a. One-Sample Z-Test and Confidence Interval
b. One-Sample t-Test and Confidence Interval
c. Two-Sample t-Test and Confidence Interval
d. Paired t-Test and Confidence Interval
e. Test and Confidence Interval of a Proportion
f. Test and Confidence Interval of Two Proportions
g. Correlation
h. Regression and Residuals

Introduction to Minitab

I. Capabilities

Minitab is a powerful statistical software package that provides a wide range of data analysis and graphing capabilities to the user. It is widely used in education, as well as in business, industry, and research. Here are some of the capabilities of Minitab:

Descriptive statistics, with both graphical and numerical summaries

-Confidence intervals
-One- and two-sample t-tests, paired t-tests
-Tests for proportions
-Normality tests
-Tests for equal variances
-Simple and multiple linear regression
-Plotting regression lines with confidence and prediction bands
-Identification of unusual observations and model diagnostics
-Residual plots
-ANOVA tests
-Goodness-of-fit test
-Contingency tables
-Power calculations
-Presentation-style graphics
-Scatterplots, box plots, histograms, charts, time series plots
-Built-in graphs in analysis commands
-High-resolution dotplots
-Ability to customize all attributes of every element in a graph: color, type size, fonts, data display, and annotation
-Powerful, easy-to-use graph editor
-Ability to edit Minitab graphs in other applications

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II. The Minitab Environment

Minitab windows

· The Session window displays text output such as tables of statistics.

o Data windows are where you enter, edit, and view column data for each worksheet.

o Graph windows display graphs.

o The Project Manager window contains folders that allow you to navigate, view, and manipulate various parts of your project. Just right-click on either the folders or their contents to access menus that allow you to manage the Session window.

Menus and Tools

· The menu bar is where you choose commands.

o The standard toolbar displays buttons for commonly used functions.

· The toolbar is dynamic and will change depending on the active window.

o The project manager toolbar provides shortcuts to Project Manager folders.

o The status bar displays explanatory text whenever you are pointing to a menu item or toolbar button.

o Shortcut menus appear when you right-click on any window in Minitab or on any folder in the Project Manager.

o Two graph editing palettes, the tool palette and the attribute palette, let you add and change elements on graphs.

Getting Answers and Information

· Online help: Complete documentation on each Minitab feature and concept, written for users of menus and dialog boxes.
Get to it by:

o Help > Search Help

o Click the Help button in any dialog box

o Press F1 at any time

o Click ? on the toolbar

· Session command help: Documentation on each session command, including syntax and examples.
Get to it by:

o From the Start menu, choose Programs > Minitab 13 for Windows > Session Command Help

o Choose Help > Session Command Help

· StatGuide: Provides statistical guidance after you run a procedure in Minitab, primarily focusing on interpreting results.
Get to it by:

o the symbol with the three sheets with sigma on the front sheet

o Press shift + F1

o Right-click in the active window or on a session title in the Project

· Manager Session folder and choose StatGuide

o Choose Help > StatGuide

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III. Data Management

· Three types of data:

1. Numeric data: Numbers

2. Text data: Characters that can consist of a mix of letters, numbers, spaces, and special characters

3. Date/time: Can be dates in any format, times, or both. Minitab stores dates and times internally as numbers, but displays them in a format of your choice

· Forms of data:

o Column: Contains any type of data and is referred to by C + a number or by a name.

o Stored constant: Contains a single number or text string and is referred to by K + a number or by a name.

o Matrix: Contains a rectangular block of cells containing numbers and is referred to by M + a number or by name.

· Using the data window:

o View the columns of data stored in the worksheet

o Enter and edit values

o Manipulate columns by changing format, font, name, width, description, and position of columns

· Entering data:

o The data window works similar to a spreadsheet for data entry. Note the arrow in the upper left hand corner of the data window.

o When the arrow is pointing down, data may be entered column-wise and pressing tab or enter will move you down a column.

o When the arrow is pointing to the right, data may be entered row-wise and pressing tab or enter will move you across a row.

o You may also enter data within a block. Highlight the area within which you wish to work. Enter the data. The active cell moves only within the selected area.

o If you make a mistake, just highlight the old value and type a new one.

o You may copy and paste data within Minitab, or into Minitab from other applications available at RVGS, including Microsoft Excel, a table in a word processor, text in the body of a word processing document, or another Minitab session window.

