A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Though the two brands have been comparable in the past, some technological advances were recently made in the Brand 2 manufacturing process, and the consumer group is testing to see if Brand 2 will outperform Brand 1. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1.

According to Wikipedia, the speed of an adult cheetah varies Normally with a mean of 71.5 mph (miles per hour) and a standard deviation of 3.5 mph.

Hint: For each question ask yourself if the question is about the population information or Sampling distribution of sample means.

QUESTIONS BELOW:

1.What is the probability that a randomly chosen cheetah will run faster than 77.77mph? (Draw a picture with relevant values (x,z,p center, spread) and inflection points identified, and an appropriate label to support your full-sentence answer.)

2.What is the probability that a random selection of 16 cheetahs will have an average speed of 77.77 mph or slower? (Draw a picture with relevant values (x,z,p center, spread) and inflection points identified, and an appropriate label to support your full-sentence answer.)

3.How fast does a cheetah have to run to be in the top 10% of fastest cheetahs? (Draw a picture with relevant values (x,z,p center, spread) and inflection points identified, and an appropriate label to support your full-sentence answer.)

4.What is the probability that a random selection of 25 cheetahs will have an average speed between 65 and 80mph? (Draw a picture with relevant values (x,z,p center, spread) and inflection points identified, and an appropriate label to support your full-sentence answer.)

Based on what you observe here, would you recommend changing or keeping the warranty that goes along with this type of tire? If you change it, what would you recommend it to be? You must explain what are the possible pros and cons of your recommendations? While you don't need to do a financial analysis, present some of the costs that you considered in making your decisions. A tire company is testing their mileage warranty of 30,000 miles.

1. Some data gathered by the Department of Education which relates education levels based on

scores: achievement tests given to high school students for example

urban: factor. Is the school located in an urban area?

distance: distance from a 4-year college (in 10 miles)

tuition: average state 4year college tuition (in 1000 USD).

        Coefficients:

               Estimate Std. Error t value Pr(>|t|)    

        (Intercept)  9.141015   0.148905  61.388  < 2e-16 ***

        score        0.095596   0.002679  35.686  < 2e-16 ***

        urbanyes     0.025619   0.057090   0.449   0.6536    

        distance    -0.048723   0.010539  -4.623 3.88e-06 ***

        tuition     -0.142627   0.068517  -2.082   0.0374 *  

        ---

        Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

        Residual standard error: 1.58 on 4734 degrees of freedom

        Multiple R-squared:  0.221,   Adjusted R-squared:  0.2203 

        F-statistic: 335.7 on 4 and 4734 DF, p-value: < 2.2e-16

1. What is the estimated regression equation?
2. What variables are significant?
3. How do you interpret the variable urban (yes/no)?
4. How much of the variance in the model can be explained by the variables that you included?
5. In general what information does VIF regression give you in assessing a model?
6. An output from R shown below, gives the Variance Inflation Factors for your model. What do these numbers tell you?

        score     urban     distance  tuition 

        1.031628  1.105871  1.112577  1.027281 

1. Consider the following data set regarding six company employees who report to the same manager in a local office:

List the column letter(A,B,C,D,E,F) associated with the following questions.

a. Which variables arecategorical (qualitative)? Answer: ___________________

b. Which variables are numerical (quantitative)?Answer: ___________________

c. Which of the variables, if any, arediscrete?     Answer: ___________________

d. Which variables, if any, are continuous?         Answer: ___________________

e. Which variables, if any, requireanIntervalScale? Answer: ________________

f. Which variables, if any, requirean OrdinalScale? Answer: ________________

g. Which variables, if any, requirea NominalScale? Answer: ________________

h. Which variables, if any, requirea Ratio Scale?     Answer: _______________

2.32 The following are the grades that 50 students obtained on an accounting test:

Convert the distribution from classes 30-39, 40-49, 50-59, …, and 90-99 into cumulative “less than” distribution, beginning with “less than 30”.

2.34The following are the miles per gallon obtained with 40 tankful of gas:

Group these figures into a distribution having the classes 23.0-23.4, 23.5-23.9, 24.0-24.4, 24.5-24.9, 25.0-25.4, and 25.5-25.9.

b) Convert the distribution obtained in part (a) into a cumulative "or more" distribution, beginning with "23.0 or more" and ending with "26.0 or more."

Robin Hood and his Merry Men are now in trouble because wealthy travelers (their source of revenue) are avoiding the forest. As is often common in an entrepreneurial organization, the Merry Men were highly motivated by Robin Hood’s leadership. Therefore, Robin had previously relied on informal communication to organize and implement operations. Robin is pleased with the growing size and influence of his organization. However, growth has meant that specialized duties have begun taking up most of the men’s time, leaving a command vacuum between Robin and the first line recruits. In addition, they are now all located in a large encampment that can be seen for miles. This creates the probability of a surprise attack on their position. Growth has also put great pressures on resources, so now they must harvest the forest more thoroughly. Where will additional revenue come from? Rich travelers are avoiding the forest, so in desperation Robin is considering robbing the poorer travelers, which means his lieutenants must now tell their men to rob their brothers and fathers. What started as a rebellion is in danger of being routinized into banditry. Robin must therefore begin to evaluate the Merry Men’s mission in view of the changing environment.

1. What business is Robin Hood’s organization in?

2. What strategic problems does Robin Hood have?

3. What issues need to be addressed?

4. What decisions need to be made?

5. What strategy should Robin Hood implement?

For each situation indicate when a company should recognize revenue: