In an industrial experiment, a job was performed by 10 workers using Method I, and by 7 workers using Method II. The experiment yielded the following data. The unit of measurement is minute. A statistician wants to test for the equality of two variances and the difference in the mean times to complete the job using the two methods. (This is a case of two independent samples drawn from two normal populations). Method 1 Method 2 12 22 19 15 10 16 15 22 26 13 6 10 7 12 6 10 12 n1=10 Mean=17 Variance=26 n2=7 Mean=9 Variance=7 (a) Test at the 5% significance level whether the two variances are equal. (Give null and the alternative hypotheses, test statistic, rejection rule, conclusion) (b) Estimate with 95% confidence the ratio of the two population variances. Briefly describe what the interval estimate tells you. (c) Briefly explain how to use the interval estimate in part (b) to test the hypotheses in (a).
In an industrial experiment, a job was performed by 10 workers using Method I, and by 7 workers using Method II. The experiment yielded the following data. The unit of measurement is minute. A statistician wants to test for the equality of two variances and the difference in the mean times to complete the job using the two methods. (This is a case of two independent samples drawn from two normal populations).
|
Method 1 |
Method 2 |
|
12 |
6 |
|
n1=10 Mean=17 Variance=26 |
n2=7 Mean=9 Variance=7 |
(a) Test at the 5% significance level whether the two variances are equal. (Give null and the alternative hypotheses, test statistic, rejection rule, conclusion)
(b) Estimate with 95% confidence the ratio of the two population variances. Briefly describe what the
(c) Briefly explain how to use the interval estimate in part (b) to test the hypotheses in (a).
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