In: Statistics and Probability
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.
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