In: Statistics and Probability
A simple random sample of 90 items from a population with σ = 7 resulted in a sample mean of 33. If required, round your answers to two decimal places.
a. Provide a 90% confidence interval for the population mean. to
b. Provide a 95% confidence interval for the population mean. to
c. Provide a 99% confidence interval for the population mean.
Solution :
Given that,
a.
Sample size = n = 90
Z/2
= 1.645
Margin of error = E = Z/2*
(
/
n)
= 1.645 * (7 /
90)
Margin of error = E = 1.21
At 90% confidence interval estimate of the population mean is,
- E <
<
+ E
33 - 1.21 <
< 33 + 1.21
A 90% confidence interval for the population mean 31.79
<
< 34.21
b.
Sample size = n = 90
Z/2
= 1.96
Margin of error = E = Z/2*
(
/
n)
= 1.96 * (7 /
90)
Margin of error = E = 1.45
At 95% confidence interval estimate of the population mean is,
- E <
<
+ E
33 + 1.45 <
< 33 + 1.45
31.55 <
< 34.45
31.55 to 34.45
A 95% confidence interval for the population mean 31.55 to 34.45
c.
Sample size = n = 90
Z/2
= 2.576
Margin of error = E = Z/2*
(
/
n)
= 2.576 * (7 /
90)
Margin of error = E = 1.90
At 99% confidence interval estimate of the population mean is,
- E <
<
+ E
33 - 1.90 <
< 33 + 1.90
31.10 <
< 34.90
A 99% confidence interval for the population mean 31.10 to 34.90