Question

In: Statistics and Probability

The proprietor of a boutique in New York wanted to determine the average age of his...

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 53 customers revealed an average age of 28 years with a standard deviation of 4 years. Determine a 98% confidence interval estimate for the average age of all his customers.

                                                                                                                                                                                    

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Expert Solution

Solution :

Given that,

Point estimate = sample mean =   = 28

Population standard deviation =    = 4

Sample size = n =53

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02/ 2 = 0.01

Z/2 = Z0.01 = 2.326 ( Using z table    )

Margin of error = E = Z/2    * ( /n)

= 2.326 * ( 4 /  53 )

= 1.28
At 98% confidence interval estimate of the population mean
is,

- E < < + E

28 - 1.28 <   < 28 + 1.28

26.72 <   < 29.28

orchestra answered 1 year ago
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