IE533_HW3 - Ashwath Kumar

.pdf

School

Purdue University *

*We aren’t endorsed by this school

Course

533

Subject

Industrial Engineering

Date

May 1, 2024

Type

pdf

Pages

5

Uploaded by DrHeron283

Ashwath Kumar – IE533 HW#3 1 Question 1) Use the data set provided on Brightspace (HW 3 Problem 1) to perform an ANOVA, check the assumptions and indicate if there is any reason to do a nonparametric test ( include plot supporting your decision). Regardless of your decision, fit a Kruskal-Wallis test to the data. Include the ANOVA table and the Kruskal-Wallis output. What do you conclude about the impact of storage medium on tastiness with respect to the output and assumption checks? Answer 1) Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Storage Medium 2 1460 729.94 8.93 0.001 Error 27 2206 81.72 Total 29 3666 The residual plots, except for the histogram, indicate that the data closely adheres to a normal distribution. As a result, in an ideal situation, a non-parametric test may not be required. However, it is still viable to conduct further hypothesis testing based on the median using nonparametric analysis, such as the Kruskal-Wallis method. Kruskal-Wallis: Descriptive Statistics Storage Medium N Median Mean Rank Z-Value Foil 10 81.0737 18.4 1.28 Jar 10 80.9010 19.4 1.72 Pouch 10 66.0452 8.7 -2.99 Overall 30 15.5
Ashwath Kumar – IE533 HW#3 2 Test Null hypothesis H₀: All medians are equal Alternative hypothesis H₁: At least one median is different DF H-Value P-Value 2 9.01 0.011 In conclusion, both the ANOVA and Kruskal-Wallis methods yield p-values below 5%. Thus, we can reject the null hypothesis and assert that there is a significant relationship between the storage medium and tastiness. Question 2 ) (1.25 Point) Generate a data set to mimic the location tag experiment from lecture.Use the following generating distributions to draw 20 observations for each of three locations: Location1 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 ( 𝜆 = 3.2) Location2 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 ( 𝜆 = 5.2) Location3 ~ 𝑃𝑜𝑖𝑠𝑠𝑜𝑛 ( 𝜆 = 11.5) Perform a Mixed Effects Model with a single random effect (location) for the number of items of your brand purchased. Include the ANOVA table , what is your conclusion about the impact of location on the number of buys? What is the value of the Intra-Class Correlation coefficient from your model? What is the variance estimate for location effect? Why is the Standard Error of the location variance so large? Answer 2) Method Variance estimation Restricted maximum likelihood DF for fixed effects Kenward-Roger Factor Information Factor Type Levels Values Location_combined Random 3 Location1, Location2, Location3 Variance Components Source Var % of Total SE Var 95% CI Z-Value P-Value Location_combined 12.854693 66.86% 13.173469 (1.72485, 95.8014) 0.975802 0.165 Error 6.372807 33.14% 1.193736 (4.41455, 9.1997) 5.338539 0.000 Total 19.227500
Ashwath Kumar – IE533 HW#3 3 With a p-value of 0.165, exceeding the 5% threshold, we fail to reject the null hypothesis and conclude that there is insufficient evidence to support a relationship between location and observations (buys). The Intra-Class Correlation coefficient is calculated to be 66.856%. The variance estimate for the location effect is 12.854 , with a large standard error of 13.2. This significant standard error is attributed to the wide range of deviation among observations, ranging from 3.2 to 11.5, when comparing location and the number of buys. This broader spread of observations leads to an increase in the standard error variance. Questions 3) (0.5 Point) Use the data set provided on Brightspace (HW 3 Data Problem 3) to analyze the Randomized Complete Block design as in lecture. Include the ANOVA table , what do you conclude about the impact of tire tread on noise level? Answer 3) Analysis of Variance for Tire Noise Source DF SS MS F P Trailer Batch 7 657.97 93.9956 151.52 0.000 Tread Pattern 3 154.06 51.3543 82.78 0.000 Error 21 13.03 0.6203 Total 31 825.06 In conclusion, with a p-value of 0 , we reject the null hypothesis and affirm that the tread pattern has a significant impact on the noise level. Question 4) (0.5 Point) Using the data from problem 3, check your assumption about no interaction. Include the interaction plot and comment on if the assumption appears to hold. Answer 4) In conclusion, given that the majority of lines in the middle do not exhibit parallel plots to each
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
  • Access to all documents
  • Unlimited textbook solutions
  • 24/7 expert homework help