Question

A car company developed a certain car model to appeal to young consumers. The car company claims the average age of drivers of this certain car model is 28.00 years old. Suppose a random sample of 17 drivers was​ drawn, and the average age of the drivers was found to be 29.00 years. Assume the standard deviation for the age of the car drivers to be 2.2 years.

Required:
a. Construct a 95% confidence interval to estimate the average age of the car driver.
b. Does this result lend support to the car's company's claim?
c. What assumption needs to be made to construct this's interval?

Answer 1

(27.954, 30.046)

Yes

Explanation:

Given that :

Mean (m) = 29

Standard deviation (σ) = 2.2

Sample size (n) = 17

Confidence interval (α) = 95%

Average age as claimed by the company = 28

Confidence interval formula :

Mean ± (Zcritical * σ/sqrt(n))

Zcritical at 95% = 1.96

(Zcritical * σ/sqrt(n)) = (1.96 * (2.2/sqrt(17)) = (1.96 * 0.5335783) = 1.0458136

Lower boundary = (29 - 1.0458136) = 27.954186

Upper boundary = (29 + 1.0458136) = 30.045813

(27.954, 30.046)

b. Does this result lend support to the car's company's claim?

Yes, it does, 28 falls in between the the calculated confidence interval.