True or False

1) A correlation coefficient based on a scatter plot measures the proportion of data lying on the regression line.

2)Which of the following is/are incorrect statement(s) about the correlation between two quantitative variables ?X and ?Y?

I. A correlation of -0.8 indicates a stronger linear association between X and Y than a correlation of 0.5.
II. A correlation of 0 implies ?X and ?Y are not related at all.
III. A correlation of -1 indicates that ?=−?Y=−X.

Helen Keplinger must choose the amount of two wine types she will produce. Each liter of Red wine returns $7 profit, while each liter of White wine returns $2 profit. The labor hours and bottling time used for each type of wine are given in the table below. Resources available include 169 labor hours and 74.25 hours of bottling process time. Assume the Helen Keplinger has more than enough grapes available to supply any feasible production plan.

a) Formulate a linear programming model that will enable Helen Keplinger to determine the number of liters of each type of wine to produce in order to maximize her profit. (15 pts)

b) Suppose Helen Keplinger labor hours varies from 150 to 250 with 10-unit increments. Use SolverTable to determine her expected profit? Would her bottling plan change? Explain your answer. (5 pts)

Today’s Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Phyllis Weinberger, who is responsible for advising the president of Today’s Electronics on electronic manufacturing equipment, has developed the following table concerning a proposed facility:

a. Develop an opportunity loss table.

b. What is the minimax regret decision?

Use .7 alpha for Hurwicz

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

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.

(a)

Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

State the null and alternative hypotheses.

H₀: The type of ticket purchased is not independent of the type of flight.
H_a: The type of ticket purchased is independent of the type of flight. H₀: The type of ticket purchased is not mutually exclusive from the type of flight.
H_a: The type of ticket purchased is mutually exclusive from the type of flight.     H₀: The type of ticket purchased is independent of the type of flight.
H_a: The type of ticket purchased is not independent of the type of flight. H₀: The type of ticket purchased is mutually exclusive from the type of flight.
H_a: The type of ticket purchased is not mutually exclusive from the type of flight.

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 =

It might be predicted that consumer buying behavior would vary with the location of products in a store. Therefore, a team of market researchers looked at the sales per day for a well-known and unknown brand of candy bars. Additionally, the researchers placed the candy bars in the usual location and next to the cash register in different stores. What can the market researchers conclude with an α of 0.05?

a) Compute the appropriate test statistic(s) to make a decision about H₀.
Location: critical value =  ; test statistic =  


Brand: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


b) Compute the corresponding effect size(s) and indicate magnitude(s).
Location: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Brand: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


c) Make an interpretation based on the results.

There is a location difference on candy bar sales.There is no location difference on candy bar sales.     

There is a brand difference on candy bar sales.There is no brand difference on candy bar sales.     

There is a location by brand interaction on candy bar sales.There is no location by brand interaction on candy bar sales.

For the following scenario, answer the following questions. The underlined text is the name of the StatCrunch data set to be used for that part. Please note, do not conduct inference in this problem; just answer each question.

Heights of Fathers and Sons. To test the claim that sons are taller than their fathers on average, a researcher randomly selected 13 fathers who have adult male children. She records the height of both the father and son in inches.
Note: to answer the questions below, subtract (Son’s Height – Father’s Height).

Data:

Sons   Fathers

64.4 79
69.2 67.1
76.4 70.9
69.2 66.8
78.2 72.8
76.9 70.4
71.8 70.3
79 70.1
75.8 79.5
72.3 65.5
69.2 65.4
66.9 69.1
64.5 74.5

1. a) What is (are) the parameter(s) of interest? Choose one of the following symbols the population mean)D (the mean difference from paired (dependent) data)2 (the difference of two independent means) and describe the parameter in context of this question in one sentence.

2. b) Depending on your answer to part (a), construct one or two relative frequency histograms. Remember to properly title and label the graph(s). Copy and paste these graphs into your document.

3. c) Describe the shape of the histogram(s) in one sentence.

4. d) Depending on your answer to part (a), construct one or two boxplots and copy and paste these graphs into your document.

5. e) Does the boxplot (or do the boxplots) show any outliers? Answer this question in one sentence and identify any outliers if they are present.

6. f) Considering your answers to parts (c) and (e), is inference appropriate in this case? Why or why not? Defend your answer using the graphs in two to three sentences.

Caffeine is the world's most widely used stimulant, with approximately 80% consumed in the form of coffee. Participants in a study investigating the relationship between coffee consumption and exercise were asked to report the number of hours they spent per week on moderate (e.g., brisk walking) and vigorous (e.g., strenuous sports and jogging) exercise. Based on these data the researchers estimated the total hours of metabolic equivalent tasks (MET) per week, a value always greater than 0. The table below gives summary statistics of MET for women in this study based on the amount of coffee consumed.

Caffeinated coffee consumption

(a) Write the hypotheses for evaluating if the average physical activity level varies among the different levels of coffee consumption.

• A: Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
  Ha: μ₁ ≠ μ₂ ≠ μ₃ ≠ μ₄ ≠ μ₅
• B: Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
  Ha: At least one pair of means is the same
• C: Ho: μ₁ = μ₂ = μ₃ = μ₄ = μ₅
  Ha: At least one of the means is different

(b) Assume that all of the conditions required for this inference are satisfied.
(c) Below is part of the output associated with this test. Fill in the empty cells.

(d) What is the p-value associated with the ANOVA test?
p =

(e) What is the conclusion of the test?

