Question

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 (left column) Post-1964 (right column) 6.2774 5.7014 6.2358 5.7475 6.1502 5.7018 5.9989 5.5945 6.1266 5.7258 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 6.1648 5.5728 6.2683 5.5571 6.2727 5.5877 6.1944 5.6873 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 6.1726 5.6022 6.3267 5.6012 a) Let the weights of pre-1964 quarters represent population 1. Let the weights of post-1964 quarters represent population 2. What are the null and alternative hypotheses? b) Identify the test statistic: c) Identify the p-value: d) Compare the p-value: e) Compare the p-value with the given significance level, α=0.05, to determine whether or not to reject the null hypothesis. Reject H0 if the p-value is less than or equal to the significance level α. Fail to reject H0 if the p-value is greater than α. Interpret the result in terms of the original claim.

          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 (left column)    Post-1964 (right column)
6.2774    5.7014
6.2358    5.7475
6.1502    5.7018
5.9989    5.5945
6.1266    5.7258
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
6.1648    5.5728
6.2683    5.5571
6.2727    5.5877
6.1944    5.6873
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
6.1726    5.6022
6.3267    5.6012

a) Let the weights of pre-1964 quarters represent population 1. Let the weights of post-1964 quarters represent population 2.
What are the null and alternative hypotheses?
b) Identify the test statistic:
c) Identify the p-value:
d) Compare the p-value:
e) Compare the p-value with the given significance level, α=0.05, to determine whether or not to reject the null hypothesis. Reject H0 if the p-value is less than or equal to the significance level α. Fail to reject H0 if the p-value is greater than α. Interpret the result in terms of the original claim.

Added by Joaquin C.

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