Reference no: EM131135745

1. According to a Gallup Poll, the extent to which employees are engaged with their workplace varies from country to country. Gallup reports that the percentage of U.S workers engaged with their workplace is more than twice as high as the percentage of German workers. The study also shows that having more engaged workers leads to increased innovation, productivity, and profitability, as well as reduced employee turnover. The results of the poll are summarized in the following table:

Country
Engagement United States Germany Total
Engaged 550 246 796
Not Engaged 1,345 1,649 2,994
Total 1,895 1,895 3,790

If an employee is selected at random, what is the probability that he or she

a. Is engaged with his or her workplace?

b. Is a U.S worker?

2. . According to a Gallup Poll, the extent to which employees are engaged with their workplace varies from country to country. Gallup reports that the percentage of U.S workers engaged with their workplace is more than twice as high as the percentage of German workers. The study also shows that having more engaged workers leads to increased innovation, productivity, and profitability, as well as reduced employee turnover. The results of the poll are summarized in the following table:

Country
Engagement United States Germany Total
Engaged 550 246 796
Not Engaged 1,345 1,649 2,994
Total 1,895 1,895 3,790
a. Given that a worker is from the United States, what is the probability that the worker is engaged?
b. Given that a worker is from the United States, what is the probability that the worker is not engaged?
c. Given that a worker is from Germany, what is the probability that the worker is engaged?
d. Given that a worker is from Germany, what is the probability that the worker is not engaged?

3. Enzyme- Linked immunosorbent assay (ELISA) is the most common type of screening test for detecting the HIV virus. A positive result from an ELISA indicates that the HIV virus is present. For most populations, ELISA has a high degree of sensitivity (to detect infection) and specificity (to detect noninfection). Suppose the probability that a person is infected with the HIV virus for a certain population is 0.015. If the HIV virus is actually present, the probability that the ELISA test will give a positive result is 0.995. If the HIV virus is not actually present, the probability of a positive result from ELISA is .01. If the ELISA has given a positive result, use Bayes' thermo to find the probability that the HIV virus is actually present.

4. you are trying to develop a strategy for investing in two different stocks. The anticipated annual return for 1,000 dollar investment in each stock under four different economic conditions has the following probabilitydistribution:

Returns

Probability Economic Condition Stock x Stock Y
0.1 Recession -100 50
0.3 Slow growth 0 150
0.3 Moderate Growth 80 -20
0.3 Fast Growth 150 -100

A. Compute the expected return for stock X and for stock Y

B. Standard deviation for stock X and for stock Y

C. Covariance of stock X and Stock Y

D. Would you invest in stock X or stock Y? Explain?

5. Suppose that in problem 12 you wanted to create a portfolio that consist of stock X and stock Y. Compute the portfolio expected return and portfolio risk for each of the following percentages invested in stock X:

a. 30%
b. 50%
c. 70%
d. On the basis of the results of a through c which portfolio would you recommend and why?

6. When a customer places an order with Rudy's online office supplies, a computerized accounting information system (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 customers place orders. Assume that the number of customers that the AIS detects as having exceeding their credit limit is distributed as a binomial random variable.

a. What are the mean and standard deviation of the number of customers exceeding their credit limits?

b. What is the probability that zero customers will exceed their limits

c. What is the probability that one customer will exceed his or her limit?

d. What is the probability that two or more customers will exceed their limits?

7. J.D Power and associates calculates and publishes various statistics concerning car quality. The initial quality score measures the number of problems per new car sold. For 2009 model cars, Ford had 1.02 problems per car and Dodge had 1.34 problems per car. Let the random variable X be equal to the number of problems with a newly purchased 2009 Ford.

a. What assumptions must be made in order for X to be distributed as a Poisson random variable? Are these assumptions reasonable?
Make the assumptions as in (a), if you purchased a 2009 Ford, what is the probability that the new car will have
B. Zero Problems
C. Two or fewer problems
D. Give an operational definition for problem. Give an operational definition for problem. Why is the operational definition important in interpreting the initial quality score?

