Solution :
Given that,
Point estimate = sample mean = = 35
sample standard deviation = s = 13
sample size = n = 16
Degrees of freedom = df = n - 1 = 16 - 1 = 15
At 90% confidence level
= 1 - 90%
=1 - 0.90 =0.10
/2
= 0.05
t/2,df
= t0.05,15 = 1.753
Margin of error = E = t/2,df * (s /n)
= 1.753 * ( 13 / 16)
Margin of error = E = 5.7
The 90% confidence interval estimate of the population mean is,
- E < < + E
35 - 5.7 < < 35 + 5.7
29.3 < < 40.7
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