A manufacturing supervisor

Question 1

1. Scenario for Question 4:

A manufacturing supervisor at a soft drink company is responsible for ensuring that bottles are filled with proper amounts of soft drink. He is concerned about one particular beverage that appears, visually, to have had several 20 ounce bottles that are underfilled.

The amount of soft drink inserted into a 20 ounce bottle is expected to have a small amount of variation and is assumed to be normally distributed. According to the company’s quality control specifications, the company wants to have 99.74% of its bottles to be within 19.7 ounces and 20.3 ounces. The supervisor wants to determine if there is a problem with this beverage’s filling machine. He collects data on a random sample of bottles from this machine, and reports that the sample mean is 19.85.

Consider the following ways in which the manager could analyze this information:

Option 1: The supervisor can conclude that the machine is definitely not filling the population of bottles with 20 ounces of beverage, on average, because the sample mean, 19.85, is not equal to 20 ounces.

Option 2: The supervisor can conclude that the machine is filling bottles with the desired amount of beverage, on average, because the sample mean 19.85 is reasonably close to 20 ounces, based on this standard deviation.

Option 3: The supervisor cannot make conclusions about machine performance based only on the sample mean. He must look at the individual observations in the sample, and see if any of them are outside the range 19.7 to 20.3. If so, he can conclude that the mean amount filled by the machine is probably not equal to 20 because of the presence of these points.

Option 4: The supervisor cannot conclude anything definitive about the performance of the machine using only this information. He would need to perform a hypothesis test, taking into account the sample size, to accurately determine if the population mean is equal to 20.

Question 4 – Analyzing Information:Which of the statements above best describes the supervisor’s preliminary conclusions based on the sample mean and sample standard deviation? Briefly explain, using one or two sentences, why you chose the answer you did.

Answer:

Question 2

1. Scenario for Bonus Questions 1 & 2:

A store manager has concerns about a seemingly unusual number of recent events in which cashier drawers have not balanced properly. Prior to the last six months, the store manager noted that, on average, she seemed to have to deal with about one problem of this nature per month. However, over the last six months, she suspects that there has been an increase in problems.

The store manager wants to determine whether she has an actual problem with employees, or if these recent events could be just due to coincidence (randomness). If there is a problem with employees, the manager will need to begin the time consuming process of identifying which employees may be involved in dishonest activity. Any accusations she makes must be supported, or the company could be sued for wrongful termination.

Now consider the following options the manager has to define the problem:

Option 1: The store manager assumes that that the (population) mean number of problems per month has increased, that is, that it is in fact, greater than 1 (the previous value). She wants to collect data and see if she can prove, with a high degree of certainty, that the mean number of problems per month is less than or equal to 1.

Option 2: The store manager assumes that that the (population) mean number of problems per month has NOT increased, that is, that it is in fact, less than or equal to 1 (the previous value). She wants to collect data and see if she can prove, with a high degree of certainty, that the mean number of problems per month is greater than 1.

Option 3: The store manager assumes that that the (population) mean number of problems per month is exactly equal to 1 (the previous value). She wants to collect data and see if she can prove, with a high degree of certainty, that the mean number of problems per month is not equal to 1 (that is, is either less than or greater than 1).

Option 4: The store manager assumes that that the (population) mean number of problems per month is not equal to 1 (the previous value). She wants to collect data and see if she can prove, with a high degree of certainty, that the mean number of problems per month is exactly equal to 1.

Question 1: Problem Definition.Which of the above options correctly describes the store manager’s problem? Briefly explain, using one or two sentences, why you chose the answer you did.

Answer:

Question 3

1. Scenario for Question 3:

As a summer intern for a construction management company, some of your duties include working with the purchasing manager to negotiate materials needed for a new hotel. Your office has just received bids from two different suppliers for the electronic control unit that will manage lights, heating and cooling, and Wi-Fi access for each guest room.

The finished hotel will need 1000 of these control units. It is not unusual that some of the units will be defective, and each supplier will replace, free of charge, any units that don’t work. However, the suppliers have different response times. Delays are costly for the construction company so even though there is no charge for the replacement unit, and it is guaranteed to work, the company does assess a cost per defective to cover the cost of the delay.

Your boss is in favor of working with Supplier A rather than Supplier B because of its lower purchase cost per unit; however, you have noted that Supplier B has a smaller percentage of defective parts and replaces defective parts more quickly. Specifically:

Cost and Quality Information

Supplier A Supplier B

Purchase Price per Unit $100 $105

Percent Defective 15% 5%

Cost per Defective $20 $10

Demand 1000 1000

Question 3: Evaluating and Choosing Alternatives

Using this information, calculate the Expected Costs for 1000 items from each Supplier (including both purchase costs and the cost of defective items) and use your results to make a recommendation to your boss as to whether you expect it to be cheaper to order from Supplier A or Supplier B. In your answer report the total cost if you order from Supplier A and the total cost if you order from Supplier B. Finally, make a recommendation for the supplier.

