The data refer to 5 suppliers of the Levi-Strauss clothing manufacturing plant in Albuquerque. The firm's quality control department collects weekly data on percentage waste y (run-up). The sample means (ỹ;) and sample standard deviations s, are given in the JMP output below (last table) for each supplier (labeled as 1, 2, 3, 4, 5). Response Run-Up Residual by Predicted Plot Oneway Analysis of Run-Up By Supplier Plant Number 20 25 15 10 20 15 -10 -15 10 -20 -25 -15 -10 -5 10 15 20 25 Run-Up Predicted Residual Normal Quantile Plot 20 -10 15 -15 10 Supplier Plant Number • Oneway Anova * Analysis of Variance Sum of Squares Mean Square 544.6349 F Ratio Prob >F 0.0084 Source DF Supplier Plant Number Error 136.159 37.236 3.6566 -5 88 3276.7896 92 3821.4245 C. Total Means and Std Deviations -10 Std Err Mean Lower 96% Upper 95% Level Number Mean Std Dev -15 21 2.7047619 5.4155772 1.1817758 0.2396207 5.1699031 21 5.9095238 7.0884346 1.5468232 19 4.8315789 4.4031621 1.0101547 2.6829071 9.1361405 -20 2.7093228 6.9538351 19 7.4894737 3.6570928 0.8389946 5.7268114 9.252136 13 10.376923 9.5550296 2.6500884 4.6028765 16.15097 Normal Quantle --- ... S0'0 L00 empe dn-unu empsy dn-uny dn-ure
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
See the attached image for the introduction.
Based on the JMP outputs and plots above, make comments on the appropriateness of assumptions for the one-way ANOVA model.
• Constant variance:
• Normality:
Assumptions of the one-way ANOVA model:
Normality:
The data in the population or the populations from which the samples are selected are normally distributed.
Independence within groups:
Independence within groups means that the participants are independently observed within groups is made but not between groups.
Homogeneity of variance:
Homogeneity of variance means that the variance in each population is the same as the other populations.
Homogeneity of covariance:
Homogeneity of covariance means that the participant scores in each group are related.
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