TMTH 3360: Confidence Interval Estimate of the Mean using Minitab
A national soft drink company is checking the amount of soda that is actually placed in a 2-liter bottle. The Quality
Division obtains a random sample of 36 2-liter bottles and measures the contents with the following results.
Establish a 95% confidence interval estimate of the true average amount of soda in each bottle. What do you
conclude about the volume of the bottles?
2.071
1.988
2.009
1.945
2.014
1.984
2.094
1.970
1.965
1.982
1.989
1.949
1.986
2.008
1.959
2.008
2.050
1.942
2.047
1.972
1.973
1.986
2.066
2.016
2.037
2.058
2.042
2.021
2.091
2.055
2.117
1.981
1.988
1.976
1.968
1.986
Establish a 95% confidence interval estimate of the true average amount of soda in each bottle. What do you
conclude about the volume of the bottles?
Before finding the confidence interval estimate, the data is described.
Worksheet size: 100000 cells
MTB > describe c1
Descriptive Statistics
Variable
Vol. (li
N
36
Mean
2.0081
Median
1.9885
TrMean
2.0061
Variable
Vol. (li
Minimum
1.9420
Maximum
2.1170
Q1
1.9737
Q3
2.0458
StDev
0.0450
SE Mean
0.0075
MTB > stem and leaf c1
Character Stem-and-Leaf Display
Stem-and-leaf of Vol. (li
Leaf Unit = 0.010
4
10
(9)
17
12
10
5
3
1
19
19
19
20
20
20
20
20
21
N
= 36
4445
667777
888888888
00011
23
44555
67
99
1
MTB > ZInterval 95.0 .045 'Vol. (liters)'.
Z Confidence Intervals
The assumed sigma = 0.0450
Variable
Vol. (li
Goodson/ 3360cimt
N
36
Mean
2.00814
StDev
0.04504
SE Mean
0.00750
95.0 % CI
( 1.99344, 2.02284)
1
Conclusion:
With 95% confidence, it is estimated that the average contents of the bottles
of soda is between 1.993 liters and 2.023 liters. The company appears to
provide a volume of soda that is consistent with the specified amount )2liters.
Note: if all possible samples of size 36 were taken and the mean was
calculated for each sample, 95% of the intervals would contain the true
population mean.
Goodson/ 3360cimt
2