You are trying to reduce the variance in a key characteristic of one of your pro
ID: 3385266 • Letter: Y
Question
You are trying to reduce the variance in a key characteristic of one of your products. The data given 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
25.54577 25.67327 23.50771 23.86543 23.42485 24.81563 25.1212 24.30567 27.54136 24.9152 25.45593 23.34938 26.44874 27.30754 24.70758 24.58797 24.49469 23.2799 21.1739 26.01773 24.74459 27.75141 24.69975 25.60878 24.07189 25.24285 27.35402 24.66639 23.39427 27.38071 24.51747 26.07484 23.45714 23.60644 26.27789 25.42054 26.17935 23.55516 25.19157 27.08357 26.09361 22.75457 25.57301 26.29129 24.75137 26.03199 25.05291 25.5516 27.43376 26.48897 23.91109 26.68481 23.35028 25.91504 27.21022 24.53085 23.42229 23.50098 26.10368 24.0603 25.33961 25.57939 25.21537 24.04842 28.30589 24.53672 24.10033 24.90996 23.73595 26.02011 23.48726 24.85433 29.80506 24.62203 24.54368 24.16696 22.40298 24.12955 24.72677 23.39158 23.00081 26.72716 25.04782 24.93902 25.05025 24.93112 25.05267 24.92321 25.05509 24.91531 25.05751 24.90741 25.05993 24.8995Explanation / Answer
Var(A) = 2.4675
Var(B)= 1.4065
n1=n2 = 47
Use F test to compare the variances
F = s1^2/s2^2 = 1.754
df = n1-1, n2-1 = 46,46
Set up hypotheses as:
H0: Var A = Var B
Ha: Var A>Var B
Right tailed test
p = 0.0299
At 5% sign level alpha = 0.05
As p <alpha, reject null hypothesis
Variance B is less than variance A is statistically evident at 5% sign level,.
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