8. A statistical analysis of 1,000 long-distance telephone calls made from the headquarters of the Bricks and Clicks computer corporation indicates that the length of these calls is normally distributed, with u=240 and O = 40 seconds. (The u and o has tails on them)

a. What is the probability that a call lasted less than 180 seconds?
b. What is the probability that a call lasted between 180 and 300 seconds?
c. What is the probability that a call lasted between 110 and 180 seconds?
d. 1% of all calls will last less then how many seconds?

9. Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with a diameter of 22.000 mm, but shafts with diameters between 21.990 mm and 22.010 mm are acceptable. Suppose that the manufacturing process yields shafts with diameters normally distributed, with a mean of 22.002 mm and a standard deviation of 0.005 mm. For this process what is?

a. The proportion of shafts with a diameter between 21.99 mm and 22.00 mm?
B. The probability that a shaft is acceptable?
c. The diameter that will exceed by only 2% of the shafts?
d. What would be your answers in (a) through (c) if the standard deviation of the shaft diameters were 0.004mm?

10. Time spent using email-per session is normally distributed, with µ= 8 and σ= 2 minutes. If you select a random sample of 25 sessions,

a. What is the probability that the sample mean is between 7.8 and 8.2 minutes?

B. What is the probability that the sample mean is between 7.5 and 8 minutes?

C. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes?

D. Explain the difference in the results of (a) and (c)

11. The manager of a paint supply store wants to estimate the actual amount of paint contained in 1 gallon cans purchased from a nationally known manufacturer. The manufacturer's specifications state that the standard deviation of the amount of paint is equal to 0.02 gallon. A random sample of 50 cans is selected, and the sample mean amount of paint per 1 gallon can is 0.995 gallon.

a. Construct a 99% confidence interval estimate for the population mean amount of paint included in a 1-gallon can.
B. On the basis of these results, do you think that the manager has a right to complain to the manufacturer? Why?
C. Must you assume that the population amount of paint per can is normally distributed here? Explain?
D. Construct a 95% confidence interval estimate. How does this change your answer to B?

12. If you want to be 99% confident of estimating the population proportion to within a sampling error of ± 0.04, what sample size is needed?

13. If you use a 0.10 level of significance in a (two tailed)

Hypothesis test, what is your decision rule for rejecting null hypotheses that the population mean is 500 if you use the Z test?

a) If you use a 0.01 level of significance in a (two tail) hypothesis test, what is your decision rule for rejecting Ho: µ= 12.5 if you use the Z test.
b) What is your decision in problem 4 if Zstat= -2.61
c). What is the P value if, in a two tail hypothesis test, Zstat = +2.00

14. Do students at your school study more than, less than, or about the same as students at other business schools? Business Week reported that at the top 50 business schools, students studied an average of 14.6 hours per week.(Data extracted from (Cracking the books," Special Report/online extra, www.businessweek.com, March 19, 2007). Set up a hypothesis test to try to prove that the mean number of hours is studied at your school is different from the 14.6 hour per week benchmark reported by business week.

a. State the null and alternative hypotheses
B. Compute the p-value and interpret its meaning
c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.
D. Compare the results of A and C. What conclusions do you reach?

15. A manufacturer of chocolate candies uses machines to package as they move along the filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051 ounce.

a. Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of significance)

B. Determine the P value and interpret its meaning.

16. A bank with a branch located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 hour lunch period. The waiting time (operationally defined as the time elapsed from when a customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected, and the results (in minutes) are as follows (and stored in bank 1):

4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20
4.50 6.10 0.38 5.12 6.46 6.19 3.79

Suppose that another branch, located in a residential area, is also concerned with the noon to 1 lunch period. A random sample of 15 customers is selected, and the results are as follows (and stored in bank 2)

9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35
10.49 6.68 5.64 4.08 6.17 9.91 5.47

a. Assuming that the population variances from both banks are equal, is there evidence of a difference in the mean waiting time between the two branches? ( use α=0.05.)

