- Label the first column as act2 and the second column as orville.
- Enter the first kernel popping times from the class into the appropriate columns. Make sure to keep the information paired up.

The variable that is supposed to be normally distributed is the difference in the times. What we have available to us are the actual times, not the difference in the times. So, we first need to find the differences if we're going to check and see if they're normally distributed.

- Label the third column as d (for difference)
- Go to Calc / Calculator.
- Store the results in d (C3)
- The expression is "C1-C2" (no quotes)
- Click OK

- Go to Stats / Basic Statistics / Normality Test
- Choose d (C3) for the variable.
- Click OK

- Use either the normal probability plot or the Anderson-Darling p-value to determine normality.

- If you didn't find the third column d as described in the last section on checking normality, go back and do steps 1 and 2 now. You'll need that to find the descriptive statistics for the difference.
- Go to Stat / Basic Statistics / Display Descriptive Statistics
- Use all three variables (C1-C3)
- Click OK

Minitab doesn't give critical values when it does hypothesis testing. You will need to use the degrees of freedom, level of significance, type of test, and distribution used to look up the critical value(s) from the textbook.

For those who enjoy technology, Minitab can be used to find the critical values, much like we used Excel on the last test. It uses something called the "Inverse Cumulative Probability" which takes the area in the left tail and returns the critical value for that. Note that this is different than the critical value notation, which always uses the right tail area. Here's how to find the critical value on Minitab.

- Go to Calc / Probability Distributions and choose the appropriate distribution
- Choose the "Inverse cumulative probability".
- Enter the degrees of freedom
- Choose "Input Constant" and enter the
area in the left tail.
- If you have a left tail test, just enter the area. For example, if you have 0.05 in the left tail, just enter 0.05.
- If you have a right tail test, you have to take 1-area to get the left tail area. For example, if you have 0.05 in the right tail, then you have 1-0.05=0.95 in the left tail. Enter 0.95 into Minitab.
- If you have a two-tail test, divide the area by two and repeat this exercise twice. For example, 0.10 in two tails means 0.10/2 = 0.05 in each tail. Run through this once and choose the left tail area with 0.05 and then again with a right tail area of 0.05 (follow the instructions in part ii)

- Click OK

- Go to Stat / Basic Statistics / Paired t
- Enter act2 for the first sample and orville for the second sample
- Go
into Options
- Notice that we're doing hypothesis testing which requires a level of significance, but Minitab is asking for a confidence level instead. Make sure you enter the confidence level that agrees with our level of significance
- The test mean is how much difference we want. In this case, we want no difference, so the value should stay at zero.
- The alternative hypothesis is how you tell Minitab whether it is a left tail, right tail, or two tail test.
- Click OK

- Click OK

- Notice that the summary statistics are given here, so if you would have known that earlier, you could have saved some time.
- The confidence interval given by Minitab corresponds to the values of the difference that would fall into the non-critical region.

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Last updated
July 7, 2003 7:13 AM