Question

In: Statistics and Probability

An online used car company sells second-hand cars. For 40 randomly selected transactions, the mean price...

An online used car company sells second-hand cars. For 40 randomly selected transactions, the mean price is 2600 dollars.

Assuming a population standard deviation transaction prices of 250 dollars, obtain a 99% confidence interval for the mean price of all transactions. Please carry at least three decimal places in intermediate steps. Give your final answer to the nearest two decimal places.

is this the answer? (2498.18, 2701.82)

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 2600

Population standard deviation =    = 250

Sample size = n = 40

At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576

Margin of error = E = Z/2 * ( /n)

= 2.576 * ( 250 /  40 )

= 101.825

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

- E < < + E

2600 - 101.825 <   < 2600 + 101.825

2498.175 <   < 2701.825

( 2498.18 , 2701.82 )

At 99% confidence interval is ( 2498.18 , 2701.82 )

orchestra answered 2 years ago
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