Mini Tab Workbook

8/3/2019 Mini Tab Workbook

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Student Guide to Minitab 15

Accompanies videos found at

http://student.ccbcmd.edu/elmo/math141s/Minitab/minitab.htm

Written by Donna TupperDepartment of MathematicsCCBC-EssexCopyright 2008

For Math 153 Introduction to StatisticalMethods


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Getting Started in Minitab 15

When you open Minitab 15, you will have three windows, a Session Window, a Worksheet Window anda Project Window.


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The Session Window displays a text output of any statistical analysis you have done.

The Worksheet or Data Window is where you will enter all of your data. This is a spreadsheet similar towhat you see in Excel or Access.

The Project Window is minimized when you first open Minitab. This windowcontains folders that enable you to manage your project.

If you are working with raw data, you will enter your data in the Worksheet window. In the examplebelow, we will enter the data for the Dow Jones Industrial Average for the week ending September 19,2008.

The data set consist of

10917.15, 11059.02, 10609.66, 11019.69 and 11388.44


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Here the data was rounded to one decimal place, but money needs to be rounded to two decimalplaces. To change the data formatting, from the menu bar, select EDITOR >> FORMAT COLUMN >>NUMERIC.

Since we want to format for money, under Category: select the radio button next to Currency. Changethe number of decimal places to 2 and hit OK.


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The data will now look like

Creating a Histogram using Minitab 15

EXAMPLE: Create a frequency table and then histogram in Minitab version 15 using the runs scored bythe 2003 Baltimore Orioles.

The formula for the class width is the (largest data value - smallest data value) / (number of classes)

The formula for the class midpoint is (lower class limit + upper class limit) / 2

Our first step will be to enter all of the runs scored by the 2003 Baltimore. The data was found athttp://www.usatoday.com/sports/baseball/sba/sba03team.htm. The entire data set is

1, 68, 43, 70, 32, 75, 80, 28, 25, 65, 8, 26, 7, 61, 6, 22, 76, 5, 3, 3, 21, 2, 14, 4

Enter the data in column C1. Make sure the arrow in the upper left corner of the screen (called theEntry Direction Key) is pointing downward.

Place your cursor above row 1. This will enable us to label our columns. Label column C1 as Runs, C5 asLower, C6 as Upper, C7 as Tally and C8 as midpoint.

Your Minitab worksheet should resemble the one below.


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To make working with your data easier, it might help to SORT the data. To sort data in Minitab, from themenu bar select DATA >> SORT.

You will be presented with the dialog box below. In the Sort column(s ): box, enter C1. In the Bycolumn : box, again select C1. Under Store sorted data in: select Original columns(s) . That will putyour sorted data back into column C1.


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Now we will create the frequency table by hand. We will use 7 classes. First, we need to determine theclass width. Using the formula

class width = = 12 when rounded up.

Starting with the smallest data element (or a number slightly smaller if it is more convenient), we willadd our class width to get the next lower class limit. Keep going until you have all seven lower classlimits.

The lower class limits are 0, 12, 24, 36, 48, 60 and 72.

Now we see our corresponding upper class limits are 11, 23, 35, 47, 59, 71 and 83.

Lower ClassLimit

Upper ClassLimit

Tally (orFrequency)

0 11


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12 23

24 35

36 47

48 59

60 71

72 83

The next step is to count the number of batters who scored between 0 and 11 runs. Here, we have 9batters. There were 3 batters who scored between 12 and 23 runs. Similarly we have 4 batters whoscored between 24 and 35 runs, 1 between 36 and 47, 0 between 48 and 59, 4 between 60 and 71 and

finally 3 between 72 and 83 runs scored.

