Question

14. A car company developed a certain car model to appeat to young consumers. The car company claims the average age of drivers of this certain car model is 25,00 years old. Suppose a random sampie of 19 drivers was drawn, and the average age of the drivers was found to be 26.20 years. Assume the standard deviation for the age of the car drivers to be 2.8 years. Complete parts a through c below The 95% contdence interval for the average age of the car driver has a lower limit of upper limit of (Round to two decimal places as needed.) years old and an years old average age O B. No, because the interval does not include the company's claimed average age. OC. No, because the interval indludes the company's claimed average age. O D. Yes, because the interval does not include the companys claimed average age. c. What assumption needs to be made to construct this interval? O A The population of all car drivers' ages is normally distributed O B. The sample size is less than 30 O C. The population of the model's drivers' ages is skewed to one side. O D. The population of the model's drivers' ages is normally distributed.

Answer 1

a ) The 95 % confidence interval of the population mean $\mu$ is :

$\bar{x}\pm z^*\times \frac{\sigma}{\sqrt{n}}$

where , $\bar{x}=26.20\ , n=19\ , \sigma=2.8\ , z^*=1.96$

Required confidence interval :

The 95 % confidence interval for the average age of the car drivers has a lower limit of 24.94 years old and an upper limit of 27.46 years old .

b ) A ) Yes , because the interval includes the company's claimed average age .

c ) A ) The population of the car drivers ages is normally distributed .