Statistics - Hypothesis Testing Projects

Statistics Project Quality Associates, Inc., a consulting firm, advises its clients about sampling and

Statistics Project

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In one particular application, a client gave Quality Associates a sample of 800 observations taken during a time in which that client's process was operating satisfactorily. The sample standard deviation for these data was .21; hence, with so much data, the population standard deviation was assumed to be .21. Quality Associates then suggested that random samples of size 30 be taken periodically to monitor the process on an ongoing basis. By analyzing the new samples, the client could quickly learn whether the process was operating satisfactorily. When the process was not operating satisfactorily, corrective action could be taken to eliminate the problem. The design specification indicated the mean for the process should be 12. The hypothesis test suggested by Quality Associates follows.

\(\begin{aligned}

&H_{0}: \mu=12 \\

&H_{\mathrm{a}}: \mu \neq 12

\end{aligned}\)

Corrective action will be taken any time $H_{0}$ is rejected.

The following samples were collected at hourly intervals during the first day of operation of the new statistical process control procedure. These data are available in the data set Quality.

Sample 1	Sample 2	Sample 3	Sample 4
11.55	11.62	11.91	12.02
11.62	11.69	11.36	12.02
11.52	11.59	11.75	12.05
11.75	11.82	11.95	12.18
11.9	11.97	12.14	12.11
11.64	11.71	11.72	12.07
11.8	11.87	11.61	12.05
12.03	12.1	11.85	11.64
11.94	12.01	12.16	12.39
11.92	11.99	11.91	11.65
12.13	12.2	12.12	12.11
12.09	12.16	11.61	11.9
11.93	12	12.21	12.22
12.21	12.28	11.56	11.88
12.32	12.39	11.95	12.03
11.93	12	12.01	12.35
11.85	11.92	12.06	12.09
11.76	11.83	11.76	11.77
12.16	12.23	11.82	12.2
11.77	11.84	12.12	11.79
12	12.07	11.6	12.3
12.04	12.11	11.95	12.27
11.98	12.05	11.96	12.29
12.3	12.37	12.22	12.47
12.18	12.25	11.75	12.03
11.97	12.04	11.96	12.17
12.17	12.24	11.95	11.94
11.85	11.92	11.89	11.97
12.3	12.37	11.88	12.23
12.15	12.22	11.93	12.25

Directions: This case study is to be returned to me on or before class time on 08.04.2008. You may use any method of written presentation, but be neat and without errors. Use at least four decimal places in your final solutions. Show all work. Include a page list of the formulas that you used to complete the Managerial Report. Use the p-Value method and the Confidence Level method in your solutions. The limits of #3 are confidence intervals. The more detailed your solutions are t higher your grade will be.

Conduct a hypothesis test for each sample at the $.01$ level of significance and. what action, if any, should be taken. Provide the test statistic and $p$ -value for .
Compute the standard deviation for each of the four samples. Does the as of $.21$ for the population standard deviation appear reasonable?
Compute limits for the sample mean $\bar{x}$ around $\mu=12$ such that, as long sample mean is within those limits, the process will be considered to be satisfactorily. If $\bar{x}$ exceeds the upper limit or if $\bar{x}$ is below the lower limit, $c$ action will be taken. These limits are referred to as upper and lower cont for quality control purposes.
Discuss the implications of changing the level of significance to a larger values mistake or error could increase if the level of significance is increased?

Price: $16.41

Solution: The downloadable solution consists of 8 pages, 841 words.
Deliverable: Word Document