Need help with MATH533 applied managerial final

MATH533 Applied Managerial Statistics Final Exam Study Guide

YOU MAY WANT TO PRINT THIS GUIDE.

1. The Final Exam is open book and open notes. The maximum time you can spend in the exam is 3 hours, 30 minutes. If you have not clicked the Submit for Grading button by then, you will be exited from the exam automatically. In the Final Exam environment, the Windows clipboard is disabled, so you will not be able to copy exam questions or answers to or from other applications.
2. You should click the Save Answers button in the exam frequently. This helps prevent connection timeouts that might occur with certain Internet service providers and also minimizes lost answers in the event of connection problems. If your Internet connection does break, when you reconnect, you will normally be able to get back into your Final Exam without any trouble. Remember, though, that the exam timer continues to run while students are disconnected, so students should try to log in again as quickly as possible. The Help Desk cannot grant any student additional time on the exam.
3. See the Syllabus section “Due Dates for Assignments & Exams” for due date information.
4. Reminders

• You will only be able to enter your online Final Exam one time.
• Click the Save Answers button often.
• If you lose your Internet connection during your Final Exam, log on again and try to access it. If you are unable to enter the Final Exam, first contact the Help Desk and then your instructor.
• You will always be able to see the time remaining in the Final Exam at the top right of the page.

5. Assessments With Multiple Pages

• Make sure to click the Save Answers button before advancing to the next page (we also suggest clicking on Save Answers while you are working).
• Complete all of the pages before submitting your Final Exam for instructor review.
• Do NOT use your browser’s Back and Forward buttons during the Final Exam.
• Please use the provided links for navigation.

6. Submitting Your Final Exam

• When you are finished with the Final Exam, click on the Submit for Grading button.
• Please note: Once you click the Submit for Grading button, you will NOT be able to edit or change any of your answers.

7. Exam Questions

• There are 10 randomly selected short answer questions each worth varying points, for a total of 250 points.
• The Final Exam covers all course TCOs and Weeks 1–7.
• The Final Exam consists of 3 pages, which can be completed in any order. You may go back and forth between the pages.
• The Final Exam questions are pooled. This means that not everyone will have the same questions. Even if you do have some of the same questions, they may not be in the same order. These questions are distributed among the TCOs. The entire exam is worth 250 points.

 

8. Some of the key study areas are shown below. Although these are key areas, remember that the exam is comprehensive for all of the assigned course content and this study guide may not be all-inclusive.

• TCO A
• Descriptive Statistics and Exploratory Data Analysis
• Central Tendency
• Dispersion
• The Shape of the Distribution
• Numbers, Graphs, and Tables
• One Variable and Two Variables
• TCO B
• Contingency Tables
• The Binomial Distribution
• The Normal Distribution
• TCO C
• Confidence Intervals/Sample Sizes: For the Population Mean
• Confidence Intervals/Sample Sizes: For the Population Proportion
• TCO D
• Hypothesis Tests: For the Population Proportion
• Hypothesis Tests: For the Population Mean
• TCO E
• Simple Linear Regression
• Multiple Regression
• TCO F
• Use of Minitab in each of the above TCOs

 

 

9. Areas that were discussed in the Discussion areas will be prime targets.
10. Homework Assignments and Quizzes will also be prime targets for revisiting.
11. Reviewing the TCOs, which are listed below for your convenience, will also be a great preparation for the Final Exam.

 

A	Given a managerial problem and accompanying data set, construct graphs (following principles of ethical data presentation), calculate and interpret numerical summaries appropriate for the situation. Use the graphs and numerical summaries as aids in determining a course of action relative to the problem at hand.
B	Given a managerial problem, utilize basic probability concepts, and standard probability distributions, e.g., binomial, normal, as is appropriate, to formulate a course of action which addresses the problem.
C	Given a managerial problem and accompanying data set, for which application of a confidence interval is appropriate, construct an interval, assess its validity, and use the confidence interval in developing a course of action relative to a problem.
D	Given a managerial problem and accompanying data set, for which the test of an hypothesis is appropriate, conduct an appropriate statistical test, assess the validity of the test, and use the test results to decide on a course of action relative to a problem.
E	Given a managerial problem and accompanying data set, for which regression analysis—simple or multiple—is appropriate, fit a regression model to the data, determine the validity and utility of the model, and use the model, if appropriate, to determine a course of action intended to deal with a problem.
F	Students should be able to perform the necessary calculations for objectives A through E using technology, whether that is a computer statistical package or the TI-83, and be able to use the output to address a problem at hand.

