Question

A simple random sample of 60 items from a population with population mean = 6 resulted in a sample mean of 39.

If required, round your answers to two decimal places.

a. Provide a 90% confidence interval for the population mean.

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b. Provide a 95% confidence interval for the population mean.

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c. Provide a 99% confidence interval for the population mean.

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Answer 1

a)
Mean = 39
Sample size (n) = 60
Standard deviation (s) = 6
Confidence interval(in %) = 90
z @ 90% = 1.645
Since we know that

Required confidence interval = (39.0-1.2742, 39.0+1.2742)
Required confidence interval = (37.7258, 40.2742)

b)
Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that

Required confidence interval = (39.0-1.5182, 39.0+1.5182)
Required confidence interval = (37.4818, 40.5182)

c)
Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that

Required confidence interval = (39.0-1.9954, 39.0+1.9954)
Required confidence interval = (37.0046, 40.9954)

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