A manufacturing company designed a Factorial Experiment to determine whether the number of defective parts produced by two machines (the "Sample" row in the ANOVA table) differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system (the "Columns" row in the ANOVA table). Assuming that alpha is 0.05, and looking at the information in the "Columns" row in the ANOVA table, #1, would you Reject or Fail to Reject the Null hypothesis that the two Loading Methods produce the same average number of defective parts? And, #2, EXPLAIN specifically what you used in the ANOVA table to arrive at your decision. ANOVA Source of Variation SS df MS F P-value Sample 52.08333333 1 52.08333333 12.25490196 0.008070795 Columns 4.083333333 1 4.083333333 0.960784314 0.355697954 Interaction 18.75 1 18.75 4.411764706 0.068892487 Within 34 8 4.25 Total 108.9166667 11
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A manufacturing company designed a Factorial Experiment to determine whether the number of defective parts produced by two machines (the "Sample" row in the ANOVA table) differed and if the number of defective parts produced also depended on whether the raw material needed by each machine was loaded manually or by an automatic feed system (the "Columns" row in the ANOVA table). Assuming that alpha is 0.05, and looking at the information in the "Columns" row in the ANOVA table,
#1, would you Reject or Fail to Reject the Null hypothesis that the two Loading Methods produce the same average number of defective parts? And,
#2, EXPLAIN specifically what you used in the ANOVA table to arrive at your decision.
ANOVA
Source of Variation SS df MS F P-value
Sample 52.08333333 1 52.08333333 12.25490196 0.008070795
Columns 4.083333333 1 4.083333333 0.960784314 0.355697954
Interaction 18.75 1 18.75 4.411764706 0.068892487
Within 34 8 4.25
Total 108.9166667 11
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