 

 

The following Table provides an overview of the content of the 10 Questions on the Final Exam and the possible points for each Question.

 

#	Content	TCO	Points	Minitab and Calculator	Notes
1	Descriptive Statistics	A	33	Minitab Required
2	Contingency Table	B	18	Calculator Only
3	Binomial Distribution	B	18	Minitab Required
4	Normal Distribution	B	18	Minitab Required
5	Mean:  Confidence Interval/Sample Size	C	18	Minitab Required And Calculator
6	Proportion:  Confidence Interval/Sample Size	C	18	Minitab Required And Calculator
7	Proportion: Hypothesis Test	D	24	Minitab Required
8	Mean: Hypothesis Test	D	24	Minitab Required
9	Simple Linear Regression	E	48	Minitab Output Provided
10	Multiple Regression	E	31	Minitab Output Provided

 

What follows is a Demo Final Exam with 10 representative problems.  Actual problems will be similar, but will vary in the scenario presented, the numbers used, and the particular variation of the problem type presented.

 

 

MATH533 Sample Final Exam Demo

 

 

Question 1:

TCO A and F

The following raw data is the result of selecting a random sample of new Ford Escorts and testing these cars for fuel efficiency (results are in miles per gallon):

40.2	32.9	29.2	26.5	33.3	28.4
28.8	34.2	30.3	35.7	25.8	37.5
35.6	40.8	33.3	26.6	33.5	28.1

 

Use Minitab to run the key Descriptive Statistics, i.e., mean, median, mode, standard deviation, variance, quartiles, interquartile range, and range.  Interpret your Minitab output, including selected measures of central tendency, dispersion, and the shape of the distribution.

 

 

Answer:

Descriptive Statistics: CarsFuel

 

Total

Variable  Count   Mean  StDev  Variance  Minimum     Q1  Median     Q3  Maximum

CarsFuel     18  32.26   4.59     21.10    25.80  28.32   33.10  35.63    40.80

 

N for

Variable  Range   IQR  Mode   Mode

CarsFuel  15.00  7.30  33.3      2

 

 

Note:  The Final Exam Question may ask for only a selection of the Descriptive Statistics, along with their Interpretation.

 

Question 2:

 

TCO B

The following table gives the number of claims at a large insurance company by kind and geographical region.

	East	South	Midwest	West	Totals
Hospitalization	55	328	29	52	464
Physician’s Visit	233	514	204	251	1202
Outpatient Treatment	100	526	65	102	793
Totals	388	1368	298	405	2459

 

• If a bill is chosen at random, what is the probability that it is either from the East or from the West?
• If a bill is chosen at random, what is the probability that it is not for Hospitalization and from the South.
• Given that the bill is from the Midwest, what is the probability that it is for a Physician’s Visit?
• Given that the bill is not from either the East or the West, what is the probability that it is not for a Physician’s Visit?

 

Answers:

• (# East + #West)/Total = (388 + 405)/2459 = 0.32249
• # Not Hospitalization and Not South/Total = 2131/2459 = 0.866612
• (#from Midwest AND Physician’s Visit)/# from Midwest = 204/298 = 0.68456
• #Not Physician’s Visit/Given #Not from East or West = 948/1666 = 0.56903

Question 3:

TCO B and F

The probability of obtaining a home equity loan from United Bank is 0.40.  A random sample of 10 loan applications is selected.  Use Minitab to find the following probabilities.

• Find the probability that at least five will get a loan.
• Find the probability that none will get a loan.
• Find the probability that less than three will get a loan.
• Find the probability that three or less, or more than seven will get a loan.

Answers: 

• P(X>or =5) = 0.3669
• P(X=0) = 0.006
• P(X<3) = P(X<or=2) = 0.1673
• P(X<or =3) or P(X>or = 8) = 0.38230 + 0.01229 = 0.39459

Question 4:

TCO B and F

The length of time to do a complete full battery check and replacement  (if needed) at Insta-Bat is normally distributed with a mean of 16.2 minutes and a standard deviation of 2.4 minutes.  Use Minitab to find the required probabilities.