Answer:

Question 4

1. Scenario for Bonus Questions 1 & 2:

A store manager has concerns about a seemingly unusual number of recent events in which cashier drawers have not balanced properly. Prior to the last six months, the store manager noted that, on average, she seemed to have to deal with about one problem of this nature per month. However, over the last six months, she suspects that there has been an increase in problems.

The store manager wants to determine whether she has an actual problem with employees, or if these recent events could be just due to coincidence (randomness). If there is a problem with employees, the manager will need to begin the time consuming process of identifying which employees may be involved in dishonest activity. Any accusations she makes must be supported, or the company could be sued for wrongful termination.

The manager plans to collect some data on register receipts and drawer totals over the last six months in order to investigate her problem. The store has a hundreds of employees who work over several shifts for seven days a week, and sometimes different cashiers log in and out of cash registers within a shift.

Consider the following approaches the manager could take to collect data:

Approach 1: The store manager plans to evaluate every shift and every drawer total of every cashier over the last six months, to determine the exact average number of discrepancies per month.

Approach 2: The store manager plans to look at a sample of drawer totals. To choose her sample, she will consider every Saturday (their busiest day) over the last six months. She will randomly choose 10 drawer totals from each day, allowing them to be chosen from any time of day.

Approach 3: The store manager plans to look at a sample of transactions. To choose her sample, she plans to take a random sample of 50 days (including all days of the week) from the last six months. For each day, she will look at drawer totals from the hours of 11:00 am to 1:00 pm, their busiest time.

Approach 4: The store manager plans to look at a sample of transactions. To choose her sample, she plans to take a random sample of 50 days (including all days of the week) from the last six months. For each day, she will randomly choose 10 drawer totals from each day, allowing them to be chosen from any time of day.

Question 2: Data Collection.Which of the above approaches is the appropriate way to collect data for this task? Briefly explain, using one or two sentences, why you chose the answer you did.

Answer

Question 5

1. Scenario for Bonus Question 5:

News release on March 26, 2012. NEW YORK (CNN) – The average cell phone customer now switches carriers as soon as his or her second two-year contract is up. That startling decline in loyalty is causing wireless companies to rethink the way they do business, according to a new study released Monday. The average length of relationships between carriers and their under-contract customers fell to an all-time low of 48 months last year, PricewaterhouseCoopers found in the latest edition of its North American wireless industry survey.

As an analyst for Midwest Mobile, a small wireless service company, you find this news release worrisome. The information is of concern to you because you’d hope that your customers stay with you longer than 48 months. To see where you stand, you take a sample of customer accounts and, based on the sample data, compute the following confidence interval and conduct the following hypothesis test.

95% confidence interval results:

µ : population mean

Mean Sample Mean Std. Err. DF L. Limit U. Limit

µ 50.46 0.28724 99 49.890053 51.029945

Hypothesis test results:

µ : population mean

H0 : µ = 48

HA : µ > 48

Mean Sample Mean Std. Err. DF T-Stat P-value

µ 50.46 0.28724 99 8.564267 <0.0001

Consider the following conclusions you could come to based on these analyses.

Conclusion 1: Based on the mean of 50.46 months you found in your data collection, you conclude that you are absolutely certain, based on your data, that your customers stay with your company for more than 48 months, on average, .

Conclusion 2: You conclude that there is very strong evidence that customers stay with your company for more than 48 months, on average; that is, you are very confident in making this statement to your company’s upper management.

Conclusion 3: You conclude that there is some evidence that your customers may stay with your company for more than 48 months on average, but that evidence is not very strong evidence; that is, you would not be confident in making this statement to your company’s upper management.

Conclusion 4: You can conclude that that there is no evidence whatsoever to show that your customers stay with your company for more than 48 months.

Question 5 – Interpreting Results: Based on your statistical analyses shown in the exhibit, which of the above conclusions is the best you can make about the average contract time of your customers? Briefly explain, using one or two sentences, why you chose the answer you did.

Answer:

BUS 305, Summer2014

Final Exam Instructions and Exhibits

Your final exam is worth a total of 125 points and all work must be completed and submitted no later than noon on Thursday, July 3. As with the midterm, you may use your book, notes, and computer, but you absolutely must not use another person, student or otherwise, or another person’s work. We will abide by the provisions of the Code of Student Conduct.

The exam has two separate areas (plus a bonus section) where you will do and submit your work. This Word file provides exhibits that you will need for the Blackboard portion of the exam. You may do the work in any order; just make sure you do everything! When you are finished, be sure to do the online course evaluation by following the link in the announcements.