• A: Since p < α we reject the idea that all of the means are the same and accept that all of the means are different
• B: Since p < α we reject the idea that all of the means are the same and accept that at least one of the means is different
• C: Since p < α we reject the idea that all of the means are different and accept that all of the means are the same
• D: Since p<α we reject the idea that at least one of the means is different and accept that all of the means are the same

The following data are from a completely randomized design.

1. Compute the sum of squares between treatments. Round the intermediate calculations to whole number.
     
   
2. Compute the mean square between treatments.
     
   
3. Compute the sum of squares due to error.
     
   
4. Compute the mean square due to error (to 1 decimal).
     
   
5. Set up the ANOVA table for this problem. Round all Sum of Squares to the nearest whole number. Round all Mean Squares to one decimal place. Round F to two decimal places. Round p-value to four decimal places.
   

   Source of Variation	Sum of Squares	Degrees of Freedom	Mean Square	F	p-value
   Treatments
   Error
   Total

Terry is a small business entrepreneur and owns 6 buildings for business use. The probability distribution below describes expected property losses for the group of 6 buildings. Assume that the property exposures are independent of each other.

Losses $                                                          Probability of Loss

$10,000                                                           0.20

$20,000                                                           0.10

$50,000                                                           0.06

$100,000                                                         0.03

$500,000                                                         0.01

Now suppose Terry joins a risk sharing arrangement with other small business owners and now a total of 18 buildings are in the risk sharing pool. Assume that the property losses for the additional buildings follow the same probability distribution as that given for Terry’s buildings and losses are independent.

a. Find the average or expected loss of this larger group of buildings in a given year.

b. Calculate the standard deviation of the distribution.

c. Find the Coefficient of Variation

d. What happens to variance or risk for Terry after the sharing arrangement is in place?

e. What would you expect to happen to variance or risk if the pool was extremely large? Why?

f. What is Terry’s actuarially fair premium now? What has happened to his risk premium now?

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 431 gram setting. It is believed that the machine is underfilling the bags. A 23 bag sample had a mean of 423 grams with a standard deviation of 14. Assume the population is normally distributed. A level of significance of 0.05 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.

(a)Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

State the null and alternative hypotheses.

H₀: The type of ticket purchased is not independent of the type of flight.
H_a: The type of ticket purchased is independent of the type of flight.H₀: The type of ticket purchased is not mutually exclusive from the type of flight.
H_a: The type of ticket purchased is mutually exclusive from the type of flight.    H₀: The type of ticket purchased is independent of the type of flight.
H_a: The type of ticket purchased is not independent of the type of flight.H₀: The type of ticket purchased is mutually exclusive from the type of flight.
H_a: The type of ticket purchased is not mutually exclusive from the type of flight.

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

Please explain how to get test statistic on excel and by hand.

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

Please explain how to get test statistic on excel or by hand.

p-value =

State your conclusion.

Reject H₀. We conclude that the type of ticket purchased is independent of the type of flight.

Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are independent.    

Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are not independent.

Reject H₀. We conclude that the the type of ticket purchased is not independent of the type of flight.

(b)

Discuss any dependence that exists between the type of ticket and type of flight.

The type of ticket purchased is independent of the type of flight.

A higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights. Economy class tickets are purchased more for domestic flights.    

A higher percentage of first class and business class tickets are purchased for domestic flights compared to international flights. Economy class tickets are purchased more for international flights.

A lower percentage of economy class tickets are purchased for domestic flights compared to international flights. First class and business class tickets are purchased more for domestic flights.

A magazine provided overall customer satisfaction scores for AT&T, Sprint, T-Mobile, and Verizon cell-phone services in major metropolitan areas throughout the United States. The rating for each service reflects the overall customer satisfaction considering a variety of factors such as cost, connectivity problems, dropped calls, static interference, and customer support. A satisfaction scale from 0 to 100 was used with 0 indicating completely dissatisfied and 100 indicating completely satisfied. The ratings for the four cell-phone services in 20 metropolitan areas are contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.

a. Consider T-Mobile first. What is the median rating (to 1 decimal)?

b. Develop a five-number summary for the T-Mobile service.

c. Are there outliers for T-Mobile?

_________Yes, the data contain outliersNo, the data do not contain outliers

d. Repeat parts (b) and (c) for the other three cell-phone services.

Are there outliers for AT&T?

_________Yes, the data contain outliersNo, the data do not contain outliers

Are there outliers for Sprint?

_________Yes, the data contain outliersNo, the data do not contain outliers

Are there outliers for Verizon?

_________Yes, the data contain outliersNo, the data do not contain outliers

e. Which of the following box plots accurately displays the data set?

_________Box plot #1Box plot #2Box plot #3Box plot #4

Which service did the magazine recommend as being best in terms of overall customer satisfaction?

_________AT&TSprintT-MobileVerizon

A psychologist hypothesizes that depression decreases with aging. It is known that the general population scores a 41 on a standardized depression test where a higher score indicates more depression. The psychologist obtains a sample of individuals that are all over 65 years old. What can the psychologist conclude with an α of 0.05? The data are below.

a) What is the appropriate test statistic?
---Select--- na z-test One-Sample t-test Independent-Samples t-test Related-Samples t-test

b)
Population:
---Select--- elderly standardized depression test general population depression aging
Sample:
---Select--- elderly standardized depression test general population depression aging

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
p-value =  ; Decision:  ---Select--- Reject H0 Fail to reject H0

d) Using the SPSS results, compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

e) Make an interpretation based on the results.

The elderly are significantly more depressed than the population.

The elderly are significantly less depressed than the population.    

The elderly did not significantly differ on depression than the population.

what is the difference between mutually exclusive, independent and conditional probabilities?