You are testing the claim that smiling, rather than remaining neutral, during a court proceding will lead to a different punishment from the judge (abstract). A sample of 34 people who smiled during their hearing and 34 people who kept neutral facial expressions during their hearing is given below. The values are a measure of how lenient the judgments were. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the leniency scores are normally distributed. Give answers to 3 decimal places. Data available at StatKey Smile (x1x1) Neutral (x2x2) 7 2 3 4 6 4 4.5 3 3.5 6 4 4.5 3 2 3 6 3.5 3 4.5 3 7 4.5 5 8 5 4 7.5 5 2.5 3.5 5 4.5 5.5 6.5 5.5 3.5 5 4.5 4 4.5 5 2.5 6.5 2.5 6.5 4.5 7 2.5 3.5 6 5 6 3.5 2 9 4 2.5 5.5 8.5 4 3.5 2.5 4.5 2.5 3.5 3 4.5 6.5
You are testing the claim that smiling, rather than remaining neutral, during a court proceding will lead to a different punishment from the judge (abstract). A sample of 34 people who smiled during their hearing and 34 people who kept neutral facial expressions during their hearing is given below. The values are a measure of how lenient the judgments were. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the leniency scores are
Data available at StatKey
| Smile (x1x1) | Neutral (x2x2) |
|---|---|
| 7 | 2 |
| 3 | 4 |
| 6 | 4 |
| 4.5 | 3 |
| 3.5 | 6 |
| 4 | 4.5 |
| 3 | 2 |
| 3 | 6 |
| 3.5 | 3 |
| 4.5 | 3 |
| 7 | 4.5 |
| 5 | 8 |
| 5 | 4 |
| 7.5 | 5 |
| 2.5 | 3.5 |
| 5 | 4.5 |
| 5.5 | 6.5 |
| 5.5 | 3.5 |
| 5 | 4.5 |
| 4 | 4.5 |
| 5 | 2.5 |
| 6.5 | 2.5 |
| 6.5 | 4.5 |
| 7 | 2.5 |
| 3.5 | 6 |
| 5 | 6 |
| 3.5 | 2 |
| 9 | 4 |
| 2.5 | 5.5 |
| 8.5 | 4 |
| 3.5 | 2.5 |
| 4.5 | 2.5 |
| 3.5 | 3 |
| 4.5 | 6.5 |
What are the correct hypotheses? Note this may view better in full screen
H0: Select an answer σ² μ₁ p x̅₂ s² μ₂ x̅₁ ? < ≠ ≥ ≤ = > Select an answer 0 p x̅₁ μ₂ s² μ₁ x̅₂ σ²
Ha: Select an answer p s² σ² x̅₂ x̅₁ μ₁ μ₂ ? > < ≤ = ≠ ≥ Select an answer 0 μ₂ s² σ² x̅₂ p μ₁ x̅₁
Based on the hypotheses, find the following:
Difference in means from Ha =
p-value =
The correct decision is to Select an answer accept the alternative hypothesis reject the null hypothesis accept the null hypothesis do not reject the null hypothesis reject the claim .
The correct summary would be: Select an answer There is enough evidence to reject the claim... There is not enough evidence to support the claim... There is not enough evidence to reject the claim... There is enough evidence to support the claim that there is a difference in leniency when smiling over being neutral when in trouble.
LeFrance, M. and Hecht, M.A., "Why Smiles Generate Leniency", Personality and Social Psychology Bulletin. 1995; 21:207-204. abstract
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