The Excel file has four separate tabs with problems (plus one for instructions) and comprises 65 of the possible points. Make sure that you do all of your work in the file and follow the instructions on the first tab carefully. In most cases, the location for your answer has been highlighted. Save the file using the convention in the instructions, then open it on your computer. Be sure you have saved your final version when you are finished, then email the file to me.

The exam section on Blackboard is worth 60 points. The questions are tied to the Exhibits in this file so make sure you have them ready and refer to the correct exhibit for each question.

The bonus questions are also in Blackboard. They are optional, but it is certainly in your best interest to attempt them. There are five questions, each worth up to five points.

ANOVA Exhibit

A manufacturer of light bulbs sells a model that is supposed to last for more than 1000 hours. The manufacturer makes these bulbs at four different facilities and usesthe same supplier for all raw materials. The manufacturer is interested in determining if the average length of life is the same for bulbs from each facility and so conducts an ANOVA. The results appear below.

Anova: Single Factor

SUMMARY

Groups Count Sum Average Variance

Pennsylvania 17 17954 1056.118 14970.86

China 1 19 19187 1009.842 1051.696

China 2 18 17887 993.7222 569.2712

Georgia 14 13889 992.0714 1133.764

ANOVA

Source of Variation SS df MS F P-value F crit

Between Groups 44600.15 3 14866.72 3.363501 0.02396 2.748191

Within Groups 282880.8 64 4420.013

Total 327481 67

Chi Square Exhibit 1

Historical data that shows the percentage of Indiana teachers with degrees from state supported Indiana colleges is available. For example, it shows the percentage with degrees from ISU, from Ball State, from Purdue, etc. A new survey of 200 teachers reveals the distribution of their undergraduate degrees. Observers are interested in seeing if there has been a shift in the proportion from the institutions and so conduct a Chi Square Goodness of Fit test. The results appear below.

Chi-Square goodness-of-fit results:

Observed: Observed

Expected: Expected

N DF Chi-Square P-Value

200 4 4.451137 0.3484

Chi Square Exhibit 2

Common sense indicates that Americans with different political beliefs would not all have the same opinion about political issues. A survey by the non-partisan Pew Research Institute asked respondents their opinions about immigration reform and the responses, assuming 100 participants from each political description, are shown in the table below.

Contingency table results:

Rows: Affiliation

Implement Immigration Reform

While border improvements being made Only after borders effectively controlled Other Total

Tea Party Republicans 27

67

6

100

Non Tea Party Republicans 47

47

6

100

Independents 47

43

10

100

Conservative/Moderate Democrats 53

42

5

100

Liberal Democrats 74

23

3

100

Total 248 222 30 500

Chi-Square test for independence:

Measure DF Value P-value

Chi-Square 8 49.283928 <0.0001

Multiple Regression Exhibit

Data from the regular 2011 season of the National Football League has been used to create a multiple regression model to attempt to explain the number of points scored in a game. You do not have to understand American football to be able to work this problem!From the many variables available, these have been selected to be in the initial model.

Pts/G is the number of points scored in a game.

Yds/G is the number of yards gained in a game.

1st/G is the number of first downs achieved in a game.

Lost is the number of fumbles that were recovered by the opposing team during a game.

TO is the number of turnovers in a game.

The regression output from StatCrunch is shown below.

Multiple linear regression results:

Dependent Variable: Pts/G

Independent Variable(s): Yds/G, 1st/G, Lost, TO

Parameter estimates:

Variable Estimate Std. Err. Tstat P-value

Intercept -14.231933 4.2143064 -3.3770523 0.0022

Yds/G 0.0907081 0.034934886 2.5964906 0.0151

1st/G 0.1307833 0.64571136 0.20254144 0.841

Lost 0.25354052 0.16485439 1.5379664 0.1357

TO 0.22413431 0.05000812 4.4819584 0.0001

Analysis of variance table for multiple regression model:

Source DF SS MS F-stat P-value

Model 4 800.3687 200.09218 40.01251 <0.0001

Error 27 135.02 5.000741

Total 31 935.38873

Summary of fit:

Root MSE: 2.2362337

R-squared: 0.8557

R-squared (adjusted): 0.8343

Time Series Exhibit

Daily revenue is shown in this time series plot.

Calculus Exhibit A

f(x)=-2x^3+1.5x^2+3x+2x^(-2)+4

Calculus Exhibit B

The fixed cost is $8400.00

The variable cost is $2.04

The selling price per unit is $12.54

Assume all units made can be sold.

Calculus Exhibit C

The marginal cost function is 3x + 150

Calculus Exhibit D

f(x)=(1/4) x^4-(25/3) x^3+75x^2-500