B.  Determine the p value in a and interpret its meaning

c. In addition to equal variances, what other assumption is necessary

d. Construct and interpret a 95% confidence interval estimate of the difference between the population means in the two branches.

17. A professor in the accounting department of a business school claims that there is more variability in the final exam scores of students taking the introductory accounting course who are not majoring in accounting then for students who are taking the course who are majoring in accounting. Random samples of 13 non-accounting majors and 10 accounting majors are selected from the professors class roster in his large lecture and the following results are computed based on the final exam scores:

Non-accounting: N1=13 S2/1=210.2 (the 2/1 is really a 2 over the 1 I couldn't figure out how to type it though)

Accounting: N2=10 S2/2= 36.5

A. At the 0.05 level of significance, is there evidence to support the professors' claim?

B. Interpret the p value

C. What assumption do you need to make in a about the two populations in order to justify your use of the F test?

18. A pet food company has a business objective of expanding its product line beyond its current kidney- and shrimp- based cat foods. The company developed two new products, one based on chicken livers and the other based on salmon. The company conducted an experiment to compare the two new products with its two existing ones, as well with a generic beef-based product sold in a supermarket chain.

For the experiment, a sample of 50 cats from the population at a local animal shelter was selected. Ten cats were randomly assigned to each of the five products being tested. Each of the cats was then presented with three ounces of the selected food in a dish at feeding time; the researchers defined the variable to be measured as the number of ounces of food that the cat consumed within a 10-minute interval that began when the filled dish was presented. The results of this experiment are summarized in the following table and stored in Catfood.
Kidney Shrimp Chicken Liver Salmon Beef

2.37 2.26 2.29 1.79 2.09
2.62 2.69 2.23 2.33 1.87
2.31 2.25 2.41 1.96 1.67
2.47 2.45 2.68 2.05 1.64
2.59 2.34 2.25 2.26 2.16
2.62 2.37 2.17 2.24 1.75
2.34 2.22 2.37 1.96 1.18
2.47 2.56 2.26 1.58 1.92
2.45 2.36 2.45 2.18 1.32
2.32 2.59 2.57 1.93 1.94

a. At the 0.05 level of significance, is there evidence of a difference in the mean amount of food eaten among the various products?

B. If appropriate, which products appear to differ significantly in the mean amount of food eaten?

C. At the 0.05 level of significance, is there evidence of a significant difference in the variation in the amount of food eaten among the various products?

D. What should the pet food company conclude? Fully describe the pet companies options with respect to its products?

19. A mail order catalog business that sells personal computer supplies, software, and hardware maintains a centralized warehouse for the distribution of products ordered. Management is currently examining the process of distribution from the warehouse and is interested in studying the factors that affect warehouse distribution costs. Currently, a small handling fee is added to the order, regardless of the amount of the order. Data that indicates the warehouse distribution costs and the number of orders received have been collected over the past 24 months. These are the results:
Months     Distribution Cost    Number of orders
(Thousands of Dollars)

1                     52.95                        4,015
2                     71.66                        3,806
3                     85.58                        5,309
4                     63.69                        4,262
5                     72.81                        4,296
6                     68.44                        4,097
7                     52.46                        3,213
8                     70.77                        4,809
9                     82.03                        5,237
10                   74.39                        4,732
11                   70.84                        4,413
12                   54.08                        2,921
13                   62.98                        3,977
14                   72.30                        4,428
15                   58.99                        3,964
16                   79.38                        4,582
17                   94.44                        5,582
18                   59.74                        3,450
19                   90.50                        5,079
20                   93.24                        5,735
21                   69.33                        4,269
22                   53.71                        3,708
23                   89.18                        5,387
24                   66.80                        4,161

a. Assuming a linear relationship, use the least squares method to find the regression coefficients b0 and b1
b. Predict the monthly warehouse distribution costs when the number of orders is 4,500
c. Plot the residuals versus the time period
D. Compute the Durbin-Watson Statistic. At the o.05 level of significance, is there evidence of positive autocorrelation among the residuals?
E. Based on the result of c and d, is there reason to question the validity of the model?