Ashford BUS 308 Statistics for Managers (Course)

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Week 1 DQ 2

Levels. Managers and professionals often pay more attention to the levels of their measures (means, sums, etc.) than to the variation in the data (the dispersion or the probability patterns/distributions that describe the data). For the measures, you identified in Discussion 1, why must dispersion be considered to truly understand what the data is telling us about what we measure/track. How can we make decisions about outcomes and results if we do not understand the consistency (variation) of the data? Does looking at the variation in the data give us a different understanding of results?

Week 2

Variation.Variation exists in virtually all parts of our lives. We often see variation in results in what we spend (utility costs each month, food costs, business supplies, etc.). Consider the measures and data you use (in either your personal or job activities). When are differences (between one time period and another, between different production lines, etc.) between average or actual results important? How can you or your department decide whether or not the variation is important? How could using a mean difference test help?

Week 3

Effect Size.Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data?

Week 4

Confidence Intervals.

Earlier we discussed issues with looking at only a single measure to assess job-related results. Looking back at the data examples you have provided in the previous discussion questions on this issue, how might adding confidence intervals help managers understand results better?

Chi-Square Tests.

Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?

Week 5

At times we can generate a regression equation to explain outcomes. For example, an employee’s salary can often be explained by their pay grade, appraisal rating, education level, etc. What variables might explain or predict an outcome in your department or life? If you generated a regression equation, how would you interpret it and the residuals from it?

Week 1 Quiz

1. Question : When using the Chebyshev’s theorem to obtain the bounds for 99.73 percent of the values in a population, the interval generally will be _______ the interval obtained for the same percentage if normal distribution is assumed (empirical rule).
Student Answer: narrower than
wider than
the same as

Points Received: Comments:

2. Question : An example of a qualitative variable is the mileage of a car.
Student Answer: True
False

Points Received: Comments:

3. Question : By taking a systematic sample, in which we select every 100th shopper arriving at a specific store, we are approximating a random sample of shoppers.
Student Answer: True
False

Points Received: Comments:

4. Question : All of the following are measures of central tendency except the
Student Answer: range
mode
mean
median

Points Received: Comments:

5. Question : Measurements from a population are called
Student Answer: statistics.
observations.
variables.
inferences.

Points Received: Comments:

6. Question : A normal population has 99.73 percent of the population measurements within ___ standard deviations of the mean.
Student Answer: one
two
three
four

Points Received: Comments:

7. Question : When a population is skewed to the left or right with a very long tail, what is the best measure to use for central tendency.
Student Answer: Population mean
Population mode
Population median
Population standard deviation

Points Received: Comments:

8. Question : All of the following are measures of central tendency except the
Student Answer: range
mode
mean
median

Points Received: Comments:

9. Question : Which percentile describes the first quartile Q1?
Student Answer: 25th
50th
75th
100th

Points Received: Comments:

10. Question : Any characteristic of a population unit is called a
Student Answer: measurement.
sample.
observation.
variable.

Points Received: Comments:

Week 2 Quiz

1. Question : In the application of Bayes’ Theorem the sample information is combined with prior probabilities to obtain posterior probabilities.
Student Answer: True
False

2. Question : The actual weight of hamburger patties is an example of a continuous random variable.
Student Answer: True
False

3. Question : A student’s grade on an examination was transformed to a z value which is negative. Therefore, we know that he scored
Student Answer: higher than 16% of the class.
higher than 45% of the class.
above the first quartile.
below the mean.
above the mean but below the median.

4. Question : The expected value of a discrete random variable is:
Student Answer: ?x p(x)
n ?p ?q
?(x – µx)2 p(x)

5. Question : The following formula: P(A U B) = P(A) + P(B) – P(A ? B) represents
Student Answer: the conditional probability.
the addition rule.
independence.
the multiplication rule.
None of the above.

6. Question : A standard normal distribution has a mean of ____and standard deviation of ____
Student Answer: zero, zero.
zero, one.
one, one.
one, zero.

