Objectives

To demonstrate the ability to calculate descriptive statistics using an Excel spreadsheet. (CLO1)

To demonstrate the ability to use an Excel spreadsheet with data to engage in the hypothesis testing process. (CLO3)

To be able to use critical thinking when interpreting standard deviation across samples. (CLO4)

Pre-Homework Instructions:

I have provided you with additional data Excel data sets for you to practice with (Hyp Sigma Known; Hyp Sigma Unknown) along with screen based tutorials on Blackboard. Once you feel comfortable with using Excel to obtain the values needed, then complete the homework assignment by yourself, with a partner.

Case Study Homework Problem:

Quality Associates, Inc., a consulting firm, advises its clients about sampling and statistical procedures that can be used to control their manufacturing processes. In an 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 the sample size of 30should be taken randomly and periodically to monitor the quality process on an ongoing basis. By analyzing the new 4 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 Quality Associate two-tailed hypotheses are as follows:

If the null hypothesis is rejected, corrective action needs to be taken. Please download the Excel file (Quality), which has the data of the samples.

Answer the following questions:

1. Provide the values requested by both Sample 1 and Sample 2 using the Quality Excel data set
2. Conduct a hypothesis test for each of the two samples at the .01 level of significance (which is the 99% confidence level) and determine what action, if any should be taken (accept or reject the null hypothesis Provide the test statistic and p-value for each of the two tests in the two samples.).
3. Compute the standard deviation for each of the two samples. Does the assumption of .21 for the population standard deviation appear reasonable, or does it approximate near this value number? Why or why not?
4. Discuss the implications of changing the level of significance or alpha value to a larger value. What type of error could increase if the level of significance or alpha value is increased? Explain.

Notes:

1. Upon completing the assignment, make sure to submit it via Blackboard's Drop Box by 11:59pm by next Wednesday by 11:59PM.

1. For question 1, make sure to get the following, with codes that you would need to adapt to the homework problem, but please review the tutorial video, they also appear there:
   1. Sum of Sample =SUM (A#:A#)
   2. Sample size =COUNT(A#:A#)
   3. Mean = AVERAGE (A#:A#)
   4. Standard deviation = STDEV.S(A#:A#)
   5. Level of significance (alpha) given by the problem
   6. Critical value (lower tail) = + Za/2 decimal value at the % of confidence
   7. Critical value (upper tail) = - Za/2 decimal value at the % of confidence
   8. Hypothesized value given by the problem
   9. Standard error = standard deviation/SQRT(sample size)
   10. Test statistic = (sample mean - hypothesized population mean value) / standard error)
   11. p-value (lower tail) = NORMDIST(test z statistic)

OR =NORM.S.DIST(test z statistic,TRUE)

1. p-value (upper tail) =1- p-value lower tail
   1. p-value (two tail) =2*MIN(lower tail p, upper tail p)

*You may also provide descriptive data values (for a-c), but note that you still need d-j.*

Show the formulas as well