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A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of 26.4...

A random sample of 36 mid-sized cars tested for fuel consumption gave a mean of 26.4 miles per gallon with a standard deviation of 2.3 miles per gallon. Find a 99% confidence interval for the true population mean miles per gallon. Upload the file with your answer and work.  

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Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 26.4

Population standard deviation =    = 2.3

Sample size = n = 36

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 * ( 2.3 /  36 )

= 0.99

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

- E < < + E

26.4 - 0.99 <   < 26.4 + 0.99

25.41 <   < 27.39

( 25.41 , 27.39 )

The 99% confidence interval for the true population mean is ( 25.41 , 27.39 )

orchestra answered 1 year ago
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