Hypothesis Testing

The 3-Ball data or the Angle v Distance data (providing below) and determine, using the

appropriate test, if there is a statistically significant effect the type of ball or angle has on the

response variable. Make sure you validate all assumptions and the test provided good results.

Finally, answer the practical question!

Use Minitab instruction (see below) to do the analysis. The results must be pasted into

a MS Word® as a figure; use MLA formatting. The raw data should be a table in the Appendix.

Trial Foam Whiffle Rubber1 123 109 1192 120 111 1173 118 109 1164 120 108 1145 119 107 1166 120 110 1157 120 113 1138 122 109 1139 121 108 109

10 117 108 11311 120 108 116

Trial 160⁰ 172⁰ 184⁰1 64 86 1162 66 92 1123 65 85 1154 57 81 1175 61 87 116

P a g e 1 | 14

Minitab 16 InstructionsANOVA

- Verify assumptions of normal, independent and equal variances. The verification of the assumptions would go in the appendix since it is tangential to the subject under consideration. You merely state in the report the assumptions were verified and this analysis is in appendix….

o Normal Make a column for each factor level (type of ball) Click on Stat>Basic Statistics>Normality Test

Put the variable’s name that you wish to test in the “Variable:” box in the dialog box and hit OK

Your output will be the probability plot for your variable….

P a g e 2 | 14

The Null and Alternative hypothesis for this Anderson-Darling normality test is:

Ho: Data are normalHa: Data are not normal

If the p-value is greater than alpha, typically 0.05, we fail to reject the null and assume the data are normal

Repeat the above for all three variables (hint: control-e allows you to edit your last dialog box)

o Independence Just state the data were collected in a random order to assure independence

o Equal variances Again, this analysis goes in a separate appendix You will need to stack the three columns into two columns—one for distance

and another for ball type Click on Data>Stack>Columns

P a g e 3 | 14

Fill in the dialog box like shown below and hit OK

Your worksheet should look like….

Now you can test for equal variances; click on Stat>ANOVA>Test for Equal Variances

P a g e 4 | 14

In the Response box, enter the Variable “Distance,” and in the Factor box, enter the variable “Type.” Hit the OK button.

You will

The Barlett’s Test is for normal data and the Levene’s Test is for any continuous variable. The Null and Alternative hypothesis for these tests are:

Ho: 21 = 2

2 = 23

Ha: Not all 2i’s are equal

P a g e 5 | 14

Since the p-value for both are greater than alpha, 0.05, we fail to reject the null and assume the variances are equal

- Run the ANOVA test (this should be in the body of the report)o Are the means from each ball type different?

Click on Stat>ANOVA>One-Way…

Put “Distance” in the Response box and “Type” in the Factor box and hit OK

In the Sessions window you will see your analysis

P a g e 6 | 14

o If the means are different, don’t forget to run a Tukey Post-Hoc analysis Either hit together, Cntrl-e, or Stat>ANOVA>One Way… Now check on “Store residuals” and click on “Graphs…” button

Check the Four in one radial button; click on the OK button

click on the “Comparisons…” button

P a g e 7 | 14

Check the box for Tukey’s test and hit OK, and then hit OK again on the first dialog box

Your analysis will be in the Sessions window

P a g e 8 | 14

Analyze these data and tell the reader your conclusion. Remember answer the practical question.

P a g e 9 | 14

- Validate this was a good model (note: this also goes in another separate appendix)o Check the residuals for: normality, independence, equal variance and E{i} = 0

From your last analysis, since you asked for the “Four in one” residual graph, Minitab provided the following graph…

From graph 1.), you can see the residuals are normal. Verify this by running a normality test on the residuals you stored in the Sessions window. Again, the p-value should be greater than alpha, 0.05, to confirm normality.

From graph 2.), you can determine if the residuals have equal variances. From graph 3.), you can determine if the expected value is zero. From graph 4.), you can look for independence—are there any patterns in the

graph.

P a g e 10 | 14

4.)3.)

2.)1.)

Regression- There are not assumptions to verify other than this is an appropriate test based on the data

o Run the analysis in Minitab Click on Stat>Regression>Regression

In this dialog box, put “Distance” in the Response box and “Angle” in the Predictors box. Then click on the Graphs button.

P a g e 11 | 14

Click on the radial button for the “Four in one” graphs and then the OK button.

Now click on the Storage button

P a g e 12 | 14

Now check the Standardized residuals box and click on OK, and then OK again on the Regression dialog box

In the Sessions window, you will find your analysis

o In your report, make sure you address the question—does angle affect the distance the ball travels. If so, what is the effect—quantify it!!

- Validate this was a good model (note: this also goes in another separate appendix)o Check the residuals for: normality, independence, equal variance and E{i} = 0

From your last analysis, since you asked for the “Four in one” residual graph, Minitab provided the following graph…

P a g e 13 | 14

Go to page 9 to determine what each of the four graphs are used for. Analyze your results (again, in the report, tell the reader if the residual

assumptions were validated, but reference the reader to a separate appendix.

P a g e 14 | 14