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Analyzing Data 9:57
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Research Paper Internet Library Regression is a special application of inferential statistics.
Regression Analysis 3:21 Correlation Analysis 0:47
Ranking Data 2:46
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Hypothesis Testing is a logical approach to inferential statistics.
What is a PValue? 5:56
A PValue Example 9:08

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MiniTab^{TM} Practice Set Instructions and Answers
Minitab^{TM} Generic Instructions may also be helpful to new users. Special Note:These instructions were prepared for use with MINITAB 11.
People using
3) Data sets for all problems are in our
Excel Statistics Book 
Part I Descriptive Statistics 
Problem I message: MINITAB will do an array. Find the appropriate number of
classes for
Those using Quick's worksheet should load Mini006
by choosing File and Open Worksheet.
Others must create a worksheet for CD Sales. You may want to review creating a data file on page 1 of Quick Start for MINITAB located at http://businessbookmall.com. I named my data file Mini006 for the software being used and the problem page number. The worksheet must also contain an Array variable to be filled in later. All MINITAB users should choose Manip and Sort. Highlight CD Sales and use Select to copy it into the Sort column(s) box. Put the cursor in the Store sorted column(s) in box, highlight Array, and use Select to copy Array into said box. Repeat this process to copy CD Sales into the Sort by column box and choose OK. See page PS 6 and 7 for the answer.Problem II message: We will do a frequency distribution similar to the one on page PS 6 of Quick. Those using Quick's worksheets should load worksheet Mini006. Others must add to their page 6 worksheet by adding a Group variable containing frequencies 1, 2, 5, 2, and 1. All MINITAB users should choose Stat, Tables, and Tally. Copy CD Sales and Group into the Variables box using Select. This may also be done by double clicking on each variable. Check all the items under Display, and choose OK. Both grouped and ungrouped Frequency Distributions appear. Some of these questions must be done by hand. All MINITAB users should choose Graphs and Histogram. Double click on CD Sales and use Select to copy it into the Graph variables box. Choose Options and accept the default Frequency. Other charts should be viewed later. Check Cut Point. Check Midpoint/cutpoint positions under Definition of Interval and enter 5 10 15 20 25 30 in the box. Each number should be separated by a space. Choose OK twice. Using Graphs is easy. To save the current graph choose File and Save Window As. Type Mini006a in the File name box and MINITAB will add mgf as an extension. The file Mini006a.mgf will be stored on the A drive. This file can be used by choosing File and Open Graph. To print an open graph choose File and Print Window. Print Setup is located under File of the main menu. 
Chapters 3 and 4 Measuring Central Tendency and Dispersion of Ungrouped Data Problems message: MINITAB will calculate many of these statistics. Those using Quick's worksheets should load Mini006 by choosing File and Open Worksheet. Load by double clicking on Mini006.Others should load their page 6 worksheet. All MINITAB users should choose Stat, Basic Statistics, and Descriptive Statistics. Highlight CD Sales and use select to copy it into the variables box. Choose OK. Quick Notes Statistics has or will explore many of these statistics. To calculate percentiles choose Graph and Probability Plots. Highlight CD Sales and use Select to copy it into Variables. Choose OK. Chapter 3 answers: 1A) 17 4) 16 7A) 14 7B) 21 7D) 18.4 7E) 26.1 Do others by hand. Chapter 4 answers: 1D) 5.53 Do other problems by hand. Saving work from a Session requires choosing File and Save Window As. Give your session a logical name like Mini006 in the File name box. Accept the extension default TXT and choose Save. To print an active session choose File, Print Window, and OK.
To use a saved session (text file) choose File, Open Worksheet, and Drive A:. 
Chapters 5 and 6 Measuring Central Tendency and Dispersion of Grouped Data Chapters 5 and 6 problems are very similar to those of chapters 3 and 4. These MINITAB Practice Set Instructions and Answers will explore only the ungrouped practice sets of chapters 3 and 4. 
Part II answers begin on page PS 42 and 43 of Quick. Expect minor rounding differences between Quick answers and MINITAB answers. 
Chapter 7 and 8 on Understanding Probability

Chapter 9 Discrete Probability Distributions Problem I message: These problems should be done by hand.
Problem II, III, and IV message: MINITAB will do calculations concerning Those using Quick's worksheets should load Mini054 by choosing File and Open Worksheet. Double click on Mini054.
