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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

Expert avatar
Jon
4.6
110 Answers
1. Hypotheses:

- Null hypothesis H_0: \sigma_1^2 = \sigma_2^2

- Alternative hypothesis H_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, with df_1 = 26 and df_2 = 20: 2.829

4. Decision Rule:

- If F > 2.829, reject H_0.

- Else, do not reject H_0.

5. Conclusion:

- Since 1.329 < 2.829, do not reject H_0.

- Therefore, no sufficient evidence to support that the treatment group has more variability.

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