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

Given

Sample size

For smokers = 20

Non smokers = 45

The average time to heal was 32 days (SS = 1161)

The average time to heal was 21 days (SS = 1179)

1)

Ha: Alternative Hypothesis: ₁ > ₂

(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 is given by:

Our t test statistic = 6.716

5)

At = 0.05

From Table, critical value of t = 1.669

Our critical t value = 1.669

6)

Yes , the difference in healing time between smokers and nonsmokers statistically significant

7)

Cohen's d is given by:

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

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