9-4 Two Variances or Standard Deviations 487 3. Test for Normality For the hypothesis test described in Exercise 2, the sample sizes are n1 = 2208 and n2 = 1986. When using the F test with these data, is it correct to reason that there is no need to check for normality because both samples have sizes that are greater than 30? 4. Robust What does it mean when we say that the F test described in this section is not robust against departures from normality? In Exercises 5–16, test the given claim. 5. Minting of Quarters Before 1964, quarters were 90% silver and 10% copper. After 1964, quarters were made with a copper-nickel alloy. Using the data from Data Set 40 “Coin Weights” we get the statistics shown below. Use a 0.05 significance level to test the claim that the variation of weights before 1964 is greater than the variation of weights after 1964. If that claim is supported, what is an advantage of the change? Before 1964: n = 40, s = 0.086995 g After 1964: n = 40, s = 0.061937 g 6. Minting of Pennies Before 1983, pennies were 97% copper and 3% zinc, but after 1983 they are 3% copper and 97% zinc. Using the data from Data Set 40 “Coin Weights” we get the statistics shown below. Use a 0.05 significance level to test the claim that the variation of weights before 1983 is greater than the variation of weights after 1983. If that claim is supported, what is an advantage of the change? Before 1983: n = 35, s = 0.03910 g After 1983: n = 37, s = 0.01648 g 7. Color and Creativity Researchers from the University of British Columbia conducted trials to investigate the effects of color on creativity. Subjects with a red background were asked to think of creative uses for a brick; other subjects with a blue background were given the same task. Responses were scored by a panel of judges and results from scores of creativity are given below. Use a 0.05 significance level to test the claim that creative task scores have the same variation with a red background and a blue background. Red Background: n = 35, x = 3.39, s = 0.97 Blue Background: n = 36, x = 3.97, s = 0.63 8. Color and Recall Researchers from the University of British Columbia conducted trials to investigate the effects of color on the accuracy of recall. Subjects were given tasks consisting of words displayed on a computer screen with background colors of red and blue. The subjects studied 36 words for 2 minutes, and then they were asked to recall as many of the words as they could after waiting 20 minutes. Results from scores on the word recall test are given below. Use a 0.05 significance level to test the claim that variation of scores is the same with the red background and blue background. Accuracy Scores Red Background: n = 35, x = 15.89, s = 5.90 Blue Background: n = 36, x = 12.31, s = 5.48 9. Testing Effects of Alcohol 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., Journal of Applied Psychology, Vol. 77, No. 4). Use a 0.05 significance level to test the claim that both groups have the same amount of variation among the errors.
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