Others must create a worksheet with 6 variables.
Name the variables Question 2 Data, Answer 2, Question 3 Data, Answer 3,
Question 4A Data, Answer 4A, Question 4B Data, Answer 4B,
All MINITAB users should choose Calc, Probability Distributions,
and Binomial. Accept the Problem V message: MINITAB will do calculations concerning Poison Probability Distributions. Those using Quick's worksheets should load Mini054 by choosing File and Open Worksheet. Others must create a
worksheet for page 55 information. Use 6 variables, 3 for questions and All MINITAB users should follow the procedures outline for the Binomial calculations. For question 5c, try using Cumulative probability. Problem VI message: This problem requires calculating the population mean. It equals np = (1,500)(.003) = 3. To complete the question, follow the procedures outline for questions IIV. 
Chapter 10 Continuous Normal Probability Distributions Problem I message: MINITAB will calculate probabilities associated with a normal distribution. The probability calculated will be from origin to some value on the x axis. This is different from a Z table which gives the probability from the mean to some value on the x axis. Those using Quick's worksheets should load Mini062 by choosing File and Open Worksheet. Others must create a worksheet with 2 variables. Name the first variable Question 1 Data and the other Answers 1. Insert all the parameters from question 1(ad) into the question 1 data column.
All MINITAB users should choose Calc, Probability Distributions, and Normal. Problem II and III message: These problems should be done by hand. 
Chapter 11 on Sampling and the Sampling Distribution of the Means Problem I message: MINITAB will calculate a confidence interval for the mean of a sampling distribution. Those using Quick's worksheets should load Mini068 by choosing File and Open Worksheet. Double click on Mini068. Others must create a worksheet for the variable part size. You may want to review creating a worksheet from page 1 of Quick Start for MINITAB located at http://businessbookmall.com. I named my variable "Weight". Create a data file using 36 rows and 1 column. I named my data file Mini068 for the software being used and the problem page number. All MINITAB users should select Stat, Basic Statistics, and 1Sample z. Double click on Weight to copy the file into the Variables box. Be sure the Level under Confidence interval is set to 99. Set Sigma (the standard deviation) to .065 and choose OK. Problem II message: Redo problem I with a 95% confidence interval. Problem III message: Answer this problem by hand. 
Chapter 12 on Sampling Distributions Part II Problem I message: This problem can be answered by following Practice Set 11 instructions. Those using Quick's worksheets should load Mini072 by choosing File and Open Worksheet. Others must create a worksheet for page 72. Data entered should consist of a 1 for passed and a 0 for failed. All MINITAB users should select Stat, Basic Statistics, and 1Sample z. Double click on Parts Passing to copy the file into the Variables box. Be sure the Level under Confidence interval is set to 99. Set Sigma to .3 and choose OK. Problem II, III, and IV message: Answer these problems by hand. 

Chapter 13 on Large Sample Hypothesis Testing Problem I message: This is a one sample mean test. Those using Quick's worksheets should load Mini068. Others should load their page 68 worksheet. All MINITAB users should select Stat, Basic Statistics, and 1Sample z. Double click on Weights to copy the file into the Variables box. Choose the Test Mean bull'seye and set the mean to 30. Set the Alternative (Hypothesis) to greater than and sigma to .0653. Note: the problem's sigma of .065 was rounded. Choose OK. MINITAB's answer of 2.32 is slightly different because Quick rounded the mean and sigma. The zvalue of 2.32 is not beyond 2.33 (it is less than 2.33) and H_{0} is accepted. Parts are not too heavy. Note: I use the term beyond to indicate further from H_{0} , the hypothesized population parameter. Problem II message: If a 1tail test is accepted then the 2tail test must be accepted. Here, z = 2.32 < 2.58 and H_{0} is accepted. Problem III message: Redo problem II with the new level of significance. Here z = 2.32 > 1.96 and H_{0} is rejected. 
Chapter 14 on Large Sample Hypothesis Testing Part II Problem I message: This problem tests the difference between 2 independent means. Those using Quick's worksheets should load Mini090. Others should create a worksheet with 70 rows and 2 columns (variables). In the first data variable column entitled Delivery Days enter the data for Supplier A and then the data for Supplier B. In the second source variable column entitled Supplier, enter a 0 next to Supplier A's data and a 1 next to Supplier B's data. All MINITAB users should select Stat, Basic Statistics, and 2 Samples t. Put the cursor in the box next to Samples and double click on Delivery Days. Double click on Supplier. Set the Alternative (Hypothesis) to not equal. Do not choose Assume equal variances and choose OK. The test statistic t (z) of 1.32 is not beyond 1.96 (it is greater than 1.96), the critical value of t (z), accept H_{0}. Delivery times are the same. 
