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)
= 446.1/30 = 14.87 ounces
After arranging the data in ascending order, the median was calculated. Since there are even number of data values,
Median = Average of the (n/2)th data and (n/2 + 1)th data [after sorting]
= (14.8+14.8)/2 = 14.8 ounces
Sample Variance = [Sum of all (data values – mean) 2] / (n-1)
= 8.873/29 = 0.303
Sample Standard Deviation, s = √ (Variance)
= 0.550329 ounces
Sample mean = 14.87 ounces, Sample median = 14.8 ounces, Sample sd = 0.550329 ounces
Confidence Interval for ounces in the bottles
= 14.87, s = 0.550329
Since, n ≥ 30, we can approximate the sample as large sample and use σ = s
For 95% confidence interval, α = 0.05, so Zα/2 = 1.96
Margin of Error E = Zα/2 * s/√n
= 1.96*0.550329/√30 = 0.197 ounces
Lower limit of confidence interval = – E
= 14.87 – 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....