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Statistics, section 2, Fall 2019
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Anderson et al-Stats for Business & Economics 13/e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 15 / 87

Due : Sunday, January 27, 2030 23:30 EST

Last Saved : n/a Saving... ()

Ask Your Teacher Extension Requests Print Assignment

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Points

1	2	3	4	5	6	7	8	9	10
3/4	5/11	–/17	7/14	–/6	–/6	–/4	–/14	–/5	–/6

Total

15/87 (17.2%)

Instructions

Statistics for Business and Economics, revised 13th edition, written by David Anderson, Dennis Sweeney, Thomas Williams, Jeffrey Camm, and James Cochran and published by Cengage Learning brings more out of your statistics course than simply solving equations! Statistics for Business and Economics, revised 13th edition brings together more than twenty-five years of author experience, sound statistical methodology, a proven problem-scenario approach, and meaningful applications that clearly demonstrate how statistical information informs decisions in the business world. Thoroughly updated, the text's more than 350 real business examples, cases, and memorable exercises present the latest statistical data and business information with unwavering accuracy. It also gives you the most relevant text you can get for your course, including coverage of popular commercial statistical software programs—Minitab 17 and Excel 2016. Optional chapter appendices, coordinating online data sets, and support materials such as the CengageNOW online course management system, make Statistics for Business and Economics, revised 13th edition a customizable, efficient, and powerful approach to mastering the statistical concepts important to your success!

Question 1 is a multipart question that includes pie charts and bar charts.

Question 2 demonstrates the use of a boxplot.

Question 3 features multiple question types and guides students to interpret values.

Question 4 shows the use of a tree diagram.

Question 5 presents grading of an algebraic expression.

Question 6 contains grading for a confidence interval.

Question 7 links to an Excel data file.

Question 8 presents an interactive hypothesis test.

Question 9 exhibits grading for a linear regression model and displayed scatter diagrams.

Question 10 exhibits grading for a multiple regression model and grading for predicted values using the regression model. This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

The answer key and solutions will display after the first submission for demonstration purposes. Instructors can configure these to display after the due date or after a specified number of submissions.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/4 points | Previous Answers ASWSBE13 2.E.003. My Notes

A questionnaire provides 68 Yes, 42 No, and 10 No Opinion answers.

(a)

In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers?

(b)

How many degrees would be in the section of the pie showing the No answers?

(c)

Construct a pie chart.

(d)

Construct a bar chart.

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2. 5/11 points | Previous Answers ASWSBE13 3.E.051. My Notes

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.

8,508	1,274	1,972	8,879	2,359	11,513	608
14,138	6,552	1,850	2,818	1,456	10,398	7,478
4,019	4,241	839	2,027	3,653	5,694	8,205

(a)

Provide a five-number summary (in million dollars).

minimum

million dollars first quartile million dollars median million dollars third quartile million dollars maximum

million dollars

(b)

Compute the lower and upper limits (in million dollars).

lower limit million dollars upper limit million dollars

(c)

Do the data contain any outliers?

of the values are within the limits, therefore there are

outliers.

(d)

The largest company on this list has sales of $14,138 million. Suppose a data entry error (a transposition) had been made and the sales had been entered as $41,138 million. Would the method of detecting outliers in part (c) identify this problem and allow for correction of the data entry error?

This number

have shown up as an outlier.

(e)

Show a boxplot.

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3. –/17 points ASWSBE13 4.E.033. My Notes

Students taking a test were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows.

		Undergraduate Major			Totals
		Business	Engineering	Other	Totals
Intended Enrollment Status	Full-Time	354	199	252	805
Intended Enrollment Status	Part-Time	148	159	192	499
Totals		502	358	444	1,304

(a)

Develop a joint probability table for these data. (Round your answers to three decimal places.)

		Undergraduate Major			Totals
		Business	Engineering	Other	Totals
Intended Enrollment Status	Full-Time
Intended Enrollment Status	Part-Time
Totals					1.000

(b)

Use the marginal probabilities of undergraduate major (business, engineering, or other) to comment on which undergraduate major produces the most potential MBA students.

From the marginal probabilities, we can tell that majors produce the most potential MBA students.

(c)

If a student intends to attend classes full-time in pursuit of an MBA degree, what is the probability that the student was an undergraduate engineering major? (Round your answer to three decimal places.)

(d)

If a student was an undergraduate business major, what is the probability that the student intends to attend classes full-time in pursuit of an MBA degree? (Round your answer to three decimal places.)

(e)

Let A denote the event that the student intends to attend classes full-time in pursuit of an MBA degree, and let B denote the event that the student was an undergraduate business major. Are events A and B independent? Justify your answer. (Round your answers to three decimal places.)

