# Title: Bottling Company Case Study

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Title: Bottling Company Case Study

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Bottling Company Case Study
Complaints have been received that the bottles of soda produced in our company contain less than the advertised sixteen (16) ounces of product. The purpose of ensuing study is to verify the claim of the complainers. A random sample of 30 bottles was drawn from among all the shifts of the plant.
Bottle Number
Ounces
Bottle Number
Ounces
Bottle Number
Ounces
1
14.5
11
15
21
14.1
2
14.6
12
15.1
22
14.2
3
14.7
13
15
23
14
4
14.8
14
14.4
24
14.9
5
14.9
15
15.8
25
14.7
6
15.3
16
14
26
14.5
7
14.9
17
16
27
14.6
8
15.5
18
16.1
28
14.8
9
14.8
19
15.8
29
14.8
10
15.2
20
14.5
30
14.6

Summary Statistics
Sample mean, = (Sum of product volumes of all bottles)/ (No. of bottles in sample)
...view middle of the document...

87, s = 0.550329
Since, n â‰¥ 30, we can approximate the sample as large sample and use Ïƒ = s
For 95% confidence interval, Î± = 0.05, so ZÎ±/2 = 1.96
Margin of Error E = ZÎ±/2 * s/âˆšn
= 1.96*0.550329/âˆš30 = 0.197 ounces
Lower limit of confidence interval = â€“ E
= 14.87 â€“ 0.20 = 14.67 ounces
Upper limit of confidence interval = + E
= 14.87 + 0.20 = 15.07 ounces
We can say with 95% confidence that the population mean of ounces in the bottles lies between 14.67 ounces and 15.07 ounces.
Hypothesis Test for population mean
Null Hypothesis H0: Âµ â‰¥16 [Mean ounces is greater than or equal to 16]
Alternative Hypothesis H1: Âµ < 16 [Claim] [Mean ounces is less than 16]
Level of significance Î± = 0.05. We will conduct a left-tailed z-test for population mean.
Z â€“ test statistic = ( - Âµ)/(Ïƒ/âˆšn)
= (14.87 â€“ 16)/(0.550329/âˆš30) = â€“11.246
Critical value of Z, Z c = -1.645
Since the test statistic lies in the rejection region, the null hypothesis can be rejected.
There is enough evidence to support the claim that the mean of bottle volumes is less than 16.
Conclusion
Both the confidence interval and the hypothesis test strongly indicate that the complainersâ€™ claim that the mean ounce in the bottles is less than 16 is justified. Three possible causes of the same could be â€“
Inefficient/Faulty equipment such as discharge-regulating devices such as valves, which lead to low volume of product dispensed.
Bottles of low capacity being used erroneously.
Fault in manpower â€“ Employees not doing their job properly, managers not overseeing the process thoroughly. Quality checks not being done properly.
To avoid such an eventuality in future, all equipment in the plant should be thoroughly checked. Old/obsolete equipment should be replaced. Capacity of bottles and discharge measuring devices should be checked. Other causes, if any, should be identified and corrected. Stringent quality checks should be done in future to avoid erroneous products being marketed. This will ensure consumer satisfaction and will avoid such complaints in the future.

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