Question

Acar company developed a certain car model to appeal to young consumers. The car company claims the average age of dris age of the drivers was found to be 29.10 years. Assume the standard deviation for the age of the car drivers to be 2.8 years. C a. Construct a 95% confidence interval to estimate the average age of the car driver. The 95% confidence interval for the average age of the car driver has a lower limit of years old and an upper limit of ye (Round to two decimal places as needed.) b. Does this result lend support to the car company's claim? O A. Yes, because the interval includes the company's claimed average ago. OB. No, because the interval includes the company's claimed average age. OC. No, because the interval does not include the company's claimed average age. OD. Yes, because the interval does not include the company's claimed average age. c. What assumption needs to be made to construct this interval? OA. The population of the model's drivers' ages is normally distributed. OB. The sample size is less than 30 OC. The population mean for the model's drivers will be in the confidence interval. OD. The population of all car drivers' ages is normally distributed O E. The population of the model's drivers' ages is skewed to one side. Click to select your answers).

Answer 1

Given :

Given that,

Sample mean = $\bar x$ = 29.10

Standard deviation = s = 2.8

Sample size = n = 17

Degrees of freedom = df = n - 1 = 17 - 1 = 16

At 95% confidence level, critical value of t is ,

$\alpha$ = 1 - 95% = 1 - 0.95 = 0.05

$\alpha$ / 2 = 0.05 / 2 = 0.025

t_{$\alpha$ /2,df} = t_0.025,16 = 2.120

Margin of error = E = t_{$\alpha$/2,df} * (s /$\sqrt$n)

= 2.120 × (2.8 / √17)

= 1.4397

The 95% confidence interval estimate of the population mean is,

CI = $\bar x$ - E < $\mu$ < $\bar x$ + E

= 29.10 - 1.4397 < $\mu$ < 29.10 + 1.4397

27.66 < $\mu$ < 30.54

The 95% confidence interval for the average age of the car driver has a lower limit of 27.66 years old and an upper limit of 30.54 years old.

b) No, because the interval does not includes the company's claimed average age.

c) The population of all car drivers' ages is normally distributed.