In: Statistics and Probability
Construct a 95?% confidence interval to estimate the population mean using the following data. What assumptions need to be made to construct this? interval?
x?=93 |
?=15 |
n=17 |
With 95?% ?confidence, when n=17 the population mean is between the lower limit of __ and the upper limit of __
Solution :
Given that,
= 93
= 15
n = 17
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z_{/2} = Z_{0.025} = 1.96
Margin of error = E = Z_{/2}* ( /n)
=1.96 * (15 / 17)
= 7.1305
At 99% confidence interval estimate of the population mean is,
- E < < + E
93-7.1305 < < 93+7.1305
85.8695< < 100.1305
With 95?% ?confidence, when n=17 the population mean is between the lower limit of 85.8695 and the upper limit of 100.1305