Lower ClassLimit

Upper ClassLimit

Tally (orFrequency)

0 11 9

12 23 3

24 35 4

36 47 1

48 59 0

60 71 4

72 83 3


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In order to create a histogram in Minitab which is representative of our frequency table, we need to usethe class midpoints (also called the class marks). The formula for the class mark is

class mark = = 5.5

Although you can calculate the class mark for each class individually, you can also simply add the classwidth to the first class mark to get each consecutive class mark. This gives us

Class Marks Tally (orFrequency)

5.5 9

17.5 3

29.5 4

41.5 1

53.5 0

65.5 4

77.5 3

Creating a Histogram in Minitab

To create the histogram in Minitab, from the menu bar, select GRAPH >> HISTOGRAM.


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You will see the dialog box below.

Select the Simple histogram and click on OK. You will next see the dialog box below.


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Since the data we want to graph is in C1, the RUNS column, in the Graph variables : box, select Runsand click on OK.

You will have a histogram like the one below.

The problem here is that the histogram doesnt match the frequency table. To fix that, RIGHT click onthe histogram. Each bar should be highlighted with little squares around the top.


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You should get the dialog box below. Select EDIT BARS.

Within the Edit Bars dialog box, click on the Binning tab. Under Interval Type , select Midpoint. Underthe Interval Definition box, click the radio button next to Midpoint/Cutpoint positions: In the boxbelow, enter each of the class marks, separated by a space. When you are done, click OK.


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You should now have the histogram below, which is a graphical representation of our frequency table.

Calculating Descriptive Statistics in Minitab

To determine the mean, median, standard deviation and other descriptive statistics, from the menu bar,select STAT >> BASIC STATISTICS >> DISPLAY DESCRIPTIVE STATISTICS.

You will need to fill in the dialog box on the next page.


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Since the data is in C1, enter C1 in the Variables: box. To see the different descriptive statistics youcan calculate, click on the Statistics button.


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When you are done, click OK. The results will appear in the Session window.

Creating a Binomial Probability Distribution Table

EXAMPLE: The probability of cheating in an elementary statistic class is 35%. Create a probability

distribution table for a class of 10 students.

Here, the probability of success is 0.35, the value of our sample size n is 10 and the possible values of x,which represents the number of successes, are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10.

Label column C1 x and column C 2 P(x).

In rows 1 through 11, enter the numbers 0 through 10.

From the menu bar, select CALC >> PROBABILITY DISTRIBUTION >> BINOMIAL.


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You will get the dialog box on the next page. Click the radio button next to Probability. Next toNumber of trials, enter 10 (our value of n). Next to Event probability, enter our value of p, which is

0.35. Click the radio button next to Input column:, enter x (or C1). Next to Optional storage:, enterP(x), (or C2). When your dialog box looks like the one on the next page, click on the OK button.


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The result is the binomial probability distribution table, shown below, will appear in your WorksheetWindow.


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Confidence Intervals of 1 Population Proportion

EXAMPLE: Consumer Reports magazine recently conducted a study of retired readers of their magazine.In a study of 6723 retired readers of the magazine, 4505 of them participated in a 401(k) or 403(b) planthrough their employer. Construct a 99% confidence interval for the true population proportion of Consumer Reports retired readers that participated in their employers 401(k) or 403(b) plan.

From the menu bar select STAT >> BASIC STATISTICS >> 1 PROPORTION

You will be presented with the dialog box on the next page.


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Minitab uses a 95% confidence interval as a default. If you need to change the significance level, click onthe Options button.

Simply change the Confidence level from 95.0 to the desired significance level of 99.0. Click on the

box next t o Use test and interval based on normal distribution and click on OK.


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Click on OK from the 1 Proportion Test and Confidence Interval dialog box. In the session window, youwill see

We can say with 99% confidence that the population proportion of retired readers of Consumer Reportsmagazine who participated in their 401(k) or 403(b) plans is somewhere between 65.5% and 68.4%.

Confidence Intervals of 1 Population Mean - SummaryData

EXAMPLE: New cans of a leading brand of soda state that the volume contained in each can is 12 oz.After testing 25 cans, the mean volume per can was 11.98 oz. with a standard deviation of 0.21 oz.Construct a 95% confidence interval for the true population mean volume of soda per can.

