You are the manager at a company and are asked to present a report on the year-to-date

performance of your division. What type of statistical information would you include in

your report? In particular, which descriptive statistics (mean, median, standard deviation,

etc.) do you think would best represent the main aspects of the performance of your

division? What types of graphical presentation (histogram, dot plot, stem-and-leaf, bar

chart, etc.) would you include? Explain your reasoning

Week 1 Assignment

BUS308: Statistics for Managers

1.2 Below we list several variables. Which of these variables are quantitative and which are qualitative?

1)The dollar amount of on an accounts receivable invoice

a. Quantitative; dollar amounts measures how much

2)The net profit for a company in 2009.

b. Quantitative; net profit measures how much.

3)The stock exchange on which a company’s stock is traded

c. Qualitative; which stock exchange is categorical.

4)The national debt of the United States in 2009.

d. Quantitative; national debt measures how much.

5)The advertising medium (radio, television, or print) used to promote a product.

e. Qualitative; media is categorical.

The Empirical Rule vs. Chebyshev’s Theorem

Discuss how the Empirical Rule works and how it relates to the bell curve as illustrated in Figure 3.14

(a). Then, explain Chebyshev’s Theorem and how it is different from the Empirical Rule. Give a specific

example of a population with which the Empirical Rule might be most effective and one with which

Chebyshev’s Theorem might be most effective. Respond to at least two of your classmates’ postings.

Question :

The two types of quantitative variables are

 

Student Answer: ordinal and ratio.   interval and ordinal.   nominative and ordinal.  

interval and ratio.   nominative and interval.   Points Received: 1 of 1

  Comments:

Question :

As a general rule, wh

 

en creating a stem-and-leaf display, there should be between ______ stem val

ues. 

Student Answer: 3 and 100   1 and 100   no fewer than 20   5 and 20   Points Received: 1 of 1

  Comments:

Question :

The median is the value below which and above which appr

 

oximately 50 percent of the measurements lie.

Student Answer: True   False   Points Received: 1 of 1

  Comments:

Question :

Temperature in degre

 

es Fahrenheit is an example of a ____ variable.

Student Answer:     Points Received: 1 of 1

  Comments:

Question :

Stem-and-leaf dis

 

plays and dot plots are useful for detecting

     Points Received: 1 of 1

  Comments:

Question :

Any characteristic of a p

 

opulation unit is called a

Student Answer:     Points Received: 1 of 1

  Comments:

Question :

The science of using a sample to make ge

 

neralizations about the important aspects of a population is known as

Student Answer:     Points Received: 1 of 1

  Comments:

Question :

A normal population has 99.73 percent of the population measurements wit

 

hin ___ standard deviations of the mean.

Student Answer:     Points Received: 1 of 1

  Comments:

Question :

When we are choosing a ra

 

ndom sample and we do not place chosen units back into the population, we are

Student Answer:     Points Received: 1 of 1

  Comments:

 10. Question : An example of manipulation of graphical display used to distort reality is: 

  Student Answer:   

Week 2Assignment

BUS308: Statistics for Managers

4.4 a.

This diagram produced using Tree Diagram Generator.b.

1) BBB, GGG2) BGG, GBG, GGB3) GBB, BGB, BBG4) BBB

c. Each outcome has probability of 1/8 thus,1) 2(1/8) = 1/42) 3(1/8) = 3/8 3) 3(1/8) = 3/84) 1/8

Relative Frequency. Conceptually we would expect the probability of newborn males and females to be the same. However, census reports indicate that the ratios of males and females in various countries do not conform to the theoretical prediction. What do you think accounts for this variation? Can you think of other cases where the expected probabilities do not quite agree with the empirical values?

Applications for Probability. In what situations might you use probability as a manager to approach business-related problems? What are the advantages to using probability concepts in business decisions? Are there any disadvantages or possible pitfalls to avoid in using probability in business?

