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Statistics for Business and Economics, 5e (Homework)

James Finch

Statistics, section 2, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 88

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

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10
3/12 6/6 0/5 1/2 0/5 –/6 0/4 –/12 –/3 –/33
Total
10/88 (11.4%)

  • Instructions

    Drawing from the authors’ unmatched experience as professors and consultants, Anderson/Sweeney/Williams/Camm/Cochran/Freeman/Shoesmith’s Statistics for Business and Economics, 5th edition, published by Cengage Learning, delivers sound statistical methodology, a proven problem-scenario approach, and meaningful applications that clearly demonstrate how statistical information impacts decisions in actual business practice. More than 350 real business examples, relevant cases, and hands-on exercises present the latest statistical data and business information with unwavering accuracy.

    An all new WebAssign online course management system is available with this powerful business statistics solution. WebAssign offers extensive content and interactive learning activities that will help your students master their subject. Its engaging practice problems and other learning tools, including labs, simulations and videos, bring the subjects to life and provide students with a full understanding of concepts.

    Question 1 is a multipart question that steps the student through the construction of a pie chart and frequency bar chart.

    Question 2 features multiple question types and guides students through the process of interpreting values.

    Question 3 asks students to derive a formula and then use that formula to calculate probabilities.

    Question 4 includes an interactive applet to determine the sample size necessary for a given margin of error.

    Question 5 links to an Excel data file.

    Question 6 has a Master It that walks the student through how to do the problem. This Master It guides the student through the steps necessary to compute three different confidence intervals.

    Question 7 guides the student through a hypothesis test.

    Question 8 showcases a full ANOVA table the student completes and then uses to perform a hypothesis test.

    Question 9 displays grading for a multiple regression equation that is then used to make predictions.

    Question 10 guides students through the decision analysis process. 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. 3/12 points  |  Previous Answers ASWSBE5E 2.E.003.MI.SA. My Notes
Question Part
Points
Submissions Used
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4/50 2/50 1/50 1/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
3/12
 
This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
A questionnaire provides 67 Yes, 43 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 frequency bar chart.
Step 1

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

A pie chart displays categorical data as sections of a circle, called sectors. Pie charts depict the frequency, relative frequency, or percent frequency distribution of a set of data. Each sector will cover an area that corresponds to the relative frequency for each class in the data. Recall that the relative frequencies will always sum to 1. Since there are 360 degrees in a circle, each section will cover an area that is 360(relative frequency) degrees.
Therefore, the relative frequency for the Yes answers is needed here. The relative frequency of the Yes answers is the ratio of the Yes answers to the total sample size. The total sample size can be found by taking the sum of the answers from this questionnaire.
total sample size = Yes + No + No Opinion
 = 67 + 43 + 10
 = 120 Correct: Your answer is correct. seenKey

120
Given that there are 67 Yes answers, find the corresponding relative frequency, leaving your answer as a fraction.
relative frequency = 67/122 Incorrect: Your answer is incorrect. seenKey

67/120
Step 2
Now that the relative frequency has been found, we can find the number of degrees in the Yes answers portion of the pie chart by multiplying this value,
67
120
,
 by the number of degrees in a circle, 360.
degrees in Yes portion = 
67
120 Correct: Your answer is correct. seenKey

120
360 degrees
 = 201 Correct: Your answer is correct. seenKey

201

 degrees
Step 3

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

As in part (a), first find the relative frequency of the No answers. The sample size was found to be 120, so the relative frequency will be the ratio of the number of No answers to the total sample size. There were 43 No answers. Find this ratio, leaving your answer as a fraction.
relative frequency of No answers = 
number of No answers
total number of answers
 
 = 


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2. 6/6 points  |  Previous Answers ASWSBE5E 4.E.022. My Notes
Question Part
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1/1 1/1 1/1 1/1 1/1 1/1
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6/6
 
Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know
P(A) = 0.20
 and
P(B) = 0.50.
(a)
What is
P(A ∩ B)?
P(A ∩ B)
 = Correct: Your answer is correct.
(b)
What is
P(A | B)?
P(A | B)
 = Correct: Your answer is correct.
(c)
A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Do you agree with this statement? Use the probability information in this problem to justify your answer.
Events A and B Correct: Your answer is correct. independent because Correct: Your answer is correct. , therefore I Correct: Your answer is correct. with the student.
(d)
What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
Mutually exclusive events are Correct: Your answer is correct. .
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3. 0/5 points  |  Previous Answers ASWSBE5E 6.E.025. My Notes
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Points
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0/1 0/1 0/1 0/1 0/1
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0/5
 
Consider the following exponential probability density function.
f(x) = 
1
5
e−x/5     for x ≥ 0
(a)
Write the formula for
P(X ≤ x0).
25
Incorrect: Your answer is incorrect.
(b)
Find
P(X ≤ 2).
 (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(c)
Find
P(X ≥ 5).
 (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(d)
Find
P(X ≤ 6).
 (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
(e)
Find
P(2 ≤ X ≤ 6).
 (Round your answer to four decimal places.)
Incorrect: Your answer is incorrect.
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4. 1/2 points  |  Previous Answers ASWSBE5E 8.AQ.502. My Notes
Question Part
Points
Submissions Used
1 2
1/1 0/1
3/50 1/50
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1/2
 
Use the applet "Sample Size and Interval Width when Estimating Proportions" to answer the following questions.
This applet illustrates how sample size is related to the width of a 95% confidence interval estimate for a population proportion.
(a)
At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.023?
Correct: Your answer is correct.
(b)
As the sample size decreases for any given confidence level, what happens to the confidence interval?
     Incorrect: Your answer is incorrect.
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5. 0/5 points  |  Previous Answers ASWSBE5E 9.E.028. My Notes
Question Part
Points
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1 2 3 4 5
0/1 0/1 0/1 0/1 0/1
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0/5
 
DATAfile: WildLife
You may need to use the appropriate appendix table or technology to answer this question.
Wild Life retail chain specializes in outdoor clothing and camping gear. It is considering a promotion that involves mailing discount coupons to all their credit card customers. This promotion will be considered a success if more than 12 per cent of coupon recipients use them. Before going nationwide with the promotion, coupons were sent to a sample of 100 credit card customers.
(a)
Formulate hypotheses that can be used to test whether the population proportion of those who will use the coupons is sufficient to go national.
     Incorrect: Your answer is incorrect.
(b)
The file WildLife contains the sample data.
Used Coupon?
No No No Yes No No Yes No No No
No No No No No No No No No No
No No No No Yes No No Yes No No
No No No No No No Yes No No No
No No No No No No No No No Yes
Yes No Yes No No No No No No No
No No No No No No No No Yes No
No No No Yes No No No No No No
No No No No No No No No No No
Yes No Yes Yes No No No No No No
Compute a point estimate of the population proportion.
Incorrect: Your answer is incorrect.
(c)
Use
α = 0.05
 to conduct your hypothesis test. Should Wild Life go national with the promotion?
Find the value of the test statistic. (Round your answer to two decimal places.)
Incorrect: Your answer is incorrect.
Find the p-value. (Round your answer to four decimal places.)
p-value = Incorrect: Your answer is incorrect.
what is your conclusion?
     Incorrect: Your answer is incorrect.
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6. –/6 points ASWSBE5E 11.E.002.MI. My Notes
Question Part
Points
Submissions Used
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–/6
 
You may need to use the appropriate appendix table or technology to answer this question.
A sample of 23 items provides a sample standard deviation of 6.
(a)
Compute the 90% confidence interval estimate of the population variance. (Round your answers to two decimal places.)
to
(b)
Compute the 95% confidence interval estimate of the population variance. (Round your answers to two decimal places.)
to
(c)
Compute the 95% confidence interval estimate of the population standard deviation. (Round your answers to one decimal place.)
to

