Special Note: Quick instructions were prepared for use with MINITAB 11.

MiniTab Tutorials  may also be helpful to new users.

Data sets for all problems are in our Excel Statistics Book which may be transferred to most statistics  software. Use aprilblackie to load data.

Return to Statistics Internet Library  Updated 4/15/18   Please link to, use to educate and   

Practice Sets   See Statistics Book has pdf- Version of Practice Sets

Problem I message: MINITAB will do an array. Find the appropriate number of classes for
question 2 frequency distribution by hand.

Those using Quick's worksheet should load Mini006 by choosing File and Open Worksheet.
Use the down arrow next to the Look in box to locate and click on A:. Double click on Datamini.
Load the page 6 data by double clicking on Mini006.

Others must create a worksheet for CD Sales. 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.

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.

Problems message: MINITAB will calculate many of these statistics.

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:.
Use the scroll bar next to List Files of type to choose Text. Double click on Mini006.

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.

Problem I message: These problems should be done by hand.

Problem II, III, and IV message: MINITAB will do calculations concerning
Binomial Probability Distributions. MINITAB probability distributions are more exact (not rounded) than Quick's. As a result, MINITAB answers will differ from Quick answers.

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(a-d) into the question 1 data column.

All MINITAB users should choose Calc, Probability Distributions, and Normal.
Choose Cumulative probability, tab to the Mean, and insert 25000. Tab to Standard deviation and insert 5000. Tab twice to the Input variable box, highlight Question 1 Data, and choose Select to copy it into the Inputs columns box. Highlight Answers 1 and use Select to copy it into the Optional storage box. Choose OK.

Problem II and III message: These problems should be done by hand.

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 1-Sample 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 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 1-Sample 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.

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 1-Sample z. Double click on Weights to copy the file into the Variables box. Choose the Test Mean bull's-eye 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 z-value of 2.32 is not beyond 2.33 (it is less than 2.33) and H₀ is accepted. Parts are not too heavy.

Note: I use the term beyond to indicate further from H₀ , the hypothesized population parameter.

Problem II message: If a 1-tail test is accepted then the 2-tail test must be accepted. Here, z = 2.32 < 2.58 and H₀ is accepted.

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 H₀. Delivery times are the same.

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 1-Sample 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 H₀ is barely accepted.

Problem III message: Answer this problem by hand.

Problem I message: The population proportion is a type of mean so these problems use the one-sample 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 1-Sample 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 H₀, 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.

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 2-Sample 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. H₀ is rejected because p = .0014 < .01. Training increased efficiency.

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 Xbar-R. 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.

Problem II message: This is a one-way analysis of variance (ANOVA).

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. H₀is rejected because p = .002 < .05. Part mean weights are not equal.

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.

All MINITAB users should select Stat, ANOVA, and Twoway. Double click Weight into Response, Department into Row factor, and Time into Column factor. Choose OK. MINITAB provides the data needed to calculate F. See page PS 116 for the answer.

Problem II message: Do this problem by hand and see page PS 117 for the answer.

Problem II message: This problem emphasizes the concept of statistical independence.

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 H₀ 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%).

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 1-Sample 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 non-graduates.

All MINITAB users should select Stat, Nonparametrics, and Mann-Whitney. Double click on Graduates and then Non-graduates. Set Alternative to not equal and choose OK. Reject H₀ as .0013 < .01. Median sick days differ. Note: z of 3.23 in Quick's answer leads to a p-value of .0013.

Problem II message: This is a Kruskal-Wallis 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 1-3.

All MINITAB users should select Stat, Nonparametrics, and Kruskal-Wallis. Copy Median Weight into the Response box and Department into the Factor box. Choose OK. H₀ is rejected because 10.36 > 9.21 or because .006 is < .01. The medians are not equal.

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.

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 R-Sq = .824 Other questions should be done by hand. Answers are on page PS 154.

Note: When Quick Questions can not be done with MINITAB and should be done by hand, reference has been made to the page in Quick containing the solution to the question.

Note: Problems that should be done by hand are so marked. Answers to these problems begin on page T 35 near the end of Quick Notes Statistics.

5) Cut points of 50, 60, 70, 80, and 90 results in a Histogram similar to the one on page T 36-37.

Follow similar procedures to do the other graphs.

6) Mean = 7, Median = 6, and SD = 4.34 Answer other questions by hand.

2-10) Do by hand.

11A) .7351 11B) Inserting 1 and choosing cumulative probability yields .9672 and 1 - .9672 = .0328

11C) Inserting 0 to 6 gives the distribution located on page ST 1 of Quick Notes. 11D) .0305

12A) Inserting 1 and using cumulative probability yields .0916 12B) Inserting 0 to 15 yields the page ST 2 table which may be used to draw the page T 80-81 graph.

13) See page T 82 for answers to these questions.

14) See page T 82 for answers to these questions.

15) A 1-Sample z test under Basic Statistics of Stat yields a range of 6.914 to 8.286.

16A) Using a 1-Sample z test under Basic Statistics of Stat and a Sigma of .4583 yields a range of .5934 to .8066. 16B) Do by hand.

2) Set sigma to .4, the square root of pq. z = -1.77 and p = .039 < .05, reject the Null Hypothesis, the mean is not greater than or equal to 80%. Too bad, no chocolate flavored shaving cream.

3) Chi square of 8.4 and p = .015 < .05, reject the Null Hypothesis, supplier and defects are dependent.

4) t = -4.24 and p = .0120 < .05, reject the Null Hypothesis, sales performance improved.

5) t = 2.97 and p = .0039 < .05, reject the Null Hypothesis, mean service time at these stores is not the same.

6) t = - 4.0 and p = .0006 < .01, reject the Null Hypothesis, assembly time has gone down.

7) This problem should be done by hand.

8) This problem should be done by hand.

9A) F = 5.77 and p = .024 < .05, reject the Null Hypothesis, the mean time to assemble computer parts is not equal for these three departments. 9B) Do by hand.

10) p = .1310 > .01, accept the Null Hypothesis, assembly times are equal.

11) Chi square = 11.23 and p = .004 < .01, reject the Null Hypothesis, median assembly times for these three methods are not equal.

12) MINITAB control charts look very similar to those on page T 145.

13) Do this problem by hand.

3A) .885 3B) 78.4% Do second part by hand. 3C) Do by hand.

4) See page T 160.

5) The MINITAB fitted line plot graph is similar to the graph on page T 160.

6A) y = 13.5 + 6.54 x 6B) Do by hand. 6C) The MINITAB fitted line plot graph is similar to the graph on page T 160. 6D and E) Do by hand.

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