CASE 7 – QUALITY ASSOCIATES INC.
BACKGROUND (CASE STUDY WRITE UP)
Quality Associates, Inc. is a consulting firm who advises its clients about statistical and sampling methods that can be used to control their manufacturing procedures. In this particular case we consider a production line designed to fill bottles of a shampoo with a mean weight of 12 ounces of shampoo per bottle. Quality Associates, Inc. made a quality control testing of the manufacturing machine of this client (Alibaba Machinery), to determine if the process is operating properly or if, perhaps, a machine malfunction has caused the process to begin underfilling or overfilling the bottles. The client picked a sample of 800 bottles taken during a time when the machine was
(v) For Sample 3, the median is higher than the mean. For all of the other three samples, the mean and median are equivalent (to 2 decimal places). The mean is a type of average which is affected by every observation in the sample, whereas the median is not. Thus the relatively low mean is an indication that there are low-lying weights which have affected the mean. Observing the data shows that sample 3 has the lowest weight out of all the samples, which is 11.36 fl.oz.

STATISTICAL FINDINGS:
(OUR HYPOTHESIS TESTING… SUPPORTED WITH TABLES & GRAPHS
For this hypothesis test a two-tailed test is required, about a population mean, with the population standard deviation known (p. 361). This is because Alibaba Machinery does not want to either underfill or overfill its shampoo. Underfilling may result in a complaint from customers or a government agency, and overfilling would be an unnecessary cost to the company.
According to the said hypothesis test, the null hypothesis is to be rejected if p-value ≤α. The test was calculated for each sample at the 0.01 level of significance, as follows:
Insert tables
Step by Step, up to Decision
Analysis
| Sample 1 | Sample 2 | Sample 3 | Sample 4 | Total | Result | p-value ≥ α | p-value ≥ α | p-value ≤ α | p-value ≥ α | p-value ≥α | Analysis | Accept H0 | Accept H0 | Reject H0 | Accept H0 | Accept H0 |

It is noted that the p-value is less than the