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 …show more content…
(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.
(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:
Step by Step, up to Decision
| 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