Question

A statistics practitioner took a random sample of 55 observations from a population whose standard deviation is 30 and computed the sample mean to be 101. 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 52; Confidence Interval = C. Estimate the population mean with 95% confidence, changing the population standard deviation to 7; Confidence Interval =

Answer 1

a)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

101 - 1.96 * 30 / sqrt(55) < < 101 + 1.96 * 30 / sqrt(55)

93.07 <   < 108.93

CI = (93.07 , 108.93)

b)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

101 - 1.96 * 52 / sqrt(55) < < 101 + 1.96 * 52 / sqrt(55)

87.26 <   < 114.74

CI = (87.26 , 114.74)  

c)

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

101 - 1.96 * 7 / sqrt(55) < < 101 + 1.96 * 7 / sqrt(55)

98.15 <   < 102.85

CI = (99.15 , 102.85)