Question

It is known that the mean weight of all items sent through LSUHSC's campus mail system is 30 grams. A random sample of 25 campus mail items received by the School of Public Health had an average weight of 36 grams with a sample standard deviation of 16 grams. Construct the appropriate two-sided CI for the mean weight of mail received by the School of Public Health.

Answer 1

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 36

S = 16

n = 25

df = n – 1 = 24

Confidence level = 95%

Critical t value = 2.0639

(by using t-table)

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

Confidence interval = 36 ± 2.0639*16/sqrt(25)

Confidence interval = 36 ± 6.6045

Lower limit = 36 - 6.6045 = 29.3955

Upper limit = 36 + 6.6045 = 42.6045

Confidence interval = (29.3955, 42.6045)