Problem
Part 2 of 4 points Points: 0.25 of 1 Save 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 21 people who drank ethanol and another group of 21 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 0.78 . Assume that the two populations are normally distributed. Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors. Identify the test statistic. (Round to two decimal places as needed.) example Get more help - Clear all Check answer
Solution
Step 1 ：Calculate the variance for the treatment group by squaring the standard deviation: \( \text{variance}_{\text{treatment}} = 2.2^2 = 4.84 \)
Step 2 ：Calculate the variance for the placebo group by squaring the standard deviation: \( \text{variance}_{\text{placebo}} = 0.78^2 = 0.6084 \)
Step 3 ：Calculate the test statistic by dividing the variance of the treatment group by the variance of the placebo group: \( \text{test statistic} = \frac{4.84}{0.6084} = 7.955292570677186 \)
Step 4 ：Round the test statistic to two decimal places: \( \text{test statistic rounded} = 7.96 \)
Step 5 ：\(\boxed{7.96}\)
