Question

Jim Wilson is the office manager for a large manufacturing firm. His team is studying the usage of the company’s copy machines. A random sample of ten copy machines revealed the following number of copies from each machine (reported in 1,000s):

1026

920

1193

968

986

973

1073

1229

965

1185

Jim believes that the actual mean usage of all the copy machines is well over a million copies. Develop a 95% confidence interval for the mean number of copies per machine. (10 pts.) it can be operating in excel.

Interpret this confidence interval and write a statement to Jim regarding his belief about the usage and support your comments with your results.

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 = 1051.8

S = 111.8836697

n = 10

df = n – 1 = 10 – 1 = 9

Confidence level = 95%

Critical t value = 2.2622

(by using t-table or excel)

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

Confidence interval = 1051.8 ± 2.2622*111.8836697/sqrt(10)

Confidence interval = 1051.8 ± 2.2622*35.38072294

Confidence interval = 1051.8 ± 80.0368

Lower limit = 1051.8 - 80.0368 = 971.76

Upper limit = 1051.8 + 80.0368 = 1131.84

Confidence interval = (971.76, 1131.84)

We are 95% confident that the average number of copies from all copy machines will lies between 971.76 thousands and 1131.84 thousands.

We are 95% confident that the average number of copies from all copy machines will lies between 971763.2 and 1131837.

The number of one million lies within above confidence interval, so Jim's belief is true about the usage of copy machines.