When considering the case study, the focus is to find out if the bottle of sodas being produced contains less than the 16 ounces of product being advertised. Thus, we will calculate the mean, medium, and standard deviation for the ounces in bottles develop 95 % confidence level of the ounces, and also conduct a hypothesis test to verify the claim being made by customers.
Number |
Ounces |
Number |
Ounces |
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 |
Mean
When calculating the mean, you add the values of the data then divide the value by the total number of values (Farber & Larson 2009). The formula for calculating the mean is x̄ = (∑x) / N. The sum of the data is 446.1, and the number of entries is 30; thus, 446.1/30 = 14.87
Medium
The medium is that value that lies at the midpoint of the data when all data are put in order. There are thirty entries in this case; therefore, the medium is the mean of the two entries in the middle that is (14.8+14.8)/2 = 14.8
Standard deviation
The standard deviation is considered as the difference of the entry data and the entry mean. The standard deviation (σ) is usually the square root of the variance (Farber & Larson 2009). Therefore, before calculating the standard deviation, it is necessary to calculate the variance. The formula is σ = √ [∑(x-mean) 2 / N]. In our case study, the variance is 0.302862 and the square root of this number is 0.5503. Thus, the standard deviation is 0.5503.
Confidence interval
Confidence interval refers to a specific interval estimate of a parameter that is determined by using data from raw sampling and a certain confidence level of the estimate such as the sampling of the ounces in the 30 bottles from the case study. From the case, the sample size is 30 with a mean of 14.87 and a standard deviation of 0.5503. With a desired confidence level of 985 %, the confidence interval is + or-0.2. Therefore, there is a 95 % that the population mean is between the range of 14.67 to 15.07.
Hypothesis
The alternative hypothesis is that the soda bottles produced have less than 16 ounces of product
Null hypothesis is that soda bottles do not have less than 16 ounces of product.
With the 95 % confidence interval, it is clear that the true mean lies between 14.67 and 15.07. Thus, the margin error is 15.07-14.67= 0.4/2 = 0.2
The T statistics = 147.99554
P value = 0.00025
According to the p value, the alternative hypothesis is correct as it states that the soda bottles produced have less than 16 ounces of product.
Recommendation
It is true that there are less than 16 ounces in some of the bottles. The possible causes may be because the soda in the bottles would not have settled, and it would still have frizz when the weight of the bottle was being checked. Another reason would be that the warehouse temperature and the soda temperature would cause the weight to be off when filling the bottles. It is also likely that the equipment would be out of calibration. Therefore, the recommended solution is to ensure that maintenance is completed, and employees should have training on quality assurance that will educate them on what they should look for while bottling in order to eliminate the problem in the future.
Reference
Farber, B & Larson, B (2009). Elementary statistics picturing the world New Jersey, Prentice Hall
Cohen, B Welkowitz, J & Ewen, R (2006). Introductory statistics for the behavioral science John Wiley & sons
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