Being the manager at one of the major bottling company, it has come to my attention that customers are complaining that the bottles contain less than 16 ounces of the advertised soda. My boss wishes to get this problem solved. He has therefore asked me to conduct an investigation. I therefore had to organize for my employee pull 30 bottles off the line. Each one had to pick a bottle at random from all shifts. Each employee was ten required to measure the amount of soda contained in the bottle.
The following table contains the result.
Table 1
Bottle number
ounces
Bottle number
ounces
Bottle number
ounces
1
14.23
11
15.77
21
16.23
2
14.32
12
15.8
22
16.25
3
14.98
13
15.82
23
16.31
4
15
14
15.87
24
16.32
5
15.11
15
15.98
25
16.34
6
15.21
16
16
26
16.46
7
15.42
17
16.02
27
16.47
8
15.47
18
16.05
28
16.51
9
15.65
19
16.21
29
16.91
10
15.74
20
16.21
30
16.96
By use of excel attached, the mean, the standard deviation and the median were determined. The following are the results:
Sample mean is the average value obtained by summing up the data points divided by the number of data points (Anderson, et al., 2008). The mean of the given data is 15.854 as computed in excel file attached. We are able to obtain the median of the data by arranging the data in ascending order. The number(s) that fall in between the middle of the data become our median. In our case, he central values falls between 15th and 16th observation. From, excel file, our median is computed to give 15.99. The medium is bigger than the mean implying that the data left skewed. The standard deviation is 0.66. The value of the standard deviation is relatively low implying that there is much variation between in the sample data.
A 95% confidence interval is computed in excel. This is the estimation of the mean of the population by us of a sample mean implying that the first criterion is satisfied (Brase, and Brase, 2012). In this case, the sample size should be 30 or greater. The data gives a critical value of 1.96 at 95% confidence interval. From excel file attached, we can see that the lower and upper values are 14.6 and 14.92. This means that, at a confidence level of 95%, the ounces in the bottle ranges from 14.6-14.92.
We have to now prove that the bottles have less than 16 ounces of soda by use of hypothesis test. This test will be done at a confidence level of 95%. The significance level is 0.05 (α = 1 – 0.95). The hypotheses are as follows;
The Null hypothesis, H0: μ = 16; the number of ounces in each bottle is 16.
The alternate hypothesis, H1: μ < 16; the number of ounces in each bottle is less than 16
Note that, the less than type hypothesis is carried out thereby creating a left tailed test.
Carrying out a z test with a mean of 15.854 and a standard deviation of 0.66, the test value at 95% confidence level will be;
-1.21 is less than o.o5. This implies that we must reject the null hypothesis. We can therefore state that, the number ounces in the each bottle is less than 16.
Conclusion
From the analysis done above, it can be safely concluded that each bottle contain less amounts of ounces as compared to the one advertised. There are various causes of this which may include;
i. There is a probability that the calibrations of the weighing apparatus are erased and therefore the personnel may have done mere estimations when pouring.
ii. There is also a probability that the conveyer belt could have been moving relatively faster than expected thereby making bottles to have less time of filling at the pouring point.
iii. Some of the soda could be spilling out because maybe the bottles are not properly aligned with the tap.
Recommendation
The management can take various corrective procedures to make sure that every bottle contains 16 ounces as advertised. First, the management should ensure that machine calibrations are clear. Recalibrations may be done for the worn out machines. Again, proper velocity of the conveyer belt should be set to ensure that each bottle spends enough time at the tap. Finally, each bottle should be properly aligned with the tap. This shall ensure that the bottles are filled with the correct amount of ounces and less of the soda go to waste.
References
Anderson, D. R., Sweeney, D. J., & Williams, T. A. (2008). Statistics for Business and
Economics, 10th Ed. Ohio: Thomson South-Western.
Brase, C. H. and Brase, C. P. (2012). Understandable Statistics: Concepts and Methods, 10th
Ed. Massachusetts: Brooks/Cole Cengage Learning.