7. Question : A(n) __________ is a measure of the chance that an uncertain event will occur.
Student Answer: experiment
sample space
probability
complement
population

8. Question : The MPG (mileage per gallon) for a mid-size car is normally distributed with a mean of 32 and a standard deviation of .8. What is the probability that the MPG for a selected mid-size car would be less than 33.2?
Student Answer: 43.32%
6.68%
93.32%
86.64%
13.36%

9. Question : For a Poisson random variable the mean and the variance equal the average number of occurrences over the time interval (µx = ó2x = µ)
Student Answer: True
False

10. Question : In a statistical study, the random variable X = 1, if the house is colonial, and X = 0 if the house is not colonial, then it can be stated that the random variable is continuous.
Student Answer: True
False

Week 3 Quiz

1. Question : When the sample size and sample standard deviation remain the same, a 99% confidence interval for a population mean, µ will be _____ the 95% confidence interval for µ.
Student Answer: wider than
narrower than
equal to

Points Received: Comments:

2. Question : A sample statistic is an unbiased point estimate of a population parameter if the mean of the population of all possible values of the statistic equals the population parameter.
Student Answer: True
False

Points Received: Comments:

3. Question : When the sample size and the sample proportion remain the same, a 90% confidence interval for a population proportion p will be ______ the 99% confidence interval for p.
Student Answer: wider than
narrower than
equal to

Points Received: Comments:

4. Question : A manufacturing company measures the weight of boxes before shipping them to the customers. If the box weights have a population mean and standard deviation of 90 lbs and 24 lbs respectively, then, based on a sample size of 36 boxes, the probability that the average weight of the boxes will be less than 84 lbs is
Student Answer: 16.87%.
93.32%.
43.32%.
6.68%.
84.13%.

Points Received: Comments:

5. Question : When the population is normally distributed and population standard deviation ? is unknown, then for any sample size n, the sampling distribution of is a t distribution.
Student Answer: True
False

Points Received: Comments:

6. Question : The central limit theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.
Student Answer: True
False

Points Received: Comments:

7. Question : The results of a scientific poll showed that 64 out of 400 patients at a certain hospital are not satisfied with the care they received in the hospital after major surgery. A consumer advocate claims that 20% of the major surgery patients at the hospital are dissatisfied with after-surgery care. If the advocate’s claim is true, what is the probability that 64 or fewer of 400 randomly selected patients at the hospital would say they are dissatisfied with the after-surgery care.
Student Answer: 47.72%
2.28%
97.72%
95.44%
4.56%

Points Received: Comments:

8. Question : If the population proportion is .4 with a sample size of 20, then is this sample large enough so that the sampling distribution of is a normal distribution.
Student Answer: True
False

Points Received: Comments:

9. Question : When a confidence interval for a population proportion is constructed for a sample size n = 100 and the value of, p = .4 the interval is based on the
Student Answer: z distribution.
t distribution.
Exponential distribution.
Poisson distribution.
None of the above.

Points Received: Comments:

10. Question : When the population is normally distributed, population standard deviation ó is unknown and the sample size is n = 15, the confidence interval for the population mean µ is based on
Student Answer: the z (normal) distribution.
the t distribution.
the Binomial distribution.
the Poisson Distribution.
None of the above.

Week 4 Quiz

1. Question : The manager of the quality department for a tire manufacturing company wants to study the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a Z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated Z test Statistic is a positive value that leads to a p-value of .067 for the test. If the significance level is .10, the null hypothesis would be rejected.
Student Answer: True
False

2. Question : For the chi-square goodness of fit test, the rejection point X2a is in
Student Answer: the left tail of a chi-square curve.
both the left and right tails of a chi-square curve.
the right tail of the appropriate F curve.
the right tail of a chi-square curve.

3. Question : Consider using p-value to test H0 versus Ha by setting ? equal to .10. We reject H0 at level ? of significance if and only if the p-value is:
Student Answer: Greater than ?/2
Greater than ?
Less than ?
None of the above

4. Question : Type II error is defined as the probability of ______ H0 , when it should _____
Student Answer: failing to reject, be rejected.
failing to reject, not be rejected.
rejecting, not be rejected.
rejecting, be rejected.

5. Question : The X2 statistic is used to test whether the assumption of normality is reasonable for a given population distribution. The sample consists of 5000 observations and is divided into 6 categories (intervals). The degrees of freedom for the chi-square statistic is:
Student Answer: 4999
6
5
4
3

6. Question : For a hypothesis test about a population mean or proportion, if the level of significance is less than the p-value, the null hypothesis is rejected.
Student Answer: True
False

7. Question : When carrying out a sample test (with ó known) of H0: µ = 10 vs. Ha: µ > 10 by using a rejection point, we reject Ho at level of significance a if and only if the calculated test statistic is
Student Answer: less than Za
less than – Za
greater than Za/2
greater than Za
less than the p value.

8. Question : The X2 statistic from a contingency table with 6 rows and five columns will have _____ degrees of freedom.
Student Answer: 30
24
5
20
25

9. Question : Homogeneity is a test of the null hypothesis that all multinomial probabilities are equal
Student Answer: True
False

10. Question : When using the chi-square goodness of fit test with multinomial probabilities, the rejection of the null hypothesis indicates that at least one of the multinomial probabilities is not equal to the value stated in the null hypothesis.
Student Answer: True
False

Quiz

A firm that is considering doing business abroad must have a rationale and logic for how it can compensate for and overcome the liabilities and disadvantages that arise from its _____.

