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.

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

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

Answer 1

Solution :

Given that,

Sample size = n = 30

8)

Z/2 = 1.645

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

= 1.645 * ( 20000/ 30)

= 6,006.69

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

- E < < + E

200,000 - 6,006.69 < < 200,000 + 6,006.69

193,993.31 < < 206,006.69

(193,993.31, 206,006.69)

9)

Z/2 = 2.17

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

= 2.17 * ( 20000/ 30)

= 7,923.72

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

- E < < + E

200,000 - 7,923.72 < < 200,000 + 7,923.72

192,076.28 < < 207,923.72

(192,076.28, 207,923.72)