Question :

In a statistical study, the random varia

 

ble 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   Points Received: 1 of 1

  Comments:

Question :

The set of all possib

 

le experimental outcomes is called a(n)

Student Answer: sample space.   event.   experiment.   probability.   Points Received: 1 of 1

  Comments:

Question :

If two events are indepen

 

dent, then the probability of their intersection is represented by:

Student Answer: P(A ∩ B) = P(A) + P(B)   P(A ∩ B) = 0   P(A ∩ B) = P(A) * P(B)  

P(A ∩ B) = P(A) - P(B)   P(A ∩ B) = P(A) * P(A | B)   Points Received: 1 of 1

  Comments:

QA  

uestion :

(n) __________ is a measure of the chance that an uncertain event will oc

cur.

    

 Points Receive :

1 of 1

  Comments:

Question :

The price-to-earning ratio for firms in a given industry is dist

 

ributed according to normal distribution. In this industry, a firm with a Z value e

qual to 1

     Points Received: 1 of 1

  Comments:

Question :

The expected value of a discrete random variable is:

 

    Points Received: 1 of 1

  Comments:

Question :

For a continuous distribution, P(a ≤ X ≤ b) = P(a <X< b).

 

   Points Received: 1 of 1

  Comments:

Quest

The fol

 

ion :

lowing formula: P(A U B) = P(A) + P(B) - P(A ∩ B) represents

Student Answer:    

 P ints Received:

1 of 1

  Comments:

 9. 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?

Week 3Assignment

BUS308: Statistics for Managers

7.11a.The sample mean is normally distributed. No, we do not have to make any assumptions about the shape of the population because the sample size is larger (> 30).

b. u2 = 20, 4 = 4/642 - 4/8 = .5c. = .0228Mega Stat:normal distribution P(lowe

r) P(uppe

r) z X mean std.dev.9772 .0228 2.00 21 20 0.5

d. = .1093

Mega Stat:normal distribution P(lowe

r) P(uppe

r) z X mean std.dev

.1093 .8907-

1.23 19.385 20 0.5

Unscientific Sampling. Consider question 7.45 from the text: A Milwaukee television station, WITI-TV, conducted a telephone call-in survey asking whether viewers liked the new newspaper, the Journal Sentinel. On April 26, 1995, Tim Cuprisin, a columnist for the Journal Sentinel, wrote the following comment: “WITI-TV (Channel 6) did one of those polls—which they admit are unscientific—last week and found that 388 viewers like the new Journal Sentinel and 2,629 didn’t like it. We did our own unscientific poll on whether those Channel 6 surveys accurately reflect public opinion. The results: a full 100 percent of the respondents say absolutely, positively not.”Is Cuprisin’s comment justified?

Article Review. Many articles present statistical data and list margins of error (for

example, reports on political opinion polls, growth or decline of the housing markets,

manufacturing sectors, etc.). Find one such article from a reliable source (such as EBSCO

or Proquest) in the online library that includes a construction of confidence intervals for

the data studied, and give a summary of the topic and the statistical results presented. In

particular, discuss whether there is enough information presented in the article to arrive at

the same conclusion as reported

Question :

There is little difference between the values of ta/

2 and Za/2

when the s

 

ample

Student Answer: size is small.   size is large.   mean is small.   mean is large.  standard deviation is small.   Points Received: 1 of 1

  Comments:

Question :

If the population proportion is .4 with a sample size of 20, th

 

en is this sample large enough so that the sampling distribution of is a normal dist

ribution.

Student Answer: True   False   Points Received: 1 of 1

  Comments:

Question :

For non-normal populations, as the sample size (n) __

 

_______, the distribution of sample means approaches a/an _________

_ distribution.

Student Answer: decreases, uniform   increases, normal   decreases, normal   increases,

uniform   increases, exponential   Points Received: 1 of 1

  Comments:

 4. Question : As the sample size ________the variation of the sampling distribution of ___________.

Question :

Assuming the same value of a, as the sample siz

 

e increases, the value of ta/

2 approaches the value of Za/2

.

   Points Received: 1 of 1

  Comments:

 6. Question : If the sampled population has mean 48 and standard deviation 16, then the mean and the standard deviation for the sampling distribution of for n = 16 are

 

 7. Question : The sampling distribution of x bar must be a normal distribution with a mean 0 and standard deviation 1.

 8. Question : As our sample standard deviation increases when all other parts of the confidence interval stay the same, then the confidence interval will become:

 9. 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.

