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A survey of 23 grocery stores revealed that the average price of a gallon of milk...

A survey of 23 grocery stores revealed that the average price of a gallon of milk was $3.11 with a standard error of $0.30. What is the 95% confidence interval to estimate the true cost of a gallon of milk?

Expert Solution

Solution :

Given that,

= 3.11

standard error = (s / $\sqrt$ n) = 0.30

n = 23

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,22 = 2.074

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

= 2.074 * 0.30

= 0.62

The 95% confidence interval estimate of the population mean is,

- E < < + E

3.11 - 0.62 < < 3.11 + 0.62

2.49 < < 3.73

(2.49 , 3.73)

milcah answered 1 year ago

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