# Minitab Notes for Activity 5

## Finding the Critical Value (Question 6)

### Using the Probability Calculator

The easiest way to find the critical value is to use the online probability distribution calculator. Put the confidence level 95% as the decimal 0.95 in the box that says says "conf. level" and click Calculate.

### Tables

There are statistical tables that were given to you in class or are available on the website. The quickest way to find the critical values are to go to the t-table and look at the bottom for a 95% confidence level. Then come up one row to the normal or z row and get the critical value. Remember that there are two critical values, even though the table only gives the positive one.

### Minitab

If you really insist on using Minitab, you'll have some work to do.

1. Choose Calc / Probability Distributions / Normal
2. Select Inverse cumulative probability
3. The input constant is the area to the left of the critical value. Since the confidence level is 95%, there is 5% split between the two tails. That makes 2.5% in each tail. The area to the left of the left critical value is 2.5%, which is entered as the decimal 0.025.
4. Click OK

If you want the critical value on the right side, you can use the symmetry involved and just make the critical value you found above positive. Another way to find the critical value on the right directly is to repeat the steps above, but since there is 2.5% to the right of the right critical value, there is 97.5% to the left.

## Checking the Confidence Interval (Question 9)

One purpose of this activity is to practice finding a confidence interval by hand, but you can use Minitab to check your results.

1. Go to Stat / Basic Statistics / 1 Proportion
2. Click the Summarized Data radio button
3. Enter the number of successes (x) and number of trials (n). Note, Minitab calls successes "events".
4. Click Options
1. The confidence level is 95%.
2. Check to make sure the alternative hypothesis is "Not Equal"
3. Always check the box to base the test and interval on the normal distribution (note that Minitab may complain about a small sample size, but we're not getting into non-parametric hypothesis testing at this point, so we're going to force the normal approximation).
5. Click OK

You should get some output that looks like this.

`Sample   X   N  Sample p         95% CI1       12  50  0.240000  (0.121621, 0.358379)`

The 95% Confidence Interval would be 0.121621 < p < 0.358379.

## Finding the Areas (Question 14)

### Using the Probability Calculator

The easiest way to find the areas is to use the online probability distribution calculator. Put the test statistic in the box that says score / value and click Calculate.

### Tables

There are statistical tables that were given to you in class or are available on the website. Use the Normal table. Find the test statistic as a z-score on the outside of the table and get the area to the left from inside the table. Then complete the rest of the table as we did before.

### Minitab

Choose Calc / Probability Distributions / Normal

1. Select Cumulative probability
2. The input constant is the test statistic
3. Click OK

The value returned by Minitab is the area to the left of the test statistic. You will need to take that value from 1 to find the area to the right. You will then take the smaller area and double it to find the p-value.