Question

(1 point) A statistics practitioner took a random sample of 51 observations from a population whose standard deviation is 23 and computed the sample mean to be 110. 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 48; Confidence Interval = C. Estimate the population mean with 95% confidence, changing the population standard deviation to 11; Confidence Interval =

Answer 1

a)

M = 110
Z = 1.96
s_M = √(23²/51) = 3.22

μ = M ± Z(s_M)
μ = 110 ± 1.96*3.22
μ = 110 ± 6.31

CI [103.69, 116.31]

b)

M = 110
Z = 1.96
s_M = √(48²/51) = 6.72

μ = M ± Z(s_M)
μ = 110 ± 1.96*6.72
μ = 110 ± 13.17

CI [96.83, 123.17]

c)

M = 110
Z = 1.96
s_M = √(11²/51) = 1.54

μ = M ± Z(s_M)
μ = 110 ± 1.96*1.54
μ = 110 ± 3.02

95% CI [106.98, 113.02]