Question

According to Edmunds, the average price that shoppers paid for a new car is $30,320. Assume that the standard deviation for the price shoppers pay is $8,740. A random sample of 38 people who purchased a new car paid an average of $32,700. Use a 98% confidence interval to test the validity of claim made by Edmunds.

Answer 1

The claim is valid for 98% confidence interval. A further explanation is described below.

Explanation:

The given values are:

Sample size,

n = 38

Sample mean,

`\bar{x}=32700`

Population standard deviation,

`\sigma=8740`

For 98% confidence interval,

Mean =
`(\bar{x} \pm z^** (\sigma)/(√(n) ) )`

On substituting the given values, we get

=
`(32700 \pm 2.326* (8740)/(√(38) ) )`

=
`(32700 \pm 3297.84)`

=
`(29402.16,35997.84)`

Thus the above is the appropriate solution.