Question

Assume that a sample is used to estimate a population mean μμ. Find the 95% confidence interval for a sample of size 56 with a mean of 65.3 and a standard deviation of 6.4. Enter your answer as an open-interval (i.e., parentheses) accurate to 3 decimal places.

95% C.I. =

The answer should be obtained without any preliminary rounding.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 65.3

sample standard deviation = s = 6.4

sample size = n = 56

Degrees of freedom = df = n - 1 = 56 - 1 = 55

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,55 = 2.004

Margin of error = E = t_/2,df * (s /n)

= 2.004 * (6.4 / 56)

= 1.7

The 95% confidence interval estimate of the population mean is,

- E < < + E

65.3 - 1.7 < < 65.3 + 1.7

63.6 < < 67.0

95% C.I. = (63.6 , 67.0)