You will be entering your own information for this activity.

- Label three empty columns as "card", "correct1", and "correct2". You're free to call them something else, but you'll need to adjust the instructions accordingly.
- Enter the numbers 1 through 20 in order into the card column. You may either
type them in manually or follow these instructions:
- Choose Calc / Make Patterned Data / Simple Set of Numbers from the menu
- Store the patterned data into "card".
- Start from the first value of 1 and go to the last value of 20.
- Click OK

- Fill in the "correct1" column with 0s and 1s. Use a 1 if the the suite was correctly guessed and a 0 if the suite was incorrectly guessed. Use the information from question 1 to complete this column.
- Fill in the "correct2" column with 0s and 1s the same as in step 3. However, this time use the data from the second question.
- Go File / Save Project As
- Move through the filesystem to
**R:** - Change to your section number
- Change to the
**act4**folder - Type a name that is unique to you
- Click OK

From now on, when you need to work with the project, open the one for your data.

You might have thought that it would be better to save the results as "y" or "n". The reason we stored the successes as 1 and failures as 0 is that now we can find the total number of successes after each card is dealt by adding up the correct1 or correct2 column. It's really hard to add up "y" and "n" values.

A probability is a relative frequency: the number of successes divided by
the number of trials. What we're going to do for each card is find the total
number of successes so far
divided
by
the
number
of
cards
dealt so far. The number of cards dealt is in the "card" variable.
The number of successes in the first *k* cards can be found by adding
up the first
*k* values in the correct1 or correct2 column. Adding up all the values
up through the one we're currently one is accomplished by the Partial Sum function,
abbreviated pars().

- Label two empty columns as "prob1" and "prob2"
- Choose Calc / Calculator from the menu
- Store the results into
**prob1**. - The expression should be
**pars(correct1)/card** - Click OK

- Store the results into
- Repeat step 2, except use
**prob2**and**correct2**.

You can do this by hand or you can have Minitab help. What I would do is to generate the graph on Minitab so that you're sure about what you're doing and then do it by hand. Whatever you do, you need to copy the graph onto your activity sheet, and that means by hand.

To graph the chart by hand, take the card number for the horizontal axis and the prob1 value for the vertical axis. Plot all twenty points and then connect the dots. Repeat the process again with the card number for the horizontal axis and the prob2 value for the vertical axis.

This section is completely optional and I don't want you to print it out. You're using it to see what your graph by hand should look like, so you can feel free to omit any of the optional steps (or the entire thing) if you want to.

- Choose Graph / Time Series Plot from the menu
- Double click on
**prob1**to add the first graph and**prob2**to add the second graph. - Click on Frame / Multiple Graphs. Choose to overlay graphs on the same page. Click OK.
- (Optional, recommended) Change the styles of the lines so you can tell
them apart.
- Click the word Connect under Data Display 2 and then click Edit Attributes
- Change the line types, colors, and/or line size so you can tell the lines apart.

- (Optional) Add a title. Click on Annotation / Title and add a title. Click OK.
- Click OK.

- Choose Stat / Basic Statistics / 2 Proportions... from the menu
- Check the Samples in Different Columns box
- Use "correct1" for the first sample and "correct2" for the second sample.
- Click on options
- Change the Alternative to Less Than. We're testing to see if the proportion on the second sample is greater than on the first, but Minitab always compares the first sample to the second sample. So, instead of saying "the second is greater than the first", we'll word it as "the first is less than the second".
- Click OK

- Click OK

The end of the output will contain something like this:

Estimate for p(correct1) - p(correct2): -0.05

95% upper bound for p(correct1) - p(correct2): 0.181889

Test for p(correct1) - p(correct2) = 0 (vs < 0): Z = -0.35 P-Value = 0.361

The 95% upper bound for p(correct1) - p(correct2) is the upper value on a confidence interval. If yours says "lower bound" or "95% CI" and gives and interval of values like "(-0.326313, 0.226313)", then you didn't follow the instructions above about changing the alternative to "less than". Go back and do that.

Since the value is an upper bound, the confidence interval for the difference
can be written as being less than that value. We would write the above as "p_{1} -
p_{2} < 0.181889". Since this interval does contain the value
of 0, which means no difference, we will retain the assumption that there is
no improvement when the cards are seen. If the confidence interval does not
contain 0, then we will reject the assumption that there is no improvement
when the cards are seen and say there is improvement.

The p-value is at the end of the last line, where it says "P-value = 0.361". The p-value is the chance of getting your results if there is no improvement when the cards are seen. In this case, it's a pretty good chance, so we'll have go ahead with the assumption that there is no improvement. Only when your results are really unlikely to happen by chance alone will we reject the assumption and say there is an improvement.

After you have gotten the classes data from everyone, enter it into Minitab.

- Label three blank columns as "name", "right1", and "right2"
- Enter the values that you collected into those three columns.

- Go to Stat / Basic Statistics / Descriptive Statistics
- Display the descriptive statistics for the
**right1**and**right2**variables. - Click OK.

Record the appropriate summary statistics into the table.

Since each person had 20 cards dealt to them, the easiest way to find the total number of trials is to multiply the number of students by 20.

To find the total number of successes, you could add up the number of successes for each student. However, it would be quicker to just take the mean number of successes and multiply it by the number of students. Make sure this becomes a whole number.

If you want to use Minitab to verify the number of successes for you, then you can follow these steps.

- Choose Calc / Column Statistics
- Your statistic is Sum
- Your input variable is
**right1** - Click OK
- Repeat steps 1-4 for
**right2**

- Choose Stat / Basic Statistics / 2 Proportions... from the menu.
- Check the Summarized Data radio button
- Enter the total number of trials and number of successes without looking at the cards for the first sample.
- Enter the total number of trials and number of successes with looking at the cards for the second sample.
- Go into Options and make sure the Alternative is Less Than.
- Click OK

Use the same instructions as question 8 for interpreting the output.