These instructions are provided complements of http://businessbookmall.com. 
Problem II message: MINITAB calculates z and p simultaneously.
We must redo the chapter 13 test and look for the p value.
Those using Quick's worksheets should load Mini068. Others will need to load their page 68 worksheet. All MINITAB users should select Stat, Basic Statistics, and 1Sample z. Double click on Weight to copy the file into the Variables box. Choose the Test Mean bull's eye and set the mean to 30. Set Alternative (Hypothesis) to greater than and sigma to .0653. Note: the problem's sigma of .065 was rounded. Choose OK. P = .010 and H_{0} is barely accepted. Problem III message: Answer this problem by hand. 
Chapter 15 on Hypothesis Testing of Population Proportions Problem I message: The population proportion is a type of mean so these problems use the onesample mean test described by chapter 13 directions. Those using Quick's worksheets should load Mini096. Others should create a worksheet using 1 for those who passed and 0 for those who failed. All MINITAB users should select Stat, Basic Statistics, and 1Sample z. Double click on Passed to copy the file into the Variables box. Choose the Test Mean bull's eye and set the mean to .86. Set the Alternative (Hypothesis) to greater than and sigma to the square root of pq which is .347. Choose OK. A z value of .82 and p value of .21 both result in accepting H_{0}, the proportion of parts passing inspection has not increased. Problem II message: This is a 2 sample proportion test similar to those explored in chapter 14. Those using Quick's worksheets should load Mini096. Others should create a worksheet with 200 rows and 2 columns(variables). In the first column entitled Defects, enter the data for the day shift and then the data for the night shift. Enter a 0 for passes and a 1 for failed. For the source variable named Shift, enter a 0 for day shift data and a 1 for night shift data. All MINITAB users should select Stat, Basic Statistics, and 2 Samples t. Put the cursor in the box next to Samples and double click on Defects. Double click on Shift. Set the Alternative (Hypothesis) to not equal. Choose Assume equal variances and OK. MINITAB has a t value of 2.19 and Quick has a z value of 2.20. H _{0} is accepted, shift defects are the same. 
Chapter 16 on Small Sample Hypothesis Testing Using Student's t Test Problem I message: This is an analysis of 2 independent means. It is similar to problems done earlier. Those using Quick's worksheets should load Mini100. Others should create a worksheet containing both a data variable and a source variable using procedures discussed earlier. All MINITAB users should run a 2Sample t test using Practice Set 14 procedures. Do not assume equal variances. MINITAB's t of 4.16 and p = 0.0005 results in a rejection of H _{0}, sick days taken were not the same. Problem II message: This is a paired difference test. Those using Quick's data files should load Mini100. Others should add 3 variables to their page 100 worksheet, one for the efficiency before training, one for the efficiency after training, and one to store the difference. Be sure to match each employee with their before and after efficiency rating. All MINITAB users may use the MINITAB calculator to calculate the difference between employee efficiency before and after training. Choose Calc and Calculator. Use Select to copy Difference into the Store results in variable. Highlight Before and use Select to copy it into the Expression box. Choose the calculator subtraction sign. Highlight After and use Select to copy it into the Expression box. Choose OK. Choose Stat, Basic Statistics, and 1 Sample t. Double click on Difference. Choose Test mean and leave it at 0.0. Set Alternative (Hypothesis) to less than and choose OK. H_{0} is rejected because p = .0014 < .01. Training increased efficiency. 
Chapter 17 on Statistical Quality Control 
Problem I message: This is a Quality Control problem.
Those using Quick's worksheets should load Mini104. Others should create a page 104 worksheet with a 36 row variable named Weight and a source variable named Sample Number. Each sample number will be entered 3 times. All MINITAB users should choose Stat, Control Charts, and XbarR. Double click on Weight to copy it into the Single column and double click on Sample Number to copy it into Subgroup size. Choose OK. See page PS 104 for the answer. Problem II message: As defined, this problem can not be done with MINITAB. Actual data is needed. 
Chapter 18 on Analysis of Variance 
Problem I message:
This twosample analysis of the variance should be done by hand.