P(A)P(B)

= and

P(A ∩ B)

= , so the events independent.

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4. 7/14 points | Previous Answers ASWSBE13 5.E.031. My Notes

Consider a binomial experiment with two trials and

p = 0.4.

(a)

Draw a tree diagram for this experiment (see the example figure).

(b)

Compute the probability of one success,

f(1).

f(1) =

(c)

Compute

f(0).

f(0) =

(d)

Compute

f(2).

f(2) =

(e)

Compute the probability of at least one success.

(f)

Compute the expected value, variance, and standard deviation. (Round your answer for the standard deviation to four decimal places.)

expected value variance standard deviation

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5. –/6 points ASWSBE13 6.E.005. My Notes

A company introduced a much smaller variant of its tablet, known as the tablet junior. Weighing less than 11 ounces, it was about 50% lighter than the standard tablet. Battery tests for the tablet junior showed a mean life of 10.75 hours. Assume that battery life of the tablet junior is uniformly distributed between 8.5 and 13 hours.

(a)

Give a mathematical expression for the probability density function of battery life.

f(y) =

,	8.5 ≤ y ≤ 13
,	elsewhere

(b)

What is the probability that the battery life for a tablet junior will be 9.5 hours or less? (Round your answer to four decimal places.)

(c)

What is the probability that the battery life for a tablet junior will be at least 11 hours? (Round your answer to four decimal places.)

(d)

What is the probability that the battery life for a tablet junior will be between 9.5 and 11 hours? (Round your answer to four decimal places.)

(e)

In a shipment of 100 tablet juniors, how many should have a battery life of at least 10 hours? (Round your answer to two decimal places.)

tablet juniors

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6. –/6 points ASWSBE13 8.E.002.MI. My Notes

You may need to use the appropriate appendix table or technology to answer this question.

A simple random sample of 60 items from a population with

σ = 8

resulted in a sample mean of 34. (Round your answers to two decimal places.)

(a)

Provide a 90% confidence interval for the population mean.

(b)

Provide a 95% confidence interval for the population mean.

(c)

Provide a 99% confidence interval for the population mean.

Need Help?

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7. –/4 points ASWSBE13 10.E.006. My Notes

DATAfile: Hotel

You may need to use the appropriate appendix table or technology to answer this question.

Suppose that you are responsible for making arrangements for a business convention and that you have been charged with choosing a city for the convention that has the least expensive hotel rooms. You have narrowed your choices to Atlanta and Houston. The file named Hotel contains samples of prices for rooms in Atlanta and Houston that are consistent with the results reported by Smith Travel Research.†Source: SmartMoney, March 2009 Because considerable historical data on the prices of rooms in both cities are available, the population standard deviations for the prices can be assumed to be $15 in Atlanta and $25 in Houston. Based on the sample data, can you conclude that the mean price of a hotel room in Atlanta is lower than one in Houston?

State the hypotheses. (Let μ₁ = mean hotel price in Atlanta and let μ₂ = mean hotel price in Houston.)

H₀: μ₁ − μ₂ < 0

H_a: μ₁ − μ₂ ≥ 0

H₀: μ₁ − μ₂ ≥ 0

H_a: μ₁ − μ₂ < 0

H₀: μ₁ − μ₂ > 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ ≠ 0

H_a: μ₁ − μ₂ = 0

H₀: μ₁ − μ₂ = 0

H_a: μ₁ − μ₂ ≠ 0

Calculate the test statistic. (Round your answer to two decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

p-value =

What is your conclusion?

Reject H₀. There is insufficient evidence to conclude that the mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston. Do not reject H₀. There is sufficient evidence to conclude that the mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston. Reject H₀. There is sufficient evidence to conclude that the mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston. Do not reject H₀. There is insufficient evidence to conclude that the mean price of a hotel room in Atlanta is lower than the mean price of a hotel room in Houston.

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8. –/14 points ASWSBE13 12.E.004. My Notes

You may need to use the appropriate technology to answer this question.

Benson Manufacturing is considering ordering electronic components from three different suppliers. The suppliers may differ in terms of quality in that the proportion or percentage of defective components may differ among the suppliers. To evaluate the proportion of defective components for the suppliers, Benson has requested a sample shipment of 500 components from each supplier. The number of defective components and the number of good components found in each shipment are as follows.

Component	Supplier
Component	A	B	C
Defective	13	18	38
Good	487	482	462

(a)

Formulate the hypotheses that can be used to test for equal proportions of defective components provided by the three suppliers.

