Reference no: EM13137313
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 a sample of 800 observations taken during a time in which that client's processes was operating satisfactorily. The sample standard deviation for these data was 0.21; hence, with so much data, the population standard deviation was assumed to be 0.21. Quality associates then suggested that random samples of size 30 be taken periodically to monitor the processes on an ongoing basis. By analyzing the new samples, the clients 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:
H o : μ is 12
H a: μ is not 12
Corrective action will be taken any time the null hypothesis is rejected.
The samples in the attached Excel file were collected at hourly intervals during the first day of operation of the new statistical process control procedure.
Managerial Report
1. Conduct a hypothesis test for each sample at the 0.01 level of significance and determine what action, if any should be taken. Provide a test statistic and p-value for each test. Make sure to present the results of the tests in table form.
2. Compute the standard deviation for each of the four samples. Does the assumption of 0.21 for the population standard deviation appear reasonable? Explain your answer briefly.
3. Compute the limits for the sample mean around μ =12 such that, as long as a new sample mean is within those limits, the process will be considered to be operating satisfactorily. If the sample mean exceeds the upper limit of of the sample mean is below the lower limit, corrective action will be taken. These limits are referred to as upper and lower control limits for the quality control purposes. Make sure to show me how you got your answers.
4. Discuss the implications of changing the level of significance to a larger value. What mistake or error could increase if the level of significance is increased? Any answer you give to this question must be explained, a simple answer is not worth anything.
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