A)

strategies

B)

vision

C)

mission

D)

foreignness

The evolution of _______ is a critical element in the formulation of a company’s strategy.

A)

resources

B)

business strategy

C)

corporate strategy

D)

industry structures

In the ______ stage of industry evolution, specialized channels are needed for distribution.

A)

embryonic

B)

growth

C)

maturity

D)

decline

In the _____ stage of industry evolution, there is a widening gap of buyers and a shift to mass production and distribution.

A)

embryonic

B)

growth

C)

maturity

D)

decline

In the _____ stage of industry evolution, uniform quality is assumed.

A)

embryonic

B)

growth

C)

maturity

D)

decline

In the _____ stage of industry evolution, there is a shakeout among the competition.

A)

embryonic

B)

growth

C)

maturity

D)

decline

According to Porter, the diamond framework affects the competitiveness of ____ and ____ as well as firms.

A)

competitors, complementors

B)

nations, regions

C)

customers, suppliers

D)

suppliers, competitors

In the diamond model, _____ conditions typically lead to innovations in the use materials, energy, and logistics.

A)

factor

B)

demand

C)

firm structure, strategy, and rivalry

D)

related and supporting industries

n commercializing a new technology, finding new opportunities and ____ them are the key activities.

A)

inventing

B)

exploiting

C)

standardizing

D)

providing resources for

_____ is the creation of an idea in a laboratory.

A)

Invention

B)

Innovation

C)

Discovery

D)

Exploitation

_____ ensures ____’s broad application.

A)

invention, innovation

B)

innovation, invention

C)

innovation, exploitation

D)

invention, exploitation

As industries mature, products become ______.

A)

specialized

B)

commodities

C)

scarce

D)

differentiated

In many companies, innovative people are likely to be found in foreign operations, where _____ is less prevalent.

A)

strategy

B)

mission

C)

vision

D)

groupthink

In new ventures, financial projections and risk analysis are part of a _______.

A)

strategic plan

B)

corporate plan

C)

business plan

D)

loan plan

In the _____ method of forecasting, successive requisitioning in light of initial answers sharpens the results obtained.

A)

Trend analysis

B)

Alternative scenarios

C)

Delphi

D)

Time series

In _____ societies, economic activity revolves around the manipulation and movement of “massive objects against friction and gravity.”

A)

modern

B)

industrial

C)

postindustrial

D)

contemporary
.8181819915771px;”=””>Week 1 Business Statistics Problems

1.2 Which of these variables are quantitative and which are qualitative?

a.The dollar amount on accounts receivable invoice.

b.The net profit for a company in 2009.

c.The stock exchange on which a company’s stock is traded.

d.The national debt of the United States in 2009.

e.The advertising medium (radio, television, or print) used to promote a product.
1.17 Classify each of the following qualitative variables as ordinal or nominative.

Qualitative Variable Categories

Statistics course letter grade A B C D F

Door choice on Let’s Make A Deal Door #1 Door #2

Television show classifications TV-G TV-PG TV-14 TV-MA

Personal computer ownership Yes No

Restaurant rating ***** **** *** ** *

Income tax filing status Married filing jointly Married filing separately

Single Head of household Qualifying widow(er)

3.3 Calculate the mean, median, and mode of each of the following populations of numbers:

a.9, 8, 10, 10, 12, 6, 11, 10, 12, 8

b.110, 120, 70, 90, 90, 100, 80, 130, 140

3.22 In order to control costs, a company wishes to study the amount of money its sales force spends entertaining clients. The following is a random sample of six entertainment expenses (dinner cost for four people) from expense report submitted by members of the sales force.

$157 $132 $109 $145 $125 $139

a. Calculatex, s2, and s for the expense data. In addition, show that the two different formulas for calculating s2 give the same result.

b. Assuming that the distribution of entertainment expenses is approximately normally distributed calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all entertainment expenses by the sales force.

c. If a member of the sales force submits an entertainment expense (dinner cost for four) of $190, should this expense be considered unusually high (and possibly worthy of investigation by the company)? Explain your answer.

d. Compute and interpret the z-score for each of the six entertainment expenses.