• Determine what percentage of complete full battery check and replacements (if needed) will fall between 10 and 20 minutes.
• What percentage of complete full battery check and replacements (if needed) will take less than 20 minutes?
• Using your answer from B., If 1000 cars had a complete full battery check and replacement (if needed), how many would you expect to be finished in less than 20 minutes?
• What percentage would take less than 10 minutes?
• Management wants to offer customers a guarantee that a complete full battery check and replacement (if needed) can be completed within a certain amount of time. What number of minutes should they include in their guarantee, to be sure they are achieving their goal 99% of the time?
• What number of minutes should they include in their guarantee, to be sure they are achieving their goal 95% of the time?

Answers:

• P(10<X<20) = 0.9384
• P(X<20) = 0.9433
• For 1,000 cars, 0.9433 x 1,000 = 943.3 944
• P(X<10) = 0.004893
• For P=0.99, X=? -> X=21.78 22
• For P=0.95, X=? -> X=20.15 21

Question 5:

(TCO C) Unoccupied seats on flights cause airlines to lose revenue.  Suppose a large airline wants to estimate its average number of unoccupied seats per flight over the past year.  To accomplish this, the records of 225 flights are randomly selected, and the number of unoccupied seats is noted for each of the sampled flights.  The results are the following. Sample Size = 225 Sample Mean = 11.5956 Sample Standard Deviation = 4.1026 A. Compute the 95% confidence interval for the mean number of unoccupied seats. B. Interpret the 95% confidence interval. C. How many flights should be tested if the airline wants to be 95% confident of being within 1 seat of the population mean number of unoccupied seats? How many flights should be tested if the airline wants to be 99% confident of being within 2 seats of the population mean number of unoccupied seats?     Answers: Minitab Output: One-Sample Z   The assumed standard deviation = 4.1026     N    Mean  SE Mean       95% CI 225  11.596    0.274  (11.060, 12.132)     Therefore, the 95% confidence interval is  (11.060, 12.132). B.Interpretation:  We are 95% confident the population mean for the number of unoccupied seats is between 11.060 and 12.132. C.Sample Size:  n=((1.96*4.1026)/1)**2 = 65 Sample Size: n=((2.575*4.1026)/2)**2 = 28

Question 6:

 

(TCO C) A food-products company conducted a market study by randomly sampling and interviewing 1,000 consumers to determine which brand of breakfast cereal they prefer.  Suppose 313 consumers were found to prefer the company’s brand.  Estimate the true fraction of all consumers who prefer the company’s cereal brand? Compute the 95% confidence interval for the percent of consumers who prefer the company’s brand of breakfast cereal. Interpret this confidence interval. How large a sample size will need to be selected if we wish to have a 95% confidence interval that is accurate to within 1.5%. (Assume p = .35) How large will the sample size need to be if we wish to be accurate to within 2.0%, with 95% confidence? Answers: A.Minitab Ouput Test and CI for One Proportion   Sample    X     N  Sample p         95% CI 1       313  1000  0.313000  (0.284259, 0.341741)   Using the normal approximation.   Interpretation: We are 95% confident the population proportion of consumers who prefer the company’s brand of breakfast cereal is between 0.284 and 0.342. C.Sample Size:  n= p*q*(z/E)^2 n= 0.35*0.65*(1.96/0.015)^2 n= 3885

1. Sample Size: n= p*q*(z/E)^2

n= 0.35*0.65*(1.96/0.02)^2

n= 498
Question 7:

 

(TCO D) Historically, 21% of professional tennis players use Wilson tennis balls. A randomly selected sample of 50 professional tennis players found that eight use Wilson tennis balls. Does the sample data provide evidence to conclude that the percentage of professional tennis players using Wilson tennis balls is less than 21% (with a = .10)? Use the hypothesis testing procedure, including the Hypotheses, all steps for both the p-value and rejection region approaches, and your Interpretation, using the variable and its units.

Answer:

The hypotheses include Ho: p >or=.21 and Ha: p<.21.  For the given alpha=0.10, the critical value = -1.282, and the rejection region <or=-1.282.  The test statistic z=-0.87 and the observed p-value=0.193.  Because the test statistic is not in the Rejection region, and the p-value is not less that alpha, we cannot reject the null hypothesis that the population proportion is equal to or greater than .21, and we cannot accept the alternative hypothesis, that the population mean is less than .21, when the level of significance, alpha, is equal to .10.  That is, we are less than 90% sure that less than 21% of professional tennis players use Wilson tennis balls.

 

Question 8:

 

(TCO D) A manufacturer of jogging shoes claims that the mean life of his product will exceed 50 hours. A random sample of 49 shoes leads to the following results in terms of useful life.

