Professor Smriti Tiwari

EC$-237$: Statistical Methods

Assignment $5$: Due before class on Tuesday, $11/12/2024$

ABCs of Paint and Paint & Stain, Inc. are two large paint supply companies. Table $1$ below provides salary data regarding a sample of management$-$level employees for the two companies for the current fiscal year.

Table $1.$ Salary Data by Company

$\backslash$table$[[,$ABCs of Paint,Paint & Stain, Inc.$],[$Sample Size,$72,50],[$Sample Mean $($in $$1,000),48,43],[$Sample Standard Deviation $($in $$1,000),12,10]]$

a$.$ Suppose that you are a human resources analyst at Paint & Stain, Inc. According to company policy, the average management$-$level salary should not be more than $120\%$ of the average hourly, non$-$management employee annual wage. A recent census by union representatives shows that hourly, non$-$management employees at Paint & Stain, Inc. earned $$35,000$ on average this year. If the union files a complaint based upon this information, how would you respond based upon a statistical analysis? What is your evidence? Explain.

b$.$ Again, assume that you are a human resource analyst at Paint & Stain, Inc. One of your colleagues has asserted, based upon the information in the table above, that the department should suggest a salary increase in order to remain competitive against ABCs of Paint for quality employees. Do you agree? Provide and explain your evidence. Assume dof$=115.$

$2.$ Suppose you are helping out a friend in the purchasing department at Paint & Stain, Inc. who is trying to determine whether to buy Paint Sprayer A or B$.$ The company has leased the two machines for a month. A random sample of $5$ employees has been taken. These employees have gone through a training session on both machines. In Table $2$ below you are given information on their productivity rate on both machines. $($Let the difference $d=$ Sprayer A $-$ Sprayer B$.)$

Table $2.$ Mroductivity by Sprayer Type by Employee

$\backslash$table$[[,,],[$Person$,$Sprayer $A,$Sprayer $B$