9.23 Sheila Johnson, a state procurement manager, is responsible for monitoring

Question

9.23 Sheila Johnson, a state procurement manager, is
responsible for monitoring the integrity of a wide range of
products purchased by state agencies. She is currently
examining a sample of paint containers recently received
from a long-time supplier. According to the supplier, the
process by which the cans are filled involves a small
amount of variation from one can to the next, and the standard
deviation is 0.25 fluid ounces. The 40 cans in Sheila’s
sample were examined to determine how much paint they
contained, and the results (in fluid ounces) are listed in data
file XR09023. Using the mean for this sample, and assuming
that the population standard deviation is 0.25 fluid ounces,
construct the 90% confidence interval for the population
mean volume for the cans of paint provided by the supplier.
If the labels on the paint cans say the mean content for such
containers is 100.0 fluid ounces, would your confidence interval
tend to support this possibility?

File XR09023:
Fl_Oz
99.99
99.89
99.75
99.97
100.16
100.29
99.93
99.73
99.61
100.35
100.21
100.11
99.65
99.97
99.93
99.86
100.14
99.92
99.98
99.61
100.04
100.15
99.96
100.28
100.24
99.66
100.14
99.46
100.03
99.75
100.02
99.71
99.83
99.75
100.53
100.03
99.97
99.94
99.71
100.22

Explanation / Answer

sample mean = 99.962, then 90% CI =(99.962-z(0.05)*0.25/sqrt(40), 99.962+z(0.05)*0.25/sqrt(40)) =(99.962-1.645*0.25/sqrt(40), 99.962+1.645*0.25/sqrt(40)) =(99.897, 100.027) 100 is within the 90% confidence interval, so the mean content for these containers are 100 fluid ounces.

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