# Minitab Notes for Activity 5

## Finding the Critical Value (Question 6)

The easiest way to find the critical values is to use your textbook. At the bottom of the z-table in the lower right hand corner of your inside front cover, there are common critical values.

However, if you would like to use Minitab to look up the critical value, you can do the following.

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.

## Finding 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 trials (n) and successes (x). Note, Minitab calls successes "events".
4. Click Options
1. The confidence level is 95%.
2. The test proportion is the 35% (written as 0.35) that was claimed. This really isn't necessary for finding the confidence interval, though.
3. Check to make sure the alternative hypothesis is "Not Equal"
4. 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% CI         Z-Value  P-Value
1       12  50  0.240000  (0.121621, 0.358379)    -1.63    0.103
```

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

## Finding the Areas (Question 14)

You can do this with the normal table in the book as well.

1. Choose Calc / Probability Distributions / Normal
2. Select Cumulative probability
3. The input constant is the test statistic
4. 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.