Question

The shipping department of a farm-equipment parts supplier in Amarillo, TX is experiencing troubles. Twenty independent hourly samples were obtained by observing the two workers in the shipping department. The samples showed that the duration (in minutes) their two workers were simultaneously idle are: 2.3, 1.9, 3.2, 2.5, 2.6, 2.1, 3.1, 2.5, 1.8, 1.6, 1.5, 3.2, 1.6, 2.4, 2.7, 1.8, 2.9, 2.5, 2.6 and 2.2 (with a sample mean of 2.35 minutes and sample standard deviation of 0.532 minutes). Determine a 95% confidence interval for the population mean of the amount of time in minutes that both workers would be simultaneously idle.

Answer 1

Solution:

Confidence interval for Population mean is given as below:

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

From given data, we have

Xbar = 2.35

S = 0.532

n = 20

df = n – 1 = 19

Confidence level = 95%

Critical t value = 2.0930

(by using t-table)

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

Confidence interval = 2.35 ± 2.0930*0.532/sqrt(20)

Confidence interval = 2.35 ± 0.2490

Lower limit = 2.35 - 0.2490 = 2.1010

Upper limit = 2.35 + 0.2490 = 2.5990

Confidence interval = (2.1010, 2.5990)