Special note: Much of what you use in Minitab will be intuitive. Do not be afraid to experiment with the program. You may be surprised at how easy it is to use!

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Basic Statistics

I. Display Descriptive Statistics

· To calculate descriptive statistics:

o Choose Stat > Basic Statistics > Display Descriptive Statistics.

o In Variables, enter the column(s) containing the data you want to describe or highlight those variables you wish to describe and click Select

o If you like, use one or more of the options and click OK.

· In the display in the session window, you will see each of the following statistics:

o Number of nonmissing values

o Number of missing values

o Mean

o Trimmed mean: Minitab removes the smallest 5% and the largest 5% of the values and then finds the average of the remaining data

o Standard error of the mean: Calculated by dividing the standard deviation by the square root of the number of data points

o Standard deviation: Standard sample standard deviation calculation

o Minimum

o Maximum

o Median

o First and third quartiles

· In the graphical summary of descriptive statistics, you will see each of the following statistics:

o Number of non-missing values

o Mean

o Confidence interval for the population mean

o Standard deviation

o Confidence interval for the population standard deviation

o Variance

o Minimum

o Maximum

o Median

o Confidence interval for the median

o First and third quartiles

o Skewness

o Kurtosis (A measure of how different a distribution is from normal)

o Normality test statistic, p-value

Practice

Enter the following data into a new Minitab worksheet. Name C1 'Ruth' and name C2 'Maris'. Enter the following homerun data into the appropriate columns and verify that you have entered the data correctly.

Ruth 54 59 35 41 46 25 47 60 54 46 49 46 41 34 22
Maris 13 23 26 16 33 61 28 39 14 8

Answer the following questions based on the above data:

1. What are the values for the mean number of homeruns hit by Ruth and Maris?
2. What is the 5-number summary for each of the players?
3. What is the standard deviation for the number of homeruns hit by each player?
4. Are the data for either player normally distributed? Why or why not?

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Graphing

I. Overview

Each of the graphs discussed in this section may be found in the Graph menu. Except for the character graphs, which appear in the Session window, all graphs described will appear in the graph windows.

II. Time Series Plot

A TSP displays a quantitative variable on the y-axis versus a variable stated in terms of time on the x-axis. By default, the data points on a TSP are connected by lines. An assumption is made that the dependent variable data occurred in the order that the values appear in the column, in equally-spaced time intervals. If the data did not occur that way, consider using the plot command.

The time scales can be labeled in a variety of ways:

· index units: integers that represent units of time (each individual observation is labeled with a consecutive integer)

· date/time stamp: taking values from an assigned date/time column

· calendar units: days, months, quarters, or years, or up to three in combination

· clock units: days, hours, minutes, or seconds, or up to three in combination

To create a TSP:

1. Choose Graph > Time Series Plot or Stat > Time Series > Time Series Plot.
2. In Y, enter the column of numeric data.
3. Under Time Scale, choose the appropriate time scale.

Note: When using Date/Time Stamp, enter the column that contains your desired time unit. When using Calendar or Clock, choose a time unit from the drop down menu.
4. Choose any of the graphics options and click OK.

To specify a time range or interval,
1. In the Time Series Plot main dialog box, choose a time scale.
2. Click Options for a subdialog box that contains features for the scale you chose.
3. Under Assignment of Time to Data, click in the Cycle through values box for the time you want to affect.
4. Type a range and the intervals within that range that you wish to display.

· Specify a range by typing two numbers separated by a colon

· Specify an interval by typing a slash and a number: 1:12/2 means show every other unit in the range-1 3 5 7 or January, March, May, July

5. Click OK.

To specify a start time:
1. In the Time Series Plot main dialog box, chose a time scale.
2. Click Options.
3. Under Start times, click in row 1 under the time unit you want to affect. Type the starting value.
4. Fill in start values for any other cells in row 1.
5. If you specified several time plots in the Time Series Plot dialog box, you may specify a separate set of start times for each plot.
6. Click OK.

