In: Statistics and Probability
Solution :
Given that,
= 26.7
s = 5.2
n = 15
Degrees of freedom = df = n - 1 = 15 - 1 = 14
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
t /2,df = t0.05,14 =1.761
Margin of error = E = t/2,df * (s /n)
= 1.761 * (5.2 / 15 )
=2.4
Margin of error = 2.4
The 90% confidence interval estimate of the population mean is,
- E < < + E
26.7 - 2.4 < < 26.7 + 2.4
2.70 < < 29.1
(24.3, 29.1 )