}*(  $\sigma$ /√n) <  $\mu$ < X bar + Z_{​​​​​​a/2}*( $\sigma$ /√n )

Given X bar = 18.07 ( calculated in part a ) , n = 20

For $\alpha$ = 1 - 0.9544 = 0.0456

Using z table

Z_{​​​​​​a/2} = Z_{​​​​​0.0228} = 2

So confidence interval is

18.07 - 2*(3.30/√20) <  $\mu$ < 18.07 + 2*(3.30/√20 )

16.59 < $\mu$ < 19.55

So the 95.44% confidence interval is from 16.59 gallons to 19.55 gallons.