H₀: All population proportions are not equal.
H_a: p_A = p_B = p_C H₀: Not all population proportions are equal.
H_a: p_A = p_B = p_C H₀: p_A = p_B = p_C
H_a: Not all population proportions are equal. H₀: p_A = p_B = p_C
H_a: All population proportions are not equal.

(b)

Using a 0.05 level of significance, conduct the hypothesis test.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the suppliers do not provide equal proportions of defective components. Do not reject H₀. We conclude that the suppliers do not provide equal proportions of defective components. Reject H₀. We conclude that the suppliers do not provide equal proportions of defective components. Reject H₀. We cannot conclude that the suppliers do not provide equal proportions of defective components.

(c)

Conduct a multiple comparison test to determine if there is an overall best supplier or if one supplier can be eliminated because of poor quality. Use a 0.05 level of significance. (Round your answers for the critical values to four decimal places.)

Comparison

p_i − p_j

CV_ij

Significant
Diff > CV_ij

A vs. B

A vs. C

B vs. C

Can any suppliers be eliminated because of poor quality? (Select all that apply.)

Supplier A Supplier B Supplier C none

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9. –/5 points ASWSBE13 14.E.009. My Notes

Companies in the U.S. car rental market vary greatly in terms of the size of the fleet, the number of locations, and annual revenue. In 2011, Hertz had 320,000 cars in service and annual revenue of approximately $4.2 billion. Suppose the following data show the number of cars in service (1,000s) and the annual revenue ($ millions) for six smaller car rental companies.

Company	Cars (1,000s)	Revenue ($ millions)
Company A	11.5	116
Company B	10.0	137
Company C	9.0	100
Company D	5.5	39
Company E	4.2	42
Company F	3.3	34

(a)

Develop a scatter diagram with the number of cars in service as the independent variable.

A scatter diagram has 6 points plotted on it. The horizontal axis ranges from 0 to 14 and is labeled: Cars in Service (1,000s). The vertical axis ranges from 0 to 160 and is labeled: Annual Revenue ($ millions). The points are plotted from left to right in an upward, diagonal direction starting from the lower left corner of the diagram and are between 3 to 12 on the horizontal axis and between 30 to 140 on the vertical axis. Each consecutive point is higher on the diagram than the previous point. The 3 leftmost points and the 3 rightmost points have a large amount of space between them.

(b)

What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?

There appears to be a negative linear relationship between cars in service (1,000s) and annual revenue ($ millions). There appears to be no noticeable relationship between cars in service (1,000s) and annual revenue ($ millions). There appears to be a positive linear relationship between cars in service (1,000s) and annual revenue ($ millions).

(c)

Use the least squares method to develop the estimated regression equation that can be used to predict annual revenue (in $ millions) given the number of cars in service (in 1,000s). (Round your numerical values to three decimal places.)

ŷ =

(d)

For every additional car placed in service, estimate how much annual revenue will change (in dollars). (Round your answer to the nearest integer.)

Annual revenue will increase by $ , for every additional car placed in service.

(e)

A particular rental company has 4,000 cars in service. Use the estimated regression equation developed in part (c) to predict annual revenue (in $ millions) for this company. (Round your answer to the nearest integer.)

$ million

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10. –/6 points ASWSBE13 16.E.005. My Notes

A statistical program is recommended.

A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized:

y = β₀ + β₁x + ε

where

y = traffic flow in vehicles per hour
x = vehicle speed in miles per hour.

The following data were collected during rush hour for six highways leading out of the city.

Traffic Flow (y)	Vehicle Speed (x)
1,255	35
1,327	40
1,227	30
1,333	45
1,347	50
1,122	25

In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation.

ŷ = b₀ + b₁x + b₂x²

(a)

Develop an estimated regression equation for the data of the form

ŷ = b₀ + b₁x + b₂x².

(Round b₀ to the nearest integer and b₁ to two decimal places and b₂ to three decimal places.)

ŷ =

(b)

Use α = 0.01 to test for a significant relationship.

State the null and alternative hypotheses.

H₀: One or more of the parameters is not equal to zero.
H_a: b₀ = b₁ = b₂ = 0 H₀: One or more of the parameters is not equal to zero.
H_a: b₁ = b₂ = 0 H₀: b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero. H₀: b₀ = b₁ = b₂ = 0
H_a: One or more of the parameters is not equal to zero.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

What is your conclusion?

Reject H₀. We conclude that the relationship is significant. Do not reject H₀. We cannot conclude that the relationship is significant. Reject H₀. We cannot conclude that the relationship is significant. Do not reject H₀. We conclude that the relationship is significant.

(c)

Base on the model predict the traffic flow in vehicles per hour at a speed of 38 miles per hour. (Round your answer to two decimal places.)

vehicles per hour

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