Practice

The monthly sales figures (in $1000s) for an athletic shoe store are presented below for the years 1992, 1993, and 1994. The data should be read across the rows.

- 204 188 235 227 234 264 302 293 259 229 203 229
- 242 233 267 269 270 315 364 347 312 274 237 278
- 284 277 317 313 318 374 413 405 355 306 271 306

Create a detailed time series plot of this data and answer the following questions:
1. What trends do you notice in the data?
2. Are there any particular months in which trends seem obvious year after year?
3. If you were an advertising consultant for this company, what recommendations would you make?

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III. Histogram

A histogram displays a bar for each class or group in a quantitative variable. These groups are continuous intervals of data. For each interval, the height of the bar corresponds to the class count (number of observations in the interval) or frequency. You can change the way the intervals are calculated or specify which intervals you want to display. You can also change the y-axis from a frequency scale to a percent or cumulative scale.

To create a histogram:

1. Choose Graph > Histogram.

2. In X, enter the column containing the data you wish to analyze.

3. If you would like to use any of the following options, click OK.

a. Change the way the data is displayed

b. the histogram by adding a title, text, footnotes, lines, polygons, markers, or data labels

c. Change the frame by specifying the axes, tick marks, grids, reference lines, or the scale

d. Modifying regions within the graph itself

e. Grouping the graphs in a manner other than the default

4. When changing the y-axis, you may choose to use on of six types of scales;

a. Frequency: The height of the bar equals the number of observations that fall in that interval.

b. Percent: The height of the bar equals the percentage of the total number of observations that fall in that interval.

c. Density: The height of the bar equals a function of the area of the interval. The total of all of the bars is one. The area of one bar is the proportion of the observations in that interval.

d. Cumulative Frequency, Cumulative Percent, or Cumulative Density: The height of the bar equals the frequency, percentage, or density of that interval plus all previous intervals.

5. To change the y-scale:

a. In the Histogram main dialog box, click Options.

b. Under Type of Histogram, choose the scale you want.

6. To change the placement of the tick marks:

a. In the Histogram main dialog box, click Options.

b. Under Type of Intervals, choose MidPoint or CutPoint.

c. Click OK.

7. To define the number and position of intervals:

a. In the Histogram main dialog box, click Options.

b. Under Type of histogram, choose MidPoints or CutPoints.

c. Under Definition of intervals, choose one of three options: Automatic, Number of intervals, or Midpoint/cutpoint positions.

i. If you choose Number of intervals, select how many intervals you want (from 2 to 100)

ii. If you choose Set midpoint/cutpoint positions for midpoint selection, the position of each midpoint tick must be equally spaced

iii. If you choose Set midpoint/cutpoint positions when cutpoint is selected, the first value you type is the left boundary of the first interval; the second value is the boundary between the first and the second interval, etc. The positions of the cutpoints do not have to be equally spaced.

For example, a histogram of capital expenses with ticks at cutpoints shows the first tick at 3.5 and the last tick at 38.5. You decide that it would look nicer with a range of 5 to 40, with intervals every five values. When you choose Midpoint/cutpoint positions, type 5:40/5

Practice

Use the data on Babe Ruth's and Roger Maris's homeruns to create a histograms. Use some of the options to make the histograms useful to the reader. Answer the following questions:

1. Do the data seem to be normally distributed?

2. Why is there no column above 30?

3. From the shape of the histogram, would you expect the mean to be much less than the mean, about the same as the mean, or much greater than the mean? Compare you answer with the results obtained when you calculated the basic statistics. Do they agree?

4. Instead of using the default axes, create histograms with the same axes for both Ruth and Maris. What information is apparent from looking at both of these histograms?

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IV. Chart

You can produce many kinds of charts with Minitab, including bar charts, line charts, symbol charts, and projection charts. We are going to focus on bar charts. Bar charts can take on two forms:

· A chart of counts shows the count of each unique observation.

· A chart of function by group uses one column of measurement data for the y-axis and a second column as a category or grouping of the variable that appears on the x-axis.

For a chart of counts, you will need one column of categorical data for the x-