Question

Show in excel if possible:

Suppose a sample data set of size n = 20 has a sample mean x=115, and a sample standard deviation, s = 23.

a) Develop a 80% confidence interval for the population mean.

b) In words, how do you interpret this confidence interval?

Answer 1

Part a

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 115

S = 23

n = 20

df = n – 1 = 19

Confidence level = 80%

Critical t value = 1.3277

(by using t-table or excel command =tinv(.20,19))

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 115 ± 1.3277*23/sqrt(20)

Confidence interval = 115 ± 1.3277*5.142956348

Confidence interval = 115 ± 6.8284

Lower limit = 115 - 6.8284 = 108.17

Upper limit = 115 + 6.8284 = 121.83

Confidence interval = (108.17, 121.83)

Part b

We are 80% confident that the population mean will lies between 108.17 and 121.83.