Question

Assume that a sample is used to estimate a population mean μ. Find the 99% confidence interval for a sample of size 46 with a mean of 47.2 and a standard deviation of 16.3. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.

99% C.I. =

Answer 1

df = n - 1 = 46 - 1 = 45

t critical value at 0.01 significance level with 45 df = 2.690

99% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

47.2 - 2.690 * 16.3 / sqrt(46) < < 47.2 + 2.690 * 16.3 / sqrt(46)

40.735 < < 53.665

99% C I is ( 40.735 , 53.665 )