Question

Assume that a sample is used to estimate a population mean μ . Find the 99% confidence interval for a sample of size 64 with a mean of 53.2 and a standard deviation of 6.6. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places. 99% C.I. =

The answer should be obtained without any preliminary rounding.

Answer 1

Solution:

The 99% confidence interval for population mean is given as follows:

Where, x̄ is sample mean, s is sample standard deviation, n is sample size and t_{(0.01/2, n-1)} is critical t-value to construct 99% confidence interval.

We have, x̄ = 53.2, s = 6.6 and n = 64

Using t-table we get, t_{(0.01/2, 64-1)} = 2.6561

Hence, 99% confidence interval for population mean is,

The 99% confidence interval for μ is (51.009, 55.391).

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