Consider a random sample of 15 cars of the same model. Assume that the gas mileage...

Consider a random sample of 15 cars of the same model. Assume that the gas mileage for the population is normally distributed with a standard deviation of 5.2 miles per gallon. Calculate a 90% confidence interval for the mean, given a sample mean of 26.7 miles per gallon.

Solutions

Expert Solution

Solution :

Given that,

= 26.7

s = 5.2

n = 15

Degrees of freedom = df = n - 1 = 15 - 1 = 14

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t_/2,df = t_0.05,14 =1.761

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

= 1.761 * (5.2 / $\sqrt$ 15 )

=2.4

Margin of error = 2.4

The 90% confidence interval estimate of the population mean is,

- E < < + E

26.7 - 2.4 < < 26.7 + 2.4

2.70 < < 29.1

(24.3, 29.1 )

orchestra answered 1 year ago

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