From the menu bar, select STAT >> BASIC STATISTICS >> 1 SAMPLE T


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In our example, n = 25, x- bar = 11.98 and s = 0.21. Click on the radio button labeled Summarized data .Enter the sample size, mean and standard deviation in the appropriate boxes.


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If you need to change the confide nce level, click on the Options box, change the Confidence level tothe confidence level given in the question and then click OK.

Since we want a 95% confidence interval, we can leave this alone. Simply click on the OK button fromthe 1 Sample t (Test and Confidence Interval) box. In the Session Window, the confidence interval will

appear.

We can say with 95% confidence that the true mean that the mean volume of soda in the cans labeled12 oz. is between 11.9 oz and 12.1 oz.


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Confidence Intervals of 1 Population Mean - Raw Data

EXAMPLE: The body temperatures of 30 healthy, randomly selected CCBC students are recorded in thetable below. Construct a 99% confidence interval for the true population mean temperature of all CCBCstudents.

97.6 99.1 98.6 98.8 97.3 98.3 99.9 99.2 98.6 98.9

98.8 98.2 98.4 99.6 99.3 98.6 98.4 98.2 99.5 99.4

99.0 99.0 98.2 98.7 98.5 97.9 97.6 98.3 99.0 98.2

First, we need to enter the raw data in the table into column C1 of Minitab. Then from the menu bar,

select STAT >> BASIC STATISTICS >> 1 SAMPLE T.

In the 1- Sample T (Test and Confidence Interval) box, click on the radio button labeled Samples in

columns , enter c1.


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Since we need to change the confidence level from 95% to 99%, click on the Options button.

Click on the OK button in 1-Sample t Options, and then click on OK in the 1-Sample T (Test andConfidence Interval) box. The confidence interval will appear in the Sessions Window.


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We can say with 99% confidence that the true mean temperature of all healthy CCBC students lies

between to .

Hypothesis Test of 1 Population Proportion

EXAMPLE: A recent study of 6723 retired readers of Consumer Reports Magazine found that 2555 of them had owned mutual funds outside of a retirement account. At the .05 level of significance, test theclaim that less than 40% of the retired readers of Consumer Reports magazine owned mutual fundsoutside of their retirement accounts.

This question asks us to conduct a hypothesis test for a population proportion. In order to set up andform a well-worded conclusion, it steps below might help walk you through the problem. Circle yourchoice to each of the first three questions and then use the flow chart to word your conclusion.

Claim is: H o OR H1 P-Value is less than significance level: yes OR noReject H o OR Fail to Reject H o Use Flow Chart For Conclusion

The steps for using Minitab to find your p-value and/or test statistic are nearly identical to the steps forfinding a confidence interval. The only change is that you need to tell Minitab that you also want to do ahypothesis test and fill in the options box for with the significance level and symbol for the alternatehypothesis.


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From the menu bar, select STAT >> BASIC STATISTICS >> 1 PROPORTION

You will be presented with the dialog box on the next page. Click on the radio button labeledSummarized data. The Number of Events: is what we call our number of successes, and usual labelwith the variable x. In this example, x = 2555. The Number of Trials: is what we call our sample size, n.In this example, n = 6723.

The difference between a confidence interval and a hypothesis test in Minitab is that you need to click

on the checkbox that as k you to Perform hypothesis test. In the box below, labeled Hypothesizedproportion: enter the value of your population proportion p. Here p = .40.

As with confidence intervals, Minitab uses .05 as the default significance level, which makes theconfidence level 95%. The default for the alternate hypothesis is not equal. If you need a differentsignificance level or have a different alternate hypothesis, you will need to click on the Option buttonand enter the appropriate confidence level and/or alternate hypothesis. Here, our claim is the alternatehypothesis, that p is less than 40%. Click on the select list arrow and choose less than. Then check theUse test and interval based on normal distribution checkbox and click OK. The completed 1Proportion Options dialog box is on the next page.


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The completed 1 Proportion (Test and Confidence Interval) dialog box is below.

