In: Statistics and Probability
n=30, x=94.0, s=16.5, 90% confidence
Solution :
Given that,
Point estimate = sample mean = = 94.0
sample standard deviation = s = 16.5
sample size = n = 30
Degrees of freedom = df = n - 1 = 30 - 1 = 29
At 90% confidence level the t is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
t /2,df = t0.05,29 = 1.699
Margin of error = E = t/2,df * (s /n)
= 1.699 * ( 16.5/ 30)
= 0.93
The 90% confidence interval estimate of the population mean is,
- E < < + E
94.0 - 0.93 < < 94.0 + 0.93
93.07 < < 94.93
(93.07 , 94.93)