Part a)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 54- 1 ) = 1.67
22 ± t(0.1/2, 54 -1) * 4.1/√(54)
Lower Limit = 22 - t(0.1/2, 54 -1) 4.1/√(54)
Lower Limit = 21.07
Upper Limit = 22 + t(0.1/2, 54 -1) 4.1/√(54)
Upper Limit = 22.93
90% Confidence interval is ( 21.07 , 22.93 )
Part b)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 54- 1 ) = 2.01
22 ± t(0.05/2, 54 -1) * 4.1/√(54)
Lower Limit = 22 - t(0.05/2, 54 -1) 4.1/√(54)
Lower Limit = 20.88
Upper Limit = 22 + t(0.05/2, 54 -1) 4.1/√(54)
Upper Limit = 23.12
95% Confidence interval is ( 20.88 , 23.12 )
Part c)
Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.01 /2, 54- 1 ) = 2.67
22 ± t(0.01/2, 54 -1) * 4.1/√(54)
Lower Limit = 22 - t(0.01/2, 54 -1) 4.1/√(54)
Lower Limit = 20.51
Upper Limit = 22 + t(0.01/2, 54 -1) 4.1/√(54)
Upper Limit = 23.49
99% Confidence interval is ( 20.51 , 23.49 )
Exercise 8.14 Algorithmic) A simple random sample with n 54 provided a sample mean of 22.0...
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