In: Statistics and Probability
Make a 99% confidence interval for u if:
mean= 38.54
s=3.75
n=36
Solution :
Given that,
sample mean = = 38.54
sample standard deviation = s = 3.75
sample size = n = 36
Degrees of freedom = df = n - 1 = 36 - 1 = 35
At 99% confidence level the t is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
t /2,df = t0.005,35 = 2.724
Margin of error = E = t/2,df * (s /n)
= 2.724 * ( 3.75 / 36 )
= 1.70
The 99% confidence interval estimate of the population mean is,
- E < < + E
38.54 - 1.70 < < 38.54 + 1.70
36.84 < < 40.24
( 36.24 , 40.24 )