# Minitab Notes for Activity 6

## 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.

- Choose Calc / Probability Distributions / Normal
- Select Inverse cumulative probability
- 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.
- 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.

- Go to Stat / Basic Statistics / 1 Proportion
- Click the Summarized Data radio button
- Enter the number of trials (n) and successes (x). Note, Minitab calls successes
"events".
- Click Options
- The confidence level is 95%.
- The test proportion is the 35% (written as 0.35) that was claimed. This really isn't necessary for finding the confidence interval, though.
- Check to make sure the alternative hypothesis is "Not Equal"
- 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).

- 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.