Hypothesis Test for comparing 2 independent means

Suppose that you were trying to determine if there was a difference in the lengths of the skid marks left by treaded or smooth bicycle tires on smooth concrete. The data for this experiment are below in cm. (Problem number 4 in Vardemen’s Basic Engineering: Data Collection and Analysis.

Treaded : 365, 374, 376, 391, 401, 402

Smooth: 341, 348, 349, 355, 375, 391

For two independent means confidence intervals and hypothesis test, you want to use the t distribution.

1. First, go to Stat, Basic Statistics, 2 sample t.

2. The following screen will appear.

3. Click on "Samples in Different Columns".

4. Enter the two different groups that you want to compare into first and second boxes.

5. Determine if you can assume equal variances.

i. If the ratio of the standard deviations (the largest standard deviation on top) is over 2, do not check the box next to Assume equal variances.

ii. If the ratio of the standard deviations (the largest standard deviation on top) is less than 2, check the box next to Assume equal variances.

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

7. To compute a confidence interval or hypothesis test.

i. To compute a hypothesis test

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

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

3. Chose the alternative that matches your alternative hypothesis.

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

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

ii. To Compute a Confidence Interval or Bound.

1. Enter your level of confidence.

2. Do not worry about the blank for test mean

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

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

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

8. Below is the output for a 95% two-sided confidence interval. For the example above, the standard deviation of the treaded is 15.38 and the standard deviation of the smooth is 19.17. The ratio of these two standard deviation is 1.25, so you can assume equal variances.

Two-Sample T-Test and CI: Treaded, Smooth

Two-sample T for Treaded vs Smooth

N Mean StDev SE Mean

Treaded 6 384.8 15.4 6.3

Smooth 6 359.8 19.2 7.8

Difference = mu (Treaded) - mu (Smooth)

Estimate for difference: 25.0000

95% CI for difference: (2.6457, 47.3543)

T-Test of difference = 0 (vs not =): T-Value = 2.49 P-Value = 0.032 DF = 10

Both use Pooled StDev = 17.3772