23. Late in summer of 1996, Tiger Woods became a professional golfer. This highly publicized event followed a sensational college career at Stanford University, where Tiger won three United States Amateur Championships. Tiger was not a professional very long before he had his first win on the pro tour, the Las Vegas Invitational. He received a total of $297,000 for his accomplishment. The prize money (in thousands of dollars) for the top 40 finishers in the tournament are given below.

1. Find the mean

2. Find the median

3. Find the mode

4. Find the 10% trimmed mean and compare it to the mean and the median.

5. Comment on the skewness of the distribution.

Assume that the age at onset of a certain disease is distributed normally with a mean of 43 years and a variance of 177.69 years.

a) What is the probability that an individual afflicted with the disease developed it before age 31?
probability =  

b) What is the probability that an individual afflicted with the disease developed it after age 48?
probability =  

c) What is the probability that an individual afflicted with the disease developed it between ages 31 and 48?
probability =  

uConstruct confidence intervals for the population mean of 80%, 90%, 95%, 99% using the following data and a population standard deviation of 900:

un = 100

u?x ̅ = 425

Consider a baseball world series (best of 7 game series) in which team A theoretically has a 0.55 chance of winning each game against team B. Simulate the probability that team A would win the world series against team B simulating 1,000 world series. What is the probability that team A would win? (USE R - include R output)

Imagine a class where nearly everyone scores between 83-84%, with hardly any dispersion beyond this narrow peak. How would you describe this distribution in terms of kurtosis?

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