Hypothesis Testing and Confidence Intervals for comparing 2 samples (paired)

Suppose that you wanted to determine if someone’s heart rate decreased after listening to five minutes of relaxing music. You take a random sample of 10 college students. You have them find their heart rate, listen to five minutes of music and find their heart rate again.

Before	After
70	69
56	57
82	80
74	73
92	92
85	80
100	99
54	60
72	71
76	75

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

1. First, go to Stat, Basic Statistics, Paired t.
2. The following screen will appear.

3. Enter your samples in First and Second Sample.

4. Click on the Options button to compute a confidence interval or hypothesis test.
1. 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".

2. 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.

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

Paired T-Test and CI: Before, After

Paired T for Before - After

N Mean StDev SE Mean

Before 10 76.1000 14.4872 4.5812

After 10 75.6000 12.9803 4.1047

Difference 10 0.500000 2.758824 0.872417

95% CI for mean difference: (-1.473544, 2.473544)

T-Test of mean difference = 0 (vs not = 0): T-Value = 0.57 P-Value = 0.581