Sample Size = 49 shoes
Sample Mean = 58.3 hours
Sample Standard Deviation = 10.1 hours

Does the sample data provide evidence to conclude that the manufacturer’s claim is correct (using a = .02)? Use the hypothesis testing procedure, including the Hypotheses, all steps for both the p-value and rejection region approaches, and your Interpretation, using the variable and its units.

Answer:

The hypotheses include Ho : mu <or= 50, Ha: mu>50.  For the given alpha=0.02, the critical value =2.054, and the rejection region >or= 2.054.  The test statistic z=5.75 and the observed p-value=0.000.  Because the test statistic is in the Rejection region, and the p-value is less that alpha, we can reject the null hypothesis, that the life of the jogging shoes is <or= 50 hours, and we can accept the alternative hypothesis, that the life of the jogging shoes is > 50 hours, at alpha = .02.  That is, we are at least 98% sure that the average life of shoes exceeds 50 hours.

 

Question 9:

Use Minitab and the data below to run the Linear Regression, and use the Minitab output to answer the following questions.  You can Copy and Paste the data set into Excel, and then Copy and Paste it into Minitab.

NOTE:  ON THE FINAL EXAM YOU WILL BE PROVIDED THE MINITAB OUTPUT.

 

Suppose an appliance store conducts a 5-month experiment to determine the effect of advertising on sales revenue.   Below is the output, including the scatterplot and regression output.  Answer the questions below.  (Data set:  ADSALES)

 

Advexp X ($100s)	Sales Y ($1000s)
1	1
2	1
3	2
4	2
5	4

 

 

 

1. Analyze the Minitab output to determine the regression equation.
   b. Find and interpret ? ^ 1 hat in the context of this problem.
   c. Find and interpret the coefficient of determination (r-squared).
   d. Find and interpret the coefficient of correlation.
   e. Does the data provide significant evidence (a = .05) that the advertising can be used to predict the sales? Test the utility of this model using a two-tailed test. Find the observed p-value and interpret.
   f. Find the 95% confidence interval for the mean sales generated by $400 of advertising Interpret this interval.
   g. Find the 95% prediction interval for the sales generated by $400 of advertising Interpret this interval. .
   h. What can we say about the sales generated by $800 of advertising?

Answers:

• Y hat = -0.1 + 0.7 ADVEXP_X
• B1 hat = 0.7. Interpretation:  Each $100 increase in Advertising results in an increase of $700 in Sales.
• R squared = 81.67%. Interpretation:  The independent variable Advertising explains 81.67% of the variability in Sales.
• r = 0.9037. Interpretation:  The correlation of 0.9037 indicates a strong positive relationship between Advertising and Sales.
• The null hypothesis Ho is that B1 = 0, and the alternative hypothesis Ha is that B1 is not equal 0. The p-value for the Advertising regression coefficient = 0.035.  Interpretation:   Because the p-value of 0.035 is less than the alpha = .05, we can reject the null hypothesis, that the regression coefficient = 0, and we can accept the alternative hypothesis, that the regression coefficient is not = 0.  Yes, Advertising can be used to predict Sales in the population.
• The 95% confidence interval for the mean sales generated by $400 of Advertising is (1.64450, 3.75550). Interpretation:  When the Advertising expenditure = $400, over numerous months, we can be 95% confident the mean Sales will be between $1,644.50 and $3,755.50).
• The 95% prediction interval for the sales generated by $400 of Advertising is (0.502806, 4.89719).  Interpretation:  When the Advertising expenditure = $400, in a particular month, we can be 95% confident the Sales will be between $502.81 and $4,897.19).
• Because $800 is outside the range of our Advertising variable, we cannot make a prediction about the Sales.

 

Question 10:

Use Minitab and the data below to run the Multiple Linear Regression, and use the Minitab output to answer the following questions.  You can Copy and Paste the data set into Excel, and then Copy and Paste it into Minitab.

NOTE:  ON THE FINAL EXAM YOU WILL BE PROVIDED THE MINITAB OUTPUT.

 

 

AGE       NUM-  PRICE

BIDS

127         13           1235

115         12           1080

127         7              845

150         9              1522

156         6              1047

182         11           1979

156         12           1822

132         10           1253

137         9              1297

113         9              946

137         15           1713

117         11           1024

137         8              1147

153         6              1092

117         13           1152

126         10           1336

170         14           2131

182         8              1550

162         11           1884

184         10           2041

143         6              845

159         9              1483

108         14           1055

175         8              1545

108         6              729

179         9              1792

111         15           1175

187         8              1593

111         7              785

115