Jewel, the branch manager of an outlet store of a nationwide chain of pet supply stores,...

Jewel, the branch manager of an outlet store of a nationwide chain of pet supply stores, wants to study characteristics of her customers. In particular, she decides to focus on the amount of money spent by her customers. A sample of 50 customers spent an average of $21.34 with a standard deviation of $9.25 on pet supplies.

a. What is the sampling distribution of the point estimate?

b. Calculate the margin of error for a 99% confidence interval estimating the actual average amount spent in the pet supply store.

c. Construct and interpret the confidence interval.

Solutions

Expert Solution

Solution

Given that,

a ) = 21.34

= 9.25

n =50

b ) At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576

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

= 2.576 * (9.25 / $\sqrt$ 50 )

= 3.37

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

- E < < + E

21.34 - 3.37 < < 21.34 + 3.37

17.97 < < 24.71

(17.97, 24.71 )

orchestra answered 1 year ago

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