Week 3 Business Statistics Problems
.8181819915771px;”=””>Week 3 Assignment

a. Chapter 7: 7.11, 7.30

b. Chapter 8: 8.8, 8.38

A)Chapter 7:

7.11) Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.

a)Describe the shape of the sampling distribution of the sample mean .gif”>. Do we need to make any assumptions about the shape of the population? Why or why not?

b)Find the mean and the standard deviation of the sampling distribution of the sample mean .gif”>.

c)Calculate the probability that we will obtain a sample mean greater than 21; that is calculate P(.gif”>>21). Hint find the z value corresponding to 21 by using.gif”>and .gif”> because we wish to calculate a probability about .gif”>. Then sketch the sampling distribution and the probability.

d)Calculate the probability that we will obtain a sample mean less than 19.385; that is calculate P(.gif”><19.385). 7.30) On February 8, 2002, the Gallup Organization released the results of a poll concerning American attitudes toward the 19th Winter Olympic Games in Salt Lake City, Utah. The poll results were based on telephone interviews with a randomly selected national sample of 1,011 adults, 18years and older, conducted February 4-6, 2002. a)Suppose we wish to use the poll’s results to justify the claim that more than 30 percent of Americans (18 years or older) say that figure skating is their favorite Winter Olympic event. The poll actually found that 32 percent of respondents reported that figure skating was their favorite event. If, for the sake of argument, we assume that 30 percent of Americans (18 years or older) say figure skating is their favorite event (that is p=.3) calculate the probability of observing a sample portion of .32 or more; that is calculate P(p^?.32) b) Based on the probability you computed in part a, would you conclude that more than 30 percent of Americans (18years or older) say that figure skating is their favorite Winter Olympic event? B) Chapter 8: 8.8) Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean waiting time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting time in table 1.8 is .gif">= 5.46. If we let µ denote the mean of all possible bank customer waiting times using the new system and assume that ? equals 2.47:

A)Calculate 95 percent and 99 percent confidence intervals for µ

B)Using the 95 percent confidence interval, can the bank manager be 95 percent confident that µ is less than six minutes? Explain

C)Using the 99 percent confidence interval, can the bank manager be 99 percent confident that µ is less than six minutes? Explain

D)Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?

8.38)Quality Progress, February 2005, reports on the results achieved by Bank of America in improving customer satisfaction and customer loyalty by listening to the ‘voice of the customer.’ A key measure of customer satisfaction is the response on a scale from 1 to 10 to the question: “Considering all the business you do with Bank of America?” Suppose that a random sample of 350 current customers’ results in 195 customers with a response of 9 to 10 representing “customer delight” Find a 95 percent confidence interval for the true proportion of all current Bank of America customers who would respond with a 9 or 10. Are we 95 percent confident that this proportion exceeds .48, the historical proportion of customer delight for Bank of America.?

WEEK FOUR ASSIGNMENT QUIZ and PROBLEMS

1. Perform a simple regression.

2. Perform a multiple regression.

3. Interpret the results of simple and multiple regressions.

________________________________________

Introduction

In Week Four the focus will be on single and multiple regressions. Predicting the future is a central requirement in business decision-making. Managers use existing data to predict the future values of other variables of interest. For example, marketing data is used to predict future sales. In Chapter 9 students will examine how to conduct a simple and multiple regression analysis and apply it to the business environment. The idea that variables correlate because they share common information is a powerful concept to be examined this week.

________________________________________

Required Resources

Required Text

1. Tanner, D., & Youssef – Morgan, C. (2013). Statistics for Managers. San Diego, CA: Bridgepoint Education, Inc.

This text is a Constellation™ course digital materials (CDM) title.

a. Chapter 9- Simple Regression: Predicting One Variable from Another

b. Chapter 10- Multiple Regression: Using More than One Predictor

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Simple Regression Analysis

Use the data in the chart to answer the questions below. The data indicates the number of “sick days” appliance installers take during a three month period, and the number of complaints filed by customers during the same interval. Use the Analysis Toolpak in Excel to perform this simple regression and answer the questions.

a. Is the correlation between number of sick days and number of customer complaints statistically significant?

Sick days (x) Complaints (y)

2 3

5 6

4 5

1 3

3 4

5 7

4 4

6 9

30 41

b.What is the best prediction for the number of complaints that will be registered for an installer who takes five sick days during the period?

Coefficients Standard Error t Stat P-value

Intercept(s)

Sick day

Multiple Regressions Analysis

Develop a multiple linear regression equation that describes the relationship between tenure and the other variables in the chart above. Use the Analysis Toolpak located in Excel to perform this multiple regression.

Do these two variables explain a reasonable amount of the variation in the dependent variable?

Quiz

To complete the following quiz, go to this week’s Quiz link in the left navigation.

This quiz consists of 10 questions. The amount of time the quiz will take to complete will vary by individual.

