Question
Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 27 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 0.98, and the errors for the placebo group have a standard deviation of 0.85. Use a 0.01 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed. Sample 1: treatment group, n1 = 27, s1 = 0.98. Sample 2: placebo group: n2 = 21, s2 = 0.85
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Answer to a math question Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 27 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 0.98, and the errors for the placebo group have a standard deviation of 0.85. Use a 0.01 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed. Sample 1: treatment group, n1 = 27, s1 = 0.98. Sample 2: placebo group: n2 = 21, s2 = 0.85
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4.679 Answers
1. Hypotheses:
- Null hypothesisH_0 \sigma_1^2 = \sigma_2^2
- Alternative hypothesisH_a \sigma_1^2 > \sigma_2^2
2. Test Statistic:
- Calculated F-statistic:F = \frac{s_1^2}{s_2^2} = 1.329
3. Critical Value:
- From F-distribution table at\alpha = 0.01 df_1 = 26 df_2 = 20
4. Decision Rule:
- IfF H_0
- Else, do not rejectH_0
5. Conclusion:
- Since 1.329 < 2.829, do not rejectH_0
- Therefore, no sufficient evidence to support that the treatment group has more variability.
- Null hypothesis
- Alternative hypothesis
2. Test Statistic:
- Calculated F-statistic:
3. Critical Value:
- From F-distribution table at
4. Decision Rule:
- If
- Else, do not reject
5. Conclusion:
- Since 1.329 < 2.829, do not reject
- Therefore, no sufficient evidence to support that the treatment group has more variability.
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