You are trying to reduce the variance in a key characteristic of one of your pro

Question

You are trying to reduce the variance in a key characteristic of one of your products. The data provides this characteristic for the current process (Column A) and a proposed improvement (Column B).
Prove if the proposed improvement reduces the variance in this key characteristic (95% confidence level).

A B 35.16515 38.38583 36.98549 39.76428 38.79151 40.38381 41.68407 41.9528 42.2622 42.1817 43.91782 42.86832 44.79233 43.10957 45.37124 43.26792 45.54966 44.36189 45.84619 44.8632 46.47914 44.97602 46.7756 45.29417 47.57606 45.59981 47.59831 45.96901 47.77016 46.13602 47.90537 46.52395 47.9964 46.57033 48.39685 47.06566 48.41931 47.53636 48.46 47.83135 48.54113 48.07144 48.92611 48.11763 49.14567 49.06578 49.21216 49.64195 49.25071 49.83526 49.38368 49.98726 49.41853 50.10298 49.85429 50.10678 49.89571 50.18645 50.15396 50.42476 50.29606 50.45771 50.30609 50.67484 50.33178 50.73182 50.58068 50.99201 52.75497 51.05708 52.84549 51.07034 52.85701 51.40231 52.90761 51.44312 53.17474 51.85632 53.61288 52.19431 53.95807 52.72107 54.06522 53.59983 54.55867 53.62924 55.04093 53.73043 55.05138 55.7445 55.09178 55.93301 56.11327 55.99129 56.56631 56.32652 57.05114 57.94986 58.01208 58.95599

Explanation / Answer

alternate hypotheiss

H1:

we go for F-test and F= S12/S22=23.72/22.09=1.0738 with df (49,49) with F-distribution

critical region

critical F=F(.05,49,49)=1.6073 , since critical F is less than the Calculated F=1.0738 therefor we reject null hypothesis and conclude that proposed improvement reduces the variance in this key characteristic with 95% confidence level

null hypothesis H0: 12 = 22

alternate hypotheiss

H1:

12>22     for an upper one-tailed test

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