PROJECT OPTION til:

Data file: DeliveryTimes-5518.xlsx

NOTE: Use a = 0.05 as the significance level

Scenario:

A manufacturer called Lukey Industries is facing a choice between two suppliers for a part:

Jellystone Manufacturing and Wallston Incorporated. The timing of delivery of these parts is a

primary concern, because the parts are needed at a crucial bottleneck in the manufacturer’s

process. In choosing a supplier, Lukey Industries has a couple of criteria in mind: speed and

reliability of deliveries. First, Lukey would like to choose the supplier with the fastest delivery

time. However, if both Jellystone and Wallston have similar delivery times, then Lukey would

like to choose the one with the most consistent delivery times.

Lukey Industries has hired you as a consultant to perform a statistical analysis and prepare a

report to help them choose the best supplier.

To compare Jellystone Manufacturing and Wallston, Inc., you take two random, independent

samples of deliveries of the part, and measure the time it takes from order to delivery. There

are 150 deliveries total: 78 from Jellystone and 72 from Wallston. The delivery times, in hours,

are recorded in the attached Excel data file: DeliveryTimes-5518.xlsx

A Note on Formatting: Your report should have three main headings:

Introduction: Here you should explain what the analysis is and why you are performing

it. A few sentences are usually enough.

Analysis: Here you should present your statistical analysis, including any requested

hypotheses, tables, and interpretations or decisions. All technical material should go

here.

Conclusion: Here you should briefly summarize in plain language what your statistical

analysis showed, and make your recommendation based upon it. If follow-up questions

are asked in the directions, the answers to those should go here.

Directions:

1) When performing and presenting any statistical analysis, it is important for your audience to

understand the characteristics of your data. These characteristics are summarized using

descriptive statistics that measure central tendency and dispersion for each supplier. In this

case, those descriptive statistics should be: mean, median, variance, standard deviation,

minimum, maximum, and the sample size for each sample (Jellystone and Wallston).

In Excel: The descriptive statistics may be calculated using the Descriptive Statistics

procedure in Excel’s Data Analysis tool OR using the appropriate Excel functions. If you

use the Descriptive Statistics procedure, leave all the statistics in place in the Excel

sheet, and only include the requested values in the report. If you use Excel functions,

please leave them in place in the cells of your data sheet.

In the Report:

Include a single table with the numerical descriptive statistics in the rows and a

column for each supplier (Jellystone and Wallston). Only report the specific

descriptives requested in the directions above.

Comment on the similarities and differences between the two suppliers. Note:

numbers can be similar without being equal.

2) One concern when choosing a supplier is whether the average length of time to delivery is

different between the two suppliers. To test this, you should use the methods of Chapter 10 to

decide whether there is a difference between the population mean delivery times for Jellystone

and Wallston. Since you are using Chapter 10 methods, it will help greatly if you re-read the

relevant handouts.

In Excel: You must decide on the appropriate test for the difference between the two

population means.

In section 10.1, we learned a hypothesis test for the difference between two

population means when the population standard deviations are known; that

procedure is the z-Test: Two Sample for Means in Excel’s Data Analysis tool.

In section 10.2, we learned a hypothesis test for the difference between two

population means when the population standard deviations are unknown; that

procedure is the t-Test: Two-Sample Assuming Unequal Variances in Excel’s Data

Analysis tool.

Choose the appropriate test for this particular analysis and complete the analysis in

Excel (Note: the key question to answer is: are the standard deviations that you have

here characteristics of the populations, and known prior to sampling? or are they

sample standard deviations?). Step-by-step directions for each of these tests are at the

end of the respective sections in the book, and you can also look back at the MindTap

Excel activities for Chapter 10 to review the video tutorials.

In the Report

Include a brief description of the purpose of this test. Indicate which test you

chose to perform and explain your decision.

State your hypotheses.

Show the results of the test in a table. Only include the p-value and/or critical

value that you are actually using in the analysis.

Report the correct p-value for your hypotheses and indicate whether you reject

or fail to reject the null. You may choose to use the critical value approach for

this step, but whatever you decide to do, be sure to state the basis for rejecting

or failing to reject the null hypothesis.

Interpret the results of your hypothesis test in terms of the original question: do

your results indicate that there is a difference between the population mean

delivery times for the two suppliers, or not? If so, which one is faster?

3) Lukey Industries’ second concern is the variability of completion times: if neither supplier is

faster, then they would like to choose the more consistent and reliable supplier. (Remember, if

the variance of one supplier is lower, then that supplier has more consistent delivery times).

Test whether the variances of the delivery times for Jellystone and Wallston are different by

performing an equality of variances test, which we learned in section 11.2. The step-by-step

directions for Excel are at the end of that section, and you can review the Chapter 11 MindTap

Excel activities for video tutorials. Reviewing the Chapter 11 handouts on hypothesis tests for

two population variances will help a great deal.

0 In Excel: The test to compare two population variances is the F-Test Two-Sample for

Variances in the Excel Data Analysis tool. CAREFUL: This test automatically reports a

one-tailed p-value, so you must ask yourself: are you performing a one-tailed or a two-

tailed test? and act accordingly. Excel doesn’t know what you are doing or how you have

formulated your hypotheses, so be careful to use the results appropriately.

In the Report: Include a brief description of the purpose of this test.

State your hypotheses.

Show your results in a table. Only include the correct p-value and/or critical

value for this analysis in the table.

Report the correct p-value for your hypotheses and indicate whether you reject

or fail to reject the null. You may choose to use the critical value approach for

this step, but whatever you decide to do, be sure to state your basis for rejecting

or failing to reject the null hypothesis

Now that your test has shown whether or not the variances are different, look at

the sample variances to determine which method has the lower variance.

Interpret the results of your hypothesis test in terms of the original question: do

your results indicate that one supplier has a lower variance than the other?

Which supplier has the lower variance, if either of them do?

4) In the Report: Make a recommendation about which supplier Lukey Industries should

choose: Jellystone Manufacturing or Wallston Incorporated. This recommendation should refer

to the evidence from your statistical analysis.

What other steps might Lukey Industries take before making a decision about which supplier to

adopt? What other variables could be measured that might be helpful in making this decision?

Why? (Feel free to be creative here – there are many right answers)

Last Updated on February 11, 2019 by EssayPro