 10. 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

Week 4 Assignment

BUS308: Statistics for Managers

9.13THE VIDEO GAME SATISFACTION RATING CASE Recall that “very satisfied” customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 65 satisfaction rating to provide evidence supporting the claim that the mean composition satisfaction rating for the XYZ-Box exceeds 42.

a. Letting 𝝁 represents the mean composition satisfaction rating for the XYZ-Box, set up the null hypothesis Ho and the alternative hypothesis Ha needed if we wish to attempt to provide evidence supporting the claim that 𝝁 exceeds 42.

In order to support the claim that 𝝁 exceeds 42 the null and alternative claim hypothesis is:Null Ho: 𝝁 ≤42Alternative Ha: 𝝁 > 42

b. The random sample of 65 satisfaction ratings yields a sample mean of 𝑥 ̅ = 42.954. Assuming that o equals 2.64, use critical values to test Ho verses Ha at each of a = .10, .05, .1 and .001.

By applying the z test statistic formula of:

Give an example of a hypothesis test you could perform at work or at home. State what the Null

and the Alternative hypotheses would be in your test. Explain how you would settle on a

reasonable level of significance for your scenario. Also explain what the type I and II errors

would be if you reached the incorrect conclusion in your test.

Creating Hypotheses. Assume you are the manager of a paint manufacturing factory. Your company has received complaints from customers that the containers hold less than the amount printed on them. On the other hand, corporate management is concerned that the containers hold more than the standard amount. You assign a statistician to verify these claims. A sample of containers was selected and the volume of paint in each container was measured. Assuming that the volume printed on each container is 1 gallon, how would you formulate the null and alternative hypotheses to test the customers’ claim? As a manager, what reasonable criteria will you use to set a value for the level of significance to be used in the test? After answering this question, what type of error would you suppose may result in that case?

Question :

Consider using p-value to te

 

st H0

versus Ha by setting α equal to .10. We reject H0 at level α of sign

ificance if and only if the p-value is:

Student Answer: Greater than α/2   Greater than α   Less than α   None of th above

  Points Received: 1 of 1

  Comments:

Question :

When carrying o

 

ut a sample test (with ó known) of H0: µ = 10 vs. Ha: µ > 10 by using a rejection poi

nt, 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.   Points Received: 1 of 1

  Comments:

 3. Question : When using the chi-square goodness of fit test, if the value of the chi-square statistic is large enough, we reject the null hypothesis.

 4. Question : The actual counts in the cells of a contingency table are referred to as the expected cell frequencies.

 5. 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.

 6. Question : When we carry out a chi-square test for independence, the null hypothesis states that the two relevant classifications

 7. 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.

 8. Question : A type II error is failing to reject a false null hypothesis. 9. Question : For the chi-square goodness of fit test, the rejection point X2

a is in

 10. Question : If a null hypothesis is not rejected at a significance level of .05, it will ______ be rejected at a significance level of .01.

Linear Correlation. Do you think there is a correlation between CEO salaries and the degree of success of a company? If you were to take a sample of companies with comparable size, market capitalization, and product category, and plot CEO salaries against the net profit of their respective companies, do you expect to find a linear correlation between the two? Explain.

Quality Control. Visit the websites on Quality Control (QC) listed in the Required Websites for this week. In addition, locate an article on the Internet or in the Library databases that describes an example of the use of statistics in Quality Control. In your post, briefly define Quality Control and explain its importance. Also, describe some of the most widely used tools in the industry for measuring and controlling quality, emphasizing their relationship to what you have encountered in this class. Finally, explain the example from your article of statistics as applied in a Quality Control context.

Gas Prices Linear Regression

BUS308: Statistics for Managers

Gas Prices Linear Regression

As a manager of a delivery service our bottom line and profit margins are extremely

dependent upon the rise and fall of gas prices. Thus, a report to project the effects of rising gas

prices within the next ten years is crucial to the survivability and profitability of the company.

Furthermore, it is necessary to accurately consider the effects of the gas price predictions on the

delivery business as a whole. Furthermore, there are a lot of external factors that can and will

affect the gasoline prices. For instance, “The 1990-1991 Persian Gulf crisis and other recent oil

market disruptions have brought to attention the response of retail gasoline prices to fluctuations

in world oil prices. Some observers have asserted that gasoline prices react more quickly to

increases in crude oil prices than to decreases” (Borenstein, 1997).