Question

In: Statistics and Probability

A random sample of 81 credit sales in a department store showed an average sale of...

A random sample of 81 credit sales in a department store showed an average sale of $68.00. From past data, it is known that the standard deviation of the population is $27.00. What is the 99% confidence interval of the population mean? (Round to two decimal places)

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 68

Population standard deviation = = 27

Sample size = n = 81

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z_/2* ( / $\sqrt$ n)

= 2.576 * (27 / $\sqrt$ 81)

= 7.73

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

- E < < + E

68 - 7.73 < < 68 + 7.73

60.27 < < 75.73

(60.27,75.73 )

orchestra answered 3 years ago

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