Solution :
Given that,
= 63
s = 13
n = 40
Degrees of freedom = df = n - 1 = 40 - 1 = 39
At 95% confidence level the t is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
t /2,df = t0.025,39 = 2.021
Standard error = (s /n)
= (13 / 40)
= 2.055
Standard error = 2.06
Margin of error = E = t/2,df * (s /n)
= 2.021 * (13 / 40)
= 4.163
Margin of error = 4.163
The 95% confidence interval estimate of the population mean is,
- E < < + E
63 - 4.163< < 63 + 4.163
58.837 < < 67.163
(58.83, 67.163 )
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