Question

A study of the ages of motorcyclists killed in crashes involves the random selection of

150150

drivers with a mean of

34.7634.76

years. Assuming that

sigmaσequals=8.68.6

​years, construct and interpret a

9999​%

confidence interval estimate of the mean age of all motorcyclists killed in crashes. Click here to view a t distribution table.

LOADING...

Click here to view page 1 of the standard normal distribution table.

LOADING...

Click here to view page 2 of the standard normal distribution table.

LOADING...

What is the

9999​%

confidence interval for the population mean

muμ​?

nothing less than<muμless than<nothing

​(Round to two decimal places as​ needed.)

Notice that the confidence interval limits do not include ages below 20 years. What does this​ mean?

A.

The mean age of the sample will most likely not be less than 20 years old.

B.

Motorcyclists under the age of 20 never die in crashes.

C.

The mean age of the population will most likely not be less than 20 years old.

D.

The mean age of the population will never be less than 20 years old

Answer 1

Solution :

Given that,

Point estimate = sample mean = $\bar x$ = 34.76

Population standard deviation =   $\sigma$ = 8.6

Sample size = n = 150

At 99% confidence level

$\alpha$ = 1 - 99%  

$\alpha$ = 1 - 0.99 =0.01

$\alpha$/2 = 0.005

Z$\alpha$/2 = Z_0.005 = 2.576

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 2.576 * ( 8.6 /  $\sqrt$150 )

= 1.81

At 99% confidence interval estimate of the population mean is,

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

34.76 - 1.81 <  $\mu$ < 34.76 + 1.81

(32.95 <  $\mu$ < 36.57)

correct option is = A.

The mean age of the sample will most likely not be less than 20 years old.