Question

Acar company developed a certain car model to appeal to young consumers. The car company dames the storage age of drteers of this certain car model is 26.00 years old Suppere a random sample of 18 drivers was draw, and the very age of the covers was found to be 29.90 years. Assume the population standard deviation for the age of the car drivers to be 2.8 years. Complete parts through below * Constructa 95% confidence interval to estimate the average age of the car driver The Box confidence interval for the werage age of the car shiwer has a lower imit of years old and an upper imit of yours oil Round to two decimal places as needed.) b. Does this rouland sport to the company's dam? OA. No, because the interval does not include the company's claimed werage age OB. No, because the includes the company's claimed average age OC. Yes, because the interval includes the company's claimed average age OD. Yes, because the interval does not include the company's claimed werage an c. What assumption needs to be made to construct this interval OA The population of the models drivers ages is normally distributed OB. The population of all car driversi ages is normally distributed OC. The population of the models diverse is skerwed to one side OD. The population mean for the models drivers will be in the confidence interval OE. The sample ste is less than 30

Answer 1

a) The 95% confidence interval to estimate the average age of the car driver is given by,

$CI=(\bar{x}\pm z_{\alpha /2}\times \frac{\sigma }{\sqrt{n}})$

where, $\bar{x}=29.90, \sigma =2.5, n=18$

1-a = 0.95 > a = 0.05 > a/2 = 0.025

We will get the value of from the last row of t-table.

-a/2

From t-table,  

20/2 = 20.025 = 1.96

So, the 95% confidence interval is given by,

$CI=(29.90\pm 1.96\times \frac{2.5}{\sqrt{18}})$

$=(29.90\pm 1.96\times 0.5893)$

$=(29.90\pm 1.155)$

$=(28.745,31.055)$

The 95% confidence interval for the average age of the car driver has a lower limit of 28.75 years old and an upper limit of 31.06 years old.

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

A) No, because the interval does not include the company's claimed average data.

c) What assumption needs to be made to construct this interval?

A) The population of the model's drivers' ages is normally distributed.

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