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7. 0/4 points  |  Previous Answers ASWSBE5E 12.E.014. My Notes
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1 2 3 4
0/1 0/1 0/1 0/1
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0/4
 
You may need to use the appropriate technology to answer this question.
The following 2 X 3 contingency table contains observed frequencies for a sample of 200.
Row
Variable 		Column Variable
A B C
P 16 40 46
Q 34 30 34
Test for independence of the row and column variables using the
χ2
 test with
α = 0.05.
State the null and alternative hypotheses.
     Incorrect: Your answer is incorrect.
Find the value of the test statistic. (Round your answer to three decimal places.)
Incorrect: Your answer is incorrect.
Find the p-value. (Round your answer to four decimal places.)
p-value = Incorrect: Your answer is incorrect.
State your conclusion.
     Incorrect: Your answer is incorrect.
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8. –/12 points ASWSBE5E 13.E.005. My Notes
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Points
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0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
Total
–/12
 
You may need to use the appropriate technology to answer this question.
In a completely randomized design, 11 experimental units were used for the first treatment, 13 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.)
Source
of Variation 		Sum
of Squares 		Degrees
of Freedom 		Mean
Square 		F p-value
Treatments 1,500
Error
Total 2,200
At a 0.05 level of significance, is there a significant difference between the treatments?
State the null and alternative hypotheses.
    
Find the value of the test statistic. (Round your answer to two decimal places.)
Find the p-value. (Round your answer to four decimal places.)
p-value =
State your conclusion.
    
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9. –/3 points ASWSBE5E 15.E.006. My Notes
Question Part
Points
Submissions Used
1 2 3
–/1 –/1 –/1
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–/3
 
DATAfile: MonitorRatings
A statistical program is recommended.
PC Magazine provided ratings for several characteristics of computer monitors, including an overall rating.†Source: PC Magazine website, April, 2015 The following data show the rating for contrast ratio, resolution, and the overall rating for ten monitors tested using a 0–100 point scale. The highest rated monitor was the BenQ BL3201PH, with an overall rating of 87.
Model Contrast
Ratio 		Resolution Overall
Rating
BenQ BL3201PH 78 89 87
AOC U2868PQU 98 87 86
NEC MultiSync PA322UHD 84 82 85
Acer XB280HK 78 77 82
Asus ROG Swift PG278Q 65 82 82
AOC E1759Fwu 57 78 82
Dell UltraSharp UZ2715H 56 83 81
NEC MultiSync EA244UHD 77 75 79
HP DreamColor Z27x 47 81 77
Dell UltraSharp UZ2315H 55 70 76
(a)
Develop the estimated regression equation that can be used to predict the overall rating using the contrast ratio rating. (Round your numerical values to two decimal places. Let x1 represent the contrast ratio rating and y represent the overall rating.)
ŷ =
(b)
Develop the estimated regression equation that can be used to predict the overall rating using both the contrast ratio rating and the resolution rating. (Round your numerical values to two decimal places. Let x1 represent the contrast ratio rating, x2 represent the resolution rating, and y represent the overall rating.)
ŷ =
(c)
Predict the overall rating for a computer monitor computer that has a contrast ratio rating of 85 and a resolution rating of 72. (Round your answer to the nearest integer.)
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10. –/33 points ASWSBE5E 21.XP.002. My Notes
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Points
Submissions Used
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–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50 0/50
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–/33
 
