Question

A random sample of 20 students is collected and the number of siblings students have is recorded:

1	2	2	3	4	1	2	4	3	2
0	3	4	2	2	1	3	2	3	0

Construct a 90% confidence interval for the mean number of siblings.

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 2.2

S = 1.196486083

n = 20

df = n – 1 = 19

Confidence level = 90%

Critical t value = 1.7291

(by using t-table)

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

Confidence interval = 2.2 ± 1.7291*1.196486083/sqrt(20)

Confidence interval = 2.2 ± 0.4626

Lower limit = 2.2 - 0.4626 = 1.7374

Upper limit = 2.2 + 0.4626 = 2.6626

Confidence interval = (1.7374, 2.6626)