Question

A small stock brokerage firm wants to determine the average daily sales (in dollars) of stocks to their clients. A sample of the sales for 30 days revealed an average daily sales of $200,000. Assume that the standard deviation of the population is known to be $20,000.

a) Provide a 90% confidence interval estimate for the true average daily sales.

b) Provide a 97% confidence interval estimate for the true average daily sales.

Answer 1

Solution

Given that,

= 200,000

=20,000

n = 30

a ) At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z/2 = Z0.05 = 1.645

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

=1.645 * (20,000 / 30 )

= 6006

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

- E < < + E

200,000- 6006< < 200,000 + 6006

193993 < < 206006

b ) At 97% confidence level the z is ,

= 1 - 97% = 1 - 0.97 = 0.03

/ 2 = 0.03/ 2 = 0.015

Z/2 = Z0.015 = 2.170

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

= 2.170* (20,000 / 30 )

= 7924

At 97% confidence interval estimate of the population mean is,

- E < < + E

200,000- 7924 < < 200,000 + 7924

192076 < < 207924