Those using Quick's worksheets should load Mini110. Others should create a 2 variables worksheet for page 110. One variable is for Weight data and one for Department. All MINITAB users should select Stat, ANOVA, and Oneway. Copy Weight into Response with a double click. Copy Department into Factor with a double click. Choose OK. MINITAB and Quick's answers differ because of rounding. H_{0}is rejected because p = .002 < .05. Part mean weights are not equal. 
Chapter 19 on TwoFactor Analysis of Variance 
Problem I message: This is a twoway analysis of variance (ANOVA). Those using Quick's worksheet should load Mini116.
Others should create a 3 variable file
containing data on Weight, Department, and Time.
When doing time, be sure to match each time with the
appropriate department and weight.
Problem II message: Do this problem by hand and see page PS 117 for the answer. 
Chapter 20 on Nonparametric Hypothesis Testing of Nominal Data 
Problem I message: This nonparametric test using ChiSquare should be done by hand.
Those using Quick's data worksheets should load Mini122. Others should create a 2 variable worksheet to store the data presented in the problem table. The first variable entitled Younger contains 24 and 16. The second entitled Older contains 12 and 8. All MINITAB users should select Stat, Tables, and Chisquare Test. Copy both variables (Younger2 and Older2) into Columns containing the table box and choose OK. Chi square is zero and H_{0} is accepted. Making a sale and age are independent. Chi square is zero because the buying percentage of each part of the population (60%) exactly equals the buying percentage of entire population (60%). 
Chapter 21 on Nonparametric Hypothesis Testing of Ordinal Data Part I Problem I message: This is a run rest to determine randomness. Problem data was first presented on page 68. Those using Quick's worksheets should load Mini68. Others should load their page 68 data file. All MINITAB users should select Stat, Nonparametrics, and Runs Test. Double click on Weight. Check the bull's eye next to Above and below and insert the median of 30.045. Choose OK. Using different methods, both MINITAB and Quick accept the null hypothesis that parts were drawn at random. Problem II message: This is a one sample sign test of the median. Those using Quick's worksheets should load Mini128. Others should create a one variable worksheet for the page 128 median data. All MINITAB users should select Stat, Nonparametrics, and 1Sample Sign. Double click on Median. Check the bull's eye next to Test median and insert the median of 5. Set Alternative (hypothesis) to greater than and choose OK. P of .1094 is greater than .05 and the null hypothesis is accepted. The median has not increased. Problem III This is a two sample medians test. Those using Quick's worksheets should load Mini128. Others should create a data file with 2 variables, one for sick days taken by graduates and the other for sick days of nongraduates. All MINITAB users should select Stat, Nonparametrics, and MannWhitney. Double click on Graduates and then Nongraduates. Set Alternative to not equal and choose OK. Reject H_{0} as .0013 < .01. Median sick days differ. Note: z of 3.23 in Quick's answer leads to a pvalue of .0013. 
Chapter 22 on Nonparametric Hypothesis Testing of Ordinal Data Part II 
Problem I message: This paired sample (difference) test of the median should be done by hand. Problem II message: This is a KruskalWallis test of several medians. Those using Quick's worksheets should load Mini133. Others should add 2 variables to their page 133 worksheet, one for Median Weight listed by departments and a second for Departments 13. All MINITAB users should select Stat, Nonparametrics, and KruskalWallis. Copy Median Weight into the Response box and Department into the Factor box. Choose OK. H_{0} is rejected because 10.36 > 9.21 or because .006 is < .01. The medians are not equal. 

Chapter 23 on Correlation 
Problem I message: MINITAB will calculate the coefficient of correlation. Those using Quick's worksheets should load Mini148. Others should create a data file with 2 variables. The first should contain employee ages and the second employee sales. All MINITAB users should select Stat, Basic Statistics and Correlation. Load Hours and Grades and choose OK. r = .908 Other questions should be done by hand. Answers are on page PS 148. 
Chapter 24 on Regression Analysis 
Problem I message: MINITAB will calculate the regression equation. Those using Quick's worksheets should load Mini148. Others should load their page 148 worksheet. All MINITAB users should choose Stat, Regression, and Fitted line plot. Copy Sales into the Response(y) box and Age into the Predictor(x) box. Choose OK. y = 55.9425  1.07471x and RSq = .824 Other questions should be done by hand. Answers are on page PS 154. 
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