When you are done, click OK. Your test statistic and p-value will appear in the Sessions Window.


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Since our p-value is 0.000 (and our test statistic is z = -3.34), we reject Ho. Since our claim is H1 and wereject Ho, our conclusion is that the data supports the claim that less than 40% of the retired readers of Consumer Reports magazine owned mutual funds outside of their retirement accounts.

Hypothesis Test of 1 Population Mean - Raw Data

The body temperatures of 30 healthy, randomly selected CCBC students are recorded in the tablebelow. It is commonly believed that the mean body temperature of all healthy adults is 98.6 o. At the0.01 level of significance, test the claim that the mean body temperature of all healthy CCBC students is98.6 oF.

97.6 99.1 98.6 98.8 97.3 98.3 99.9 99.2 98.6 98.9

98.8 98.2 98.4 99.6 99.3 98.6 98.4 98.2 99.5 99.4

99.0 99.0 98.2 98.7 98.5 97.9 97.6 98.3 99.0 98.2

To determine a hypothesis test in Minitab, follow the same steps as you did for a confidence interval.The only exception is that you will need to check the box labeled Perform h ypothesis test, fill in thebelieved population mean and click the options button to enter the confidence level and symbol for

alternate hypothesis.

First, we need to enter the raw data in the table into column C1 of Minitab. Then from the menu bar,select STAT >> BASIC STATISTICS >> 1 SAMPLE T.


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Since our data is stored in C1, click the radio button next to the Samples in columns box and type inC1. Click the checkbox next to Perform hypothesis test checkbox and enter the value of mu, whichhere is 98.6. Since our significance level is 0.01, our confidence level is 99%. Next, click on the

Options button and change the confidence level to 99.0. Then click OK in the 1 -Sample t Optionsbox.

The 1-Sample t (Test and Confidence Interval) box should look like the one on the next page. Click OK.


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In the Sessions window, you will have your p-value and test statistic.

The p-value is 0.746, well above our significance level of 0.01. Also, are test statistic is t = 0.33, well inthe non-critical region. Our claim was Ho and we retain Ho. Therefore, there is not sufficient evidenceto warrant rejection of the claim that the mean body temperature of healthy CCBC students is 98.6 .

Correlation Coefficients and Regression Equations

EXAMPLE: Create a scatter plot and determine the regression equation in an attempt to predict theweight of a 2008 Baltimore Raven based on their height.

Keep in mind that the heights must be converted to inches in order to do any type of analysis. Acommon mistake is to enter a height of 5' 11" as 5.11. That is not correct. Using that logic, a person whois 5' 11" would be shorter than somebody who is 5' 2" (which would be entered as 5.2). Use theconversion 12 inches = 1 foot.

The data was obtained from the Baltimore Ravens website at

http://www.nfl.com/teams/baltimoreravens/roster?team=BAL

First, enter the heights into C1. In the example, the heights in C1 were entered as feet and inches.Column C2 contains the heights converted to inches. Column C3 contains each players weight.


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To create the scatter plot, from the menu bar, select GRAPH >> SCATTERPLOT.

You will be presented with the several types of scatter plots to choose from. Select the SIMPLE scatterplot and click OK.


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You will need to fill in the Scatterplots dialog box. Since we are attempting to predict weight based onheight, the weights are the y values and the heights are the x values.

Within this dialog box, you can also add a title to your scatter plot (click on the Labels button).


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When you are done, click OK. Your scatter plot will appear in a separate window.


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Regression Data in Minitab

Using the same data that that was used for the scatter plot, next we will determine a regression

equation. From the menu bar, select STAT >> REGRESSION >> REGRESSION.

Since we are using height to predict weight, in the box labeled Response: enter C3 or double click onC3 Weight. In the box labeled Predictors: enter C2 or double click on C2 Inches. Then click on OK.


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The results will appear in the Sessions window.

In this example, our data doesnt support a linear relationship because the absolute value of R -Sq is less

than the critical value found in table A-6 of the formula card.

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