________________________________________

Assignment

To complete the following assignment, go to this week’s Assignment link in the left navigation.

Problem Set Week Four

Complete the problems below and submit your work in one Word document. Be sure to show all of your work and clearly label all calculations. Calculations completed in Excel must be copied and pasted into a single Word document. No Excel documents will be graded.

TIP: For help copying and pasting information from Excel to Word go to http://office.microsoft.com/en-us/word-help/copy-excel-data-or-charts-to-word-HP010198874.aspx or watch the “Excel Tips – Tip#48: Copy from Excel to Word” found in Week One Recommended Resources.

ASSIGNMENT

1. Problem One

The manager of a catering company is using the number of people in the party to predict the cost of the drinks that are required for the event. The following are the data for 12 recently catered events:

Event Number of People Cost of Drinks

1 12 24

2 14 30

3 15 36

4 18 38

5 20 65

6 16 44

7 14 36

8 13 30

9 18 39

10 19 76

11 20 80

12 22 85

2.

Complete the calculations below using this data. Show all of your work and clearly label each of your calculations.

a. Provide a scatterplot

b. Calculate a linear regression

c. Calculate the residuals

d. Calculate the correlation between the two variables

e. Calculate the mean, median, and standard deviation of the number of people and cost of drinks

Problem Two

You are a real estate agent and you are trying to predict home prices for your clients that want to list their house for sale. You have a very small city without much data. You will need to use the data that you have available for the past year on homes that have been sold.

Complete the calculations below using this data. Show all of your work and clearly label each of your calculations.

Conduct a multiple regression analysis to predict home prices. In your analysis complete the following:

a. Calculate the multiple regression analysis and report your data.

b. Determine the list price for your client’s home if it has three bedrooms, three bathrooms, and 1900 square footage. Provide your analysis and show all of your calculations.

1. Question : With reference to problem 1, what statistic determines the correlation of experience with productivity, controlling for age in experience?

Student Answer: The regression coefficient.

The standard error of the estimate.

The semi-partial correlation.

The multiple correlation.

2. Question : In a problem where interest rates and growth of the economy are used to predict consumer spending, which of the following will increase prediction error?

Student Answer: More homogeneous data.

A small sample.

Reducing the number of predictors.

Adding more data on interest rates.

3. Question : With reference to problem 3, how is the regression constant or the a value interpreted?

Student Answer: It indicates the amount of error in the prediction.

It gauges the number of computers when efficiency is zero.

Office efficiency with no computers, controlling for the number of workers.

Number of workers, controlling for number of computers in the office.

4. Question : Which of the following is a problem in simple regression?

Student Answer: What is the correlation between years of experience and productivity?

Is there a significant difference in job satisfaction between men and women?

Can age predict length of tenure in a position?

What is the proportion of variance in productivity explained by experience?

5. Question : In a problem where average temperature and number of daylight hours are used to predict energy consumption in homes, what does the standard error of multiple estimate gauge?

Student Answer: Prediction error

The value of the first predictor.

The error in the second predictor.

The correlation of the criterion with the predictors.

6. Question : What does “shrinkage” mean in reference to regression solutions?

Student Answer: A reduction in the error term.

The solution works less well with new data.

The sample size has been reduced.

A reduction in the number of predictor variables.

7. Question : The degree to which years of education and years of experience together correlate with annual salary is indicated in multiple correlation.

Student Answer: True

False

8. Question : The criterion variable in regression is the variable used to predict the value of y.

Student Answer: True

False

9. Question : Which of the following are consistent with the requirements of simple regression?

Student Answer: Using sales volume to predict dollar profits.

Using the sales associate’s ranking to predict job satisfaction.

Using the employee’s gender to predict their productivity ranking.

Using the employee’s gender to predict marital status.

10. Question : Larger sample diminish the standard error of the estimate.

Student Answer: True

False

BUS308 Week 5 Final Project Part 2

Final Project

To complete this project, use the “Final Project Data Set” found in your eCollege classroom in the Final Project description.

PART II:

Imagine that you are a manager at a delivery service and you are creating a report to project the effects on your company of rising gas prices in the next ten years. Using the preceding statistical analysis as your basis and outside scholarly resources to support your claims, write a 3 to 5 page paper interpreting the results from this perspective. Include the following considerations:

Introduce the project and its significance to the company. Explain the statistical analysis that you completed in Part I. Be sure to explain where the data came from, what analysis was done, and what the results were. Give conclusions that you have drawn from the data. Consider the effects of your gas price predictions on the delivery business. Also consider whether or not you believe your predicted gas prices are accurate. What could occur in the future that would change your linear regression line and therefore your prediction?

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