The accompanying data table includes weights​ (in grams) of a simple random sample of 40 quarters made before 1964 and weights of 40 quarters made after 1964. When designing coin vending​ machines, the standard deviations of​ pre-1964 quarters and​ post-1964 quarters must be considered. Use the​ Levene-Brown-Forsythe test and a 0.05 significance level to test the claim that the weights of​ pre-1964 quarters and the weights of​ post-1964 quarters are from populations with the same standard deviation. Pre-1964 Post-1964 6.2782 5.7072 6.2364 5.7445 6.1512 5.7021 5.9996 5.5994 6.1278 5.7267 6.2151 5.6114 6.2866 5.6160 6.0760 5.5999 6.1426 5.7790 6.3415 5.6841 6.1309 5.6234 6.2412 5.5928 6.1442 5.6486 6.1073 5.6661 6.1181 5.5361 6.1352 5.5491 6.2821 5.7239 6.2647 5.6555 6.2908 5.6063 6.1657 5.5713 6.2684 5.5626 6.2722 5.5895 6.1939 5.6874 6.2465 5.6274 6.3172 5.6157 6.1487 5.6668 6.0829 5.7198 6.1423 5.6694 6.1970 5.5454 6.2441 5.6646 6.3669 5.5636 6.0775 5.6485 6.1095 5.6703 6.1787 5.6848 6.2130 5.5609 6.1947 5.7344 6.1940 5.6449 6.0257 5.5804 6.1704 5.6033 6.3273 5.6032 =/= Identify the test statistic.   ​(Round to three decimal places as​ needed.)   Identify the​ P-value.   ​(Round to four decimal places as​ needed.)   What is the conclusion for this​ test?   (reject/fail to reject) H0. There (is/is not) sufficient evidence to warrant rejection of the claim that the variation among weights of quarters made after 1964 is the same as the variation among weights of quarters made before 1964.

The accompanying data table includes weights​ (in grams) of a simple random sample of 40 quarters made before 1964 and weights of 40 quarters made after 1964. When designing coin vending​ machines, the standard deviations of​ pre-1964 quarters and​ post-1964 quarters must be considered. Use the​ Levene-Brown-Forsythe test and a 0.05 significance level to test the claim that the weights of​ pre-1964 quarters and the weights of​ post-1964 quarters are from populations with the same standard deviation.

Pre-1964 Post-1964
6.2782 5.7072
6.2364 5.7445
6.1512 5.7021
5.9996 5.5994
6.1278 5.7267
6.2151 5.6114
6.2866 5.6160
6.0760 5.5999
6.1426 5.7790
6.3415 5.6841
6.1309 5.6234
6.2412 5.5928
6.1442 5.6486
6.1073 5.6661
6.1181 5.5361
6.1352 5.5491
6.2821 5.7239
6.2647 5.6555
6.2908 5.6063
6.1657 5.5713
6.2684 5.5626
6.2722 5.5895
6.1939 5.6874
6.2465 5.6274
6.3172 5.6157
6.1487 5.6668
6.0829 5.7198
6.1423 5.6694
6.1970 5.5454
6.2441 5.6646
6.3669 5.5636
6.0775 5.6485
6.1095 5.6703
6.1787 5.6848
6.2130 5.5609
6.1947 5.7344
6.1940 5.6449
6.0257 5.5804
6.1704 5.6033
6.3273 5.6032

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