Jim Wilson is the office manag
Jim Wilson is the office manager for a large manufacturing firm.His team is studying the usage of the company’s copy machines. Arandom sample of ten copy machines revealed the following number ofcopies 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 machinesis well over a million copies. Develop a 95% confidence intervalfor the mean number of copies per machine. (10 pts.) it can beoperating in excel.
Interpret this confidence interval and write a statement to Jimregarding his belief about the usage and support your comments withyour results.
Answer:
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 allcopy machines will lies between 971.76 thousands and 1131.84thousands.
We are 95% confident that the average number of copies from allcopy 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.
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