Question

A statistics practitioner took a random sample of 56 observations from a population whose standard deviation is 29 and computed the sample mean to be 97. Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

A. Estimate the population mean with 95% confidence. Confidence Interval =

B. Estimate the population mean with 95% confidence, changing the population standard deviation to 58; Confidence Interval =

C. Estimate the population mean with 95% confidence, changing the population standard deviation to 9; Confidence Interval =

Answer 1

ANSWER:

a).

95% CI [89.4, 104.6]

M = 97
t = 1.96
s_M = √(29²/56) = 3.88

μ = M ± Z(s_M)
μ = 97 ± 1.96*3.88
μ = 97 ± 7.6

b).

95% CI [81.81, 112.19]

M = 97
t = 1.96
s_M = √(58²/56) = 7.75

μ = M ± Z(s_M)
μ = 97 ± 1.96*7.75
μ = 97 ± 15.19

c).

95% CI [94.64, 99.36]

M = 97
t = 1.96
s_M = √(9²/56) = 1.2

μ = M ± Z(s_M)
μ = 97 ± 1.96*1.2
μ = 97 ± 2.36

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