## Minitab Cheat Sheet for Statistical Analyses

### Z-tests and Z-intervals for One proportion

To calculate a confidence interval and perform a hypothesis test for a single population proportion when you have summarized data:

1. Select Stat. Select Basic Statistics. Select 1 Proportion.
2. Click on the button in front of Summarized data. Type in n, the number in the random sample, in the box labeled Number of trials. Type in X, the number of successes, in the box labeled Number of successes.
3. Click on Options...  In the box after Confidence Level, type your desired confidence level.  In the box after Test Proportion, specify the value of the proportion in your null hypothesis.  Under Alternative, select the desired direction of your alternative hypothesis.  Click on box before Use test and interval based on normal distribution. Select OK.
4. Select OK.  The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.1.8.

 ```Test and Confidence Interval for One Proportion Test of p = 0.75 vs p < 0.75 Sample X N Sample p 95.0 % CI Z-Value P-Value 1 273 390 0.700000 (0.654519, 0.745481) -2.28 0.011```

### Sample Size Calculations for Tests about One Population Mean

1. Select Stat. Select Power and Sample Size. Select 1 Sample Z.
2. Click on the button in front of Calculate sample size for each power value.
3. In the box labeled Power values, type the desired power.
4. In the box labeled Difference, type the difference in the null hypothesis and the value of the mean in the alternative hypothesis that is meaningfully different from the null. The difference should be alternative minus null.
5. Select Options.... Click on the the desired Alternative Hypothesis, and specify the desired Significance level. Select OK.
6. Select OK. The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.2.7.

 ```1-Sample Z Test Testing mean = null (versus < null) Calculating power for mean = null - 65 Alpha = 0.05 Sigma = 140 Sample Target Actual Size Power Power 40 0.9000 0.9017```

### 1-sample t

To calculate a confidence interval or perform a hypothesis test for a single population mean:

1. Select Stat. Select Basic Statistics. Select 1-Sample t.
2. The 1-Sample t Pop-Up Window will appear.  In the left box, click once on the variable you want analyzed.  Click once on the Select button.  The column name (or variable name) will appear in the box labeled Variables.
3. To create a confidence interval: By default, the radio button before Confidence Level should be selected.  If it is not, click on it to select it.  In the box after Confidence Level, type the level of the confidence interval that you desire.  Ninety-five percent (95%) is the default level.
4. To perform a hypothesis test:  Click on the radio button before Test Mean.  In the box after Test Mean, type the value of the mean in the null hypothesis.  Under Alternative, select the desired direction of your alternative hypothesis.  The choices are Not Equal, Less Than, or Greater Than.
5. Select OK.  The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.3.10.

 ```Test of mu = 125.00 vs mu not = 125.00 Variable N Mean StDev SE Mean T P torque 15 127.67 9.60 2.48 1.08 0.30```

### Two-sample t-tintervals and t-tests

To calculate a confidence interval or perform a hypothesis test for the difference in the means from two independent populations:
1. Enter the data into two separate columns.
2. Select Stat. Select Basic Statistics. Select 2-Sample t.
3. The 2-Sample t Pop-Up Window will appear.  Click on the button in front of Samples in different columns. Specify one of your samples as the First sample and your other sample as the Second sample.
4. To perform a hypothesis test, under Alternative, select the desired direction of your alternative hypothesis.  The choice will depend on which sample you specified as your First sample and which sample you specified as your second sample. Minitab always considers the First mean minus the Second mean.
5. In the box after Confidence Level, type the level of the confidence interval that you desire.  Ninety-five percent (95%) is the default level.
6. If appropriate, click on the box before Assume Equal Variances.
7. Select OK.  The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.4.3. Note that the line Both use Pooled StDev means that we have assumed equal variances. Both refers to both the confidence interval and the hypothesis test. Notice the degrees of freedom are 20.

 ```Two sample T for straw vs blue N Mean StDev SE Mean straw 9 21.033 0.606 0.20 blue 13 20.89 1.01 0.28 95% CI for mu straw - mu blue: ( -0.65, 0.93) T-Test mu straw = mu blue (vs not =): T = 0.37 P = 0.71 DF = 20 Both use Pooled StDev = 0.869```

This is what the output looks like if we don't assume equal variances. Note that there is no Both use Pooled StDev line, and the degrees of freedom have been adjusted downward to 19.

 ```Two sample T for straw vs blue N Mean StDev SE Mean straw 9 21.033 0.606 0.20 blue 13 20.89 1.01 0.28 95% CI for mu straw - mu blue: ( -0.58, 0.86) T-Test mu straw = mu blue (vs not =): T = 0.41 P = 0.69 DF = 19```

### Paired t-test and Paired t-intervals

To calculate a confidence interval or perform a hypothesis test for the difference in the means from two dependent populations:
1. Select Stat. Select Basic Statistics. Select Paired t.
2. The Paired t Pop-Up Window will appear.  Specify your First Sample. Specify your Second Sample.
3. Click on Options...  In the box after Confidence Level, type your desired confidence level.  In the box after Test Mean, specify the value of the mean in your null hypothesis.  Under Alternative, select the desired direction of your alternative hypothesis.  Select OK.
4. Select OK.  The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.3.18.

 ```Paired T for ballA - ballB N Mean StDev SE Mean ballA 17 256.18 18.70 4.54 ballB 17 251.41 14.93 3.62 Difference 17 4.76 9.09 2.20 95% CI for mean difference: (0.09, 9.44) T-Test of mean difference = 0 (vs > 0): T-Value = 2.16 P-Value = 0.023```

### Chi-square test for homogeneity and/or test for independence

Assuming you have a table of summarized data:
1. Enter the table of summarized data into Minitab.
2. Select Stat. Select Tables. Select Chi-square test.
3. Specify the columns containing the table of summarized data.
4. Select OK.  The output will appear in the Session Window.

#### Example

The following is the Minitab output for Exercise #7.6.2.

 ```Data Display Row Cat1 Cat2 Cat3 Cat4 Cat5 Cat6 1 95 36 71 21 45 32 2 53 26 43 18 32 28 3 130 75 136 33 61 65 Chi-Square Test Expected counts are printed below observed counts Cat1 Cat2 Cat3 Cat4 Cat5 Cat6 Total 1 95 36 71 21 45 32 300 83.40 41.10 75.00 21.60 41.40 37.50 2 53 26 43 18 32 28 200 55.60 27.40 50.00 14.40 27.60 25.00 3 130 75 136 33 61 65 500 139.00 68.50 125.00 36.00 69.00 62.50 Total 278 137 250 72 138 125 1000 Chi-Sq = 1.613 + 0.633 + 0.213 + 0.017 + 0.313 + 0.807 + 0.122 + 0.072 + 0.980 + 0.900 + 0.701 + 0.360 + 0.583 + 0.617 + 0.968 + 0.250 + 0.928 + 0.100 = 10.176 DF = 10, P-Value = 0.425 ```