Solution :
Given that,
a) population mean = unknown
b) Point estimate = sample mean = = 82
sample standard deviation = s = 24
sample size = n = 25
Degrees of freedom = df = n - 1 = 25 - 1 = 24
c) At 90% confidence level
= 1 - 90%
=1 - 0.90 =0.10
/2
= 0.05
t/2,df
= t0.05,24 = 1.711
Margin of error = E = t/2,df * (s /n)
= 1.711 * ( 24 / 25)
Margin of error = E = 8.213
d) The 90% confidence interval estimate of the population mean is,
± E
= 82 ± 8.213
= ( 73.787, 90.213 )
e) yes
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