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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 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.)
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Answer

\(\boxed{7.96}\)

Steps

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 :\(\boxed{7.96}\)

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