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 23 people who drank ethanol and another group of 23 people given a placebo. The errors for the treatment group have a standard deviation of 2.30, and the errors for the placebo group have a standard deviation of 0.76. Use a 0.05 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. Identify the test statistic = (Round to two decimal places as needed.) Use technology to identify the P-value = (Round to three decimal places as needed.)
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Step 1
Let $\sigma_1$ be the standard deviation of errors for the treatment group and $\sigma_2$ be the standard deviation of errors for the placebo group. Null Hypothesis: $H_0: \sigma_1^2 = \sigma_2^2$ Alternative Hypothesis: $H_1: \sigma_1^2 > \sigma_2^2$ Show more…
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Test the given claim. 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 22 people who drank ethanol and another group of 22 people given a placebo. The errors for the treatment group have a standard deviation of $2.20,$ and the errors for the placebo group have a standard deviation of 0.72 (based on data from "Effects of Alcohol Intoxication on Risk Taking. Strategy, and Error Rate in Visuomotor Performance," by Streufert et al., Joumal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.
Inferences from Two Samples
Two Variances or Standard Deviations
An experiment was conducted to test the effects of alcohol. Researchers measured the breath alcohol levels for a treatment group of people who drank ethanol and another group given a placebo. The results are given in the accompanying table. Use a 0.05 significance level to test the claim that the rwo sample groups come from populations with the same mean. The given results are based on data from "Effects of Alcohol Intoxication on Risk Taking, Strategy, and Error Rate in Visuomotor Performance," by Streufert, et al., Journal of Applied Psychology VoL 77, No. 4. Treatment Group: $\quad n_{1}=22 \quad \bar{x}_{1}=0.049 \quad s_{1}=0.015$ Placebo Group: $n_{2}=22 \quad \bar{x}_{2}=0.000 \quad s_{2}=0.000$
Inference From Two Samples
Inferences About Two Means: Independent Samples
In clinical experiments involving different groups of independent samples, it is important that the groups be similar in the important ways that affect the experiment. In an experiment designed to test the effectiveness of paroxetine for treating bipolar depression, subjects were measured using the Hamilton depression scale with the results given below (based on data from "Double-Blind, Placebo-Controlled Comparison of Imipramine and Paroxetine in the Treatment of Bipolar Depression," by Nemeroff et al., American Journal of Psychiatry, Vol. 158, No. 6 ). Using a 0.05 significance level, test the claim that both populations have the same standard deviation. Based on the results, does it appear that the two populations have different standard deviations? Placebo group: $\quad n=43, \bar{x}=21.57, s=3.87$ Paroxetine treatment group: $\quad n=33, \bar{x}=20.38, s=3.91$
Comparing Variation in Two Samples
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