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# Bottling Company Case Study

Statistics

Exam Practice

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Running head: BOTTLING COMPANY CASE STUDY:
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Bottling Company Case Study:
Name:
Institution:
In statistics, mean is an average of numbers. In order to determine it in this case study, I
added all the number of ounces and divide them by the total number of bottles. The sums of

BOTTLING COMPANY CASE STUDY
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ounces are 446.1 while the number of bottles is 30. As such, the mean is 446.1 / 30 is which is
14.9.
On the other hand, the median is the middle or center number or data once they are
arranged in order. Consequently, the median is the middle number of ounces in the bottles. In this
case, the given numbers are in order. There are 30 entries (even number). Hence, the mean of 2
center numbers (14.8 and 14.8) will provide the precise median number.
14.8 +14.8= 14.8
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Standard deviation is the term used to measure the way or how numbers are spread out.
In essence, it calculated just to show the extent to which far apart some data is in a given
scenario. The symbol for standard deviation is sigma (σ). According to (Quinn & Keough, 2002),
standard deviation may be calculated by finding the difference between entry mean and the entry
data. In this scenario, once variance is obtained, it is divided by 30-1 giving rise to a standard
deviation of approximately 0.55 after rounding down to 2 decimal places.
Confidence interval is a phrase in statistics which measures probability that some
population parameter falls between 2 value sets. In sum, the confidence interval comes about as
the possibility that a certain value falls between a lower and an upper bound of the probability
distribution. Confidence intervals may take any probability numbers, with the common numbers
being 99% and 95%. So as to construct the 95 % confidence interval, several statistics are
required. The first one is the mean and in this case 14.9 due to the reality that we have already
selected a 95% confidence interval, i find margin of error so as to get the answer. With the help

BOTTLING COMPANY CASE STUDY
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of a t-score model, I computed alpha, critical probability (0. 975]) and degree of freedom (999).
From this, I found 1.96 to be the critical value. Once I multiplied it with the 0.95 confidence
interval I got 1.86 to be the margin error. In effect, the 95 % confidence interval lies between
population mean intervals of around 14.9 ± 1.86.
As far as the testing of hypothesis is concerned, it is crucial to acknowledge that a
complaint is lodged that the company’s bottles of soda contains lesser than the 16 ounces of the
commodity advertised. So as to verify whether the assertion that the said bottles have less as
customers expects, thirty bottles are pulled at random off the line in all shifts at the plant. Next
the employees are to measure the quantity of soda present in each of the bottles.
In this regard, the alternative hypothesis is: The bottles of soda generated by the company
have less in comparison to the advertised 16 ounces of soda. On the other hand, the null
hypothesis is: The bottles of soda manufactured by the company do not have less in comparison
to the advertised 16 ounces of product. The equation is used in making a
decision on whether to reject or accept the two hypotheses.
Using the figures obtained above,
z = (14.8.-14.9)/ (0.55/√16)
z= -0.1/0.1 or -1

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