ABC, Inc. is undergoing scrutiny for a possible wage discrimination suit. The following data is available: SALARY(monthly salary for each employee $), YEARS (years with the company), POSITION (position with company coded as: 1 = manual labor 2 = secretary 3 = lab technician 4 = chemist 5 = management EDUCAT (amount of education completed coded as: 1 = high school degree 2 = some college 3 = college degree 4 = graduate degree), GENDER (employee gender).

1. Using the selected model (i.e., “best” model) answer the following: a) Briefly summarize (present & calculate) the descriptive statistics of the data b)Interpret and evaluate the model coefficients for the management team and corporate lawyer of ABC, Inc. c) Test for significance of relationships (both individually and jointly for the overall model). Use a 10% level of significance. Please note if you are performing a two-tailed test or one-tailed test and justify. d) Demonstrate how ABC, Inc., could use the model for predicting employee salary. Include a sample computation. e) Verify model assumptions (e.g., residual plots) f) Identify any potential problems with the data or model & briefly discuss. g) Explicitly answer: Should ABC, Inc. be worried about possible wage discrimination charges? Deliberate about what additional variables to consider for the model.

Joseph Biggs owns his own ice cream truck an drives 30 miles from a florida beach resort. The sale of his products is higly dependent oh his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather.

A) Construct Joseph's decision tree.

B) What is the decision recommended bat the expected value criterion?

Spartan utilities distributes natural gas to households in South-West Michigan. Spartan has 25,000 miles of retail gas distribution pipelines. The distribution pipelines sometimes develop leaks due to weather conditions and corrosion. Spartan estimates that the probability of a gas pipeline developing a leak is 0.0002/year/mile of pipeline. Spartan also estimates that an average leaking pipe incident results in $10,000 in repair costs, $5,000 in natural gas lost, $8,000 in compensation to affected parties, $2,000 in other costs such as evacuation, fire safety, public notification etc. Further, the disruption in service results in loss of sales of $20,000 on which Spartan would have earned profits of $4000.

a. Estimate the expected annual cost to Spartan of such leakage.

b. Suppose an insurance company offer to cover all costs of such leaks except lost sales/profits. The premium is $130,000. Should Spartan utilities buy the insurance?

c. What other risk management options can Spartan consider in managing this risk?

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

state null and alternative hypotheses, critical value, test statistic and make TWO definitive conclusion statements.

Simple Linear Regression Analysis

2. Weight of Car: Miles gallon – Do heavier cars really use more gasoline? The following data were obtained from Consumer Reports (Vol 62 no. 4). Weight of car is in hundreds of pounds.

Car Weight 27 44 32 47 23 40 34 52
MPG 30 19 24 13 29 17 21 14

A simple linear regression of the model MPG = b0 + b1 WEIGHT
The results are shown below:

MPG & CAR WEIGHT
REGRESSION FUNCTION & ANOVA FOR MPG

MPG = 43.32625 - 0.600702 WEIGHT

R-Squared = 0.895426
Adjusted R-Squared = 0.877997
Standard error of estimate = 2.236055
Number of cases used = 8


Analysis of Variance

p-value
Source SS df MS F Value Sig Prob
Regression 256.87 1 256.87 51.37567 0.000372
Residual 29.99 6 4.99
Total 286.875 7

MPG & CAR WEIGHT
REGRESSION COEFFICIENTS FOR MPG

Two-Sided p-value
Variable Coefficient Std Error t Value Sig Prob
Constant 43.32625 3.23051 13.41156 0.000011
WEIGHT -0.60070 0.08381 -7.16768 0.000372 *

Standard error of estimate = 2.236055
Durbin-Watson statistic = 0.995097

Questions:

1. What sort of relationship exists between MPG and car weight?

2. Does the relationship make sense to you? Why or why not?

3. Test the hypotheses H0: b1 = 0 against H A: b1 ?0 a level of significance ? = 0.01. What is your conclusion?

MODEL: MPG= b0 + b1 WEIGHT

H0: b1 = 0

H A: b1 ? 0

4. What is your conclusion?

An automobile manufacturer has given its van a 47.1 47.1 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van performs under the manufacturer's MPG rating. After testing 140 140 vans, they found a mean MPG of 46.9 46.9 . Assume the population variance is known to be 4.41 4.41 . Is there sufficient evidence at the 0.02 0.02 level to support the testing firm's claim? Step 4 of 6 : Find the P-value of the test statistic. Round your answer to four decimal places.

