Hypothesis Test and Confidence Intervals for comparing 2 independent proportions

An experiment was done to see if the amount of reground powder in a pellet made a difference in the proportion of pellets that were conforming to standards. Out of 100 pellets made of 20% reground powder, 38 were conforming. Out of 100 pellets made of 50% reground, 66 were conforming. (Vardemen Basic Engineering Data Collection and Analysis Example 14 on page 112)

For two independent proportions confidence intervals and hypothesis test, you want to use the z (Standard Normal distribution).

1. First, go to Stat, Basic Statistics, 2 proportions.

2. The following screen will appear.

3. Click on "Summarized Data".

4. Enter n in the column for trials and the number of "successes" under Events.

5. Click on Options. The following box will appear.

6. To compute a confidence interval or hypothesis test.

a. To compute a hypothesis test

i. Don't worry about the confidence level box.

ii. Fill in the test mean in the box. Most likely this number will be equal to zero.

iii. Chose the alternative that matches your alternative hypothesis.

1. If you want a two-sided test, select "not equal" as your alternative.

2. If you want a one-sided test, select "less than” or  "greater than".

iv. Select the box for Use the pooled estimate of p for test.

b. To Compute a Confidence Interval or Bound.

i. Enter your level of confidence.

ii. Do not worry about the blank for test mean

iii. Determine if you want to have a two-sided confidence interval or a bound.

1. If you want a two-sided confidence interval select, "not equal" as your alternative.

2. If you want a one-sided confidence bound, select "less than" for a upper bound or "greater than" for an lower bound.

iv. Select the box for Use the pooled estimate of p for test.

8. Below is the output for a 95% two-sided confidence interval.

Test and CI for Two Proportions

Sample X N Sample p

1 38 100 0.380000

2 66 100 0.660000

Difference = p (1) - p (2)

Estimate for difference: -0.28

95% CI for difference: (-0.412931, -0.147069)

Test for difference = 0 (vs not = 0): Z = -3.96 P-Value = 0.000