Question

A group of researchers hypothesize that broken bones will take longer to heal among smokers versus nonsmokers. They test this question with a sample of 20 smokers, where the average time to heal was 32 days (SS = 1161), and a sample of 45 nonsmokers, where the average time to heal was 21 days (SS = 1179). Use the critical-value approach for the appropriate statistical test (where α = .05) to determine if there is a significant difference in bone healing time between smokers and nonsmokers.

1. Identify the alternative hypothesis

2. List your degrees of freedom

3. List your estimated standard error

4. List your t test statistic (where: smokers – nonsmokers)

5. List your critical t value(s)

6. Is the difference in healing time between smokers and nonsmokers statistically significant? (Yes/No)

7. Calculate Cohen’s d for the difference in healing time

Answer 1

(1)

Ha: Alternative Hypothesis: (The broken bones will take longer to heal among smokers versus nonsmokers. ) (Claim)

(2)

Degrees of Freedom = 20 + 45 - 2 = 63

Our degrees of freedom = 63

(3)

n1 = 20

n2 = 45

1 = 32

2 = 21

Pooled Standard Deviation is given by:

Our estimated standard error = 1.638

(4)

Test Statistic isgiven by:

Our t test statistic = 6.716

(5)

= 0.05'

From Table, critical value of t = 1.669

Our critical t value = 1.669

(6)

Correct option:

Yes

(7)

Cohen's d is given by:

Cohen’s d for the difference in healing time = 1.8051