Engineers are testing company fleet vehicle fuel economy (miles per gallon) performance by using different types of fuel. One vehicle of each size is tested. Does this sample provide sufficient evidence to conclude that there is a significant difference in treatment means?

  Click here for the Excel Data File

(a) Choose the correct statement.

• Fuel type is the blocking factor and vehicle size is the treatment.

• Fuel type is the treatment and vehicle size is the blocking factor.

(b) Fill in the boxes. (Round your SS values to 3 decimal places, F values to 2 decimal places, and other answers to 4 decimal places.)

(c) Choose the correct statement. Use α = 0.05.

• Fuel type means differ significantly and vehicle size is also a significant factor.

• Fuel type means do not differ significantly, but vehicle size is a significant factor.

• Fuel type means differ significantly, but vehicle size is not a significant factor.

• Fuel type means do not differ significantly and vehicle size is not a significant factor.

(d) Which fuel types show a significant difference in average fuel economy? Use α = 0.05. (You may select more than one answer. Click the box with a check mark for the correct answer and click to empty the box for the wrong answer.)

• Ethanol 10% and 87 Octane

• Ethanol 5% and 89 Octane

• 87 Octane and 91 Octane

• Ethanol 10% and 91 Octane

An automobile manufacturer has given its jeep a 31.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep performs under the manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 31.5. Assume the population standard deviation is known to be 1.8. Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Find the value of the test statistic. Round your answer to two decimal places.Specify if the test is one-tailed or two-tailed.

Find the P-value of the test statistic. Round your answer to four decimal places.

Identify the level of significance for the hypothesis test.

Make the decision to reject or fail to reject the null hypothesis.

An automobile manufacturer has given its jeep a 30.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this jeep since it is believed that the jeep has an incorrect manufacturer's MPG rating. After testing 110 jeeps, they found a mean MPG of 30.5 . Assume the population variance is known to be 3.61 . Is there sufficient evidence at the 0.05 level to support the testing firm's claim?

Step 1: state the null & alternative hypothesis

Step 2 : Find the value of the test statistic. Round your answer to two decimal places.

Step 3: specify if it is a one or two tailed

step 4: find the p value of the test statistic

step 5: identify the level of significance of the hypothesis test

step 6: reject or fail to reject the hypothesis Please circle answers so I can follow steps properly

Fuel consumption is commonly measured in miles per gallon​ (mi/gal). An agency designed new fuel consumption tests to be used starting with 2008 car models. Listed below are randomly selected amounts by which the measured MPG ratings decreased because of the new 2008 standards. Find the​ range, variance, and standard deviation for the sample data. Is the decrease of 4​ mi/gal unusual? Why or why​ not?

22    

11    

33    

22    

44    

11    

33    

22    

22    

22    

22    

22    

11    

22    

22    

22    

11    

22    

22    

22

The range of the sample data is

nothing

​mi/gal. ​(Type an integer or a​ decimal.)The variance of the sample data is

nothing.

​(Round to one decimal place as​ needed.)The standard deviation of the sample data is

nothing

​mi/gal.

​(Round to one decimal place as​ needed.)

Is the largest​ decrease, 4​ mi/gal,

unusual​?

Why or why​ not?

A.

The decrease of 4​ mi/gal is unusual because the smallest value in a data set is usually an outlier.  

B.

The decrease of 4​ mi/gal is not unusual because the sample is a simple random​ sample, in which no values are considered unusual.

C.The decrease of 4​ mi/gal is

unusualunusual

because it is

more thanmore than

two standard deviations

fromfrom

the mean.

D.The decrease of 4​ mi/gal is

not unusualnot unusual

because it is

withinwithin

two standard deviations

ofof

the mean.