Question

In: Statistics and Probability

3 The ten most recent cars sold at a dealership have an average price of $24,525...

3 The ten most recent cars sold at a dealership have an average price of $24,525 with a standard deviation of s = $450. Assuming that the prices of all cars sold by the dealership have an approximately normal distribution, find the 98% confidence interval for the mean price of all cars sold by the dealership, to the nearest dollar.

Conclusion: We can be ___________confident that the mean price of all cars sold by the dealership is between $ ________________ and $ ___________________3

Expert Solution

Solution :

Given that,

= $24525

s = $450

n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t_/2,df = t_0.01,9 =2.821

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

= 2.821 * (450 / $\sqrt$ 10) = 401

The 98% confidence interval estimate of the population mean is,

- E < < + E

24525 - 401 < < 24525 + 401

24124 < < 24926

(24124 , 24926 )

We can be _____98%______confident that the mean price of all cars sold by the dealership is between $24124 and $ 24926

orchestra answered 1 year ago

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