Question

A production plant has two complex fabricating systems, both of which are maintained at 2-week intervals. However, one system is twice as old as the other. The number of finished products fabricated daily by each of the systems is recorded for 30 working days, with the results given in the table. Do these data present sufficient evidence to conclude that the variability in daily production warrants increased maintenance of the older fabricating system? Use the p-value approach. (Use a = 0.05.) Old System *1 = 237 51 = 28.1 New System X2 = 246 S2 = 15.7 State the null and alternative hypotheses. o Hp: 0,2 = 0, versus Hy: 0> 0? O Ho: 0,2 = 0,22 versus H2:02+02? O Ho: 0,2 +022 versus H0,2 = 022 O Ho: 0,2 <022 versus H : 072>03? o Hp: 0,2 = 02? versus Hy: 0;? <0? State the test statistic. (Round your answer to two decimal places.) F= State the p-value. O p-value < 0.005 O 0.005 <p-value < 0.010 O 0.010 < p-value < 0.025 O 0.025 <p-value < 0.050 O 0.050 <p-value < 0.100 O p-value > 0.100 State the conclusion. O H , is rejected. There is sufficient evidence to conclude that the variability warrants increased maintenance of the older system. OH, is rejected. There is insufficient evidence to conclude that the variability warrants increased maintenance of the older system. O H, is not rejected. There is insufficient evidence to conclude that the variability warrants increased maintenance of the older system. O H, is not rejected. There is sufficient evidence to conclude that the variability warrants increased maintenance of the older system. You may need to use the appropriate appendix table or technology to answer this question.

Answer 1

The null and alternative Hypotheses: Ho: 01=02 versus Hz: 01> o The test statistic is: F= * = (25:7)2 = 3.20 The p-value is 0.0012 Answer: P-value < 0.005 Conclusion: Ho is rejected. There is sufficient evidence to conclude that the variability warrants increased maintenance of the older system.