A survey ranked the Finger Lakes region of New York state as the top wine region to visit. Finger Lakes vineyards typically specialize in growing grapes for white wines such as Chardonnay and Riesling. Seneca Hill Winery recently purchased land for the purpose of establishing a new vineyard. Management is considering two varieties of white grapes for the new vineyard: Chardonnay and Riesling. The Chardonnay grapes would be used to produce a dry Chardonnay wine, and the Riesling grapes would be used to produce a semidry Riesling wine. It takes approximately four years from the time of planting before new grapes can be harvested. This length of time creates a great deal of uncertainty concerning future demand and makes the decision concerning the type of grapes to plant difficult. Three possibilities are being considered: Chardonnay grapes only; Riesling grapes only; and both Chardonnay and Riesling grapes. Seneca management decided that for planning purposes it would be adequate to consider only two demand possibilities for each type of wine: strong or weak. With two possibilities for each type of wine it was necessary to assess four probabilities. With the help of some forecasts in industry publications management made the following probability assessments.
Chardonnay Demand Riesling Demand
Weak Strong
Weak 0.05 0.50
Strong 0.25 0.20
Revenue projections show an annual contribution to profit of $30,000 if Seneca Hill only plants Chardonnay grapes and demand is weak for Chardonnay wine, and $80,000 if the company only plants Chardonnay grapes and demand is strong for Chardonnay wine. If the company only plants Riesling grapes, the annual profit projection is $35,000 if demand is weak for Riesling grapes and $55,000 if demand is strong for Riesling grapes. If Seneca plants both types of grapes, the annual profit projections are as shown in the following table.
Chardonnay Demand Riesling Demand
Weak Strong
Weak $32,000 $50,000
Strong $36,000 $70,000
(a)
What is the decision to be made, what is the chance event, and what is the consequence?
The decision to be made is . The chance event is . The consequence is .
Identify the alternatives for the decisions and the possible outcomes for the chance events.
The alternatives for the decisions are . The possible outcomes for the chance events are .
(b)
Develop a decision tree. (Enter monetary values in thousands and percentages in decimal form.)
A decision tree has 16 answer blanks. Refer to the adjacent list for more details.
  • A decision tree begins at decision node 1 and an upper, middle, and lower branch extend from this node to the right. The upper branch, labeled Plant Chardonnay, stops at chance node 2 and an upper and lower branch extend from this node to the right. The middle branch, labeled Plant both grapes, stops at chance node 3 and four branches extend from this node to the right. The lower branch, labeled Plant Riesling, stops at chance node 4 and an upper and lower branch extend from this node to the right.
  • The branches extending from decision node 1 from top to bottom are labeled Plant Chardonnay, Plant both grapes, and Plant Riesling. The next set of branches from top to bottom are labeled Weak for Chardonnay, Strong for Chardonnay, Weak Chardonnay Weak Riesling, Weak Chardonnay Strong Riesling, Strong Chardonnay Weak Riesling, Strong Chardonnay Strong Riesling, Weak for Riesling, and Strong for Riesling. There is an answer blank at the end of each branch as well as below each branch.
(c)
Use the expected value approach to recommend which alternative Seneca Hill Winery should follow in order to maximize expected annual profit.
EV(Plant Chardonnay) EV(Plant both grapes) EV(Plant Riesling) The best decision is to plant grapes.
(d)
Suppose management is concerned about the probability assessments when demand for Chardonnay wine is strong. Some believe it is likely for Riesling demand to also be strong in this case. Suppose the probability of strong demand for Chardonnay and weak demand for Riesling is 0.05 and that the probability of strong demand for Chardonnay and strong demand for Riesling is 0.40. How does this change the recommended decision? Assume that the probabilities when Chardonnay demand is weak are still 0.05 and 0.50.
EV(Plant Chardonnay) EV(Plant both grapes) EV(Plant Riesling) The best decision is to plant grapes.
(e)
Other members of the management team expect the Chardonnay market to become saturated at some point in the future, causing a fall in prices. Suppose that the annual profit projections fall to $50,000 when demand for Chardonnay is strong and Chardonnay grapes only are planted. Using the original probability assessments, determine how this change would affect the optimal decision.
EV(Plant Chardonnay) EV(Plant both grapes) EV(Plant Riesling) The best decision is to plant grapes.
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