Question
In: Statistics and Probability
A sample of 53 night-school students' ages is obtained in order to estimate the mean age...
A sample of 53 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 25.5 years. The population variance is 13.
(b) Find the 95% confidence interval for μ. (Give your answer correct to two decimal places.)
| Lower Limit | |
| Upper Limit |
(c) Find the 99% confidence interval for μ. (Give your answer
correct to two decimal places.)
| Lower Limit | |
| Upper Limit |
Solutions
Expert Solution
Solution :
Given that,
Point estimate = sample mean = 
= 25.5
Population standard deviation = 
= 3.6
Sample size = n = 53
a)
At 95% confidence level the z is ,
Z
/2
= Z0.025 = 1.96
Margin of error = E = Z/2*
(
/
= 1.96* (3.6 /
= 0.97
At 95% confidence interval estimate of the population mean is,
- E < 
<
+ E
25.5 - 0.97 <
< 25.5 + 0.97
24.53 <
< 26.47
Lower limit = 24.53
Upper limit = 26.47
b)
At 99% confidence level the z is ,
Z/2
= Z0.005 = 2.576
Margin of error = E = Z/2*
(
/
= 2.576* (3.6 /
= 1.27
At 99% confidence interval estimate of the population mean is,
- E <
<
+ E
25.5 - 1.27 <
< 25.5 + 1.27
24.23 <
< 26.77
Lower limit = 24.23
Upper limit = 26.77
orchestra answered 2 years agoRelated Solutions
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