Rework problems 13 and 14 from section 2.4 of your textbook (page 81) about the bucket containing orange tennis balls and yellow tennis balls from which 5 balls are selected at random, but assume that the bucket contains 6 orange balls and 8 yellow balls. (1) What is the probability that, of the 5 balls selected at random, at least one is orange and at least one is yellow? equation editorEquation Editor (1) What is the probability that, of the 5 balls selected at random, at least two are orange and at least two are yellow?

The following data represents the winning percentage (the number of wins out of 162 games in a season) as well as the teams Earned Run Average, or ERA.

The ERA is a pitching statistic. The lower the ERA, the less runs an opponent will score per game. Smaller ERA's reflect (i) a good pitching staff and (ii) a good team defense. You are to investigate the relationship between a team's winning percentage - YY, and its Earned Run Average (ERA) - XX.

(a) Using R-Studio, create a scatter-plot of the data. What can you conclude from this scatter-plot?

A. There is a negative linear relationship between a teams winning percentage and its ERA.
B. There is a positive linear relationship between a teams winning percentage and its ERA.
C. There is not a linear relationship between the a teams winning percentage and its ERA.


(b) Use R-Studio to find the least squares estimate of the linear model that expressed a teams winning percentage as a linear function of is ERA. Use four decimals in each of your answers.

YˆiY^i =

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  ? + -  

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XiXi

(c) Find the value of the coefficient of determination, then complete its interpretation.

r2=r2=

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(use four decimals)

The percentage of  ? variation standard deviation the mean  in  ? a teams winning percentage a teams earned run average  that is explained by its linear relationship with  ? the teams winning percentage the teams earned run average  is

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%.

(d) Interpret the meaning of the slope term in the estimate of the linear model, in the context of the data.

As a teams  ? winning percentage earned run average  increases by  ? one percentage point one earned run  the teams  ? winning percentage earned run average  will  ? will increase by an average of will decrease by an average of will increase by will decrease by  

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. (use four decimals)

(e) A certain professional baseball team had an earned run average of 3.45 this past season. How many games out of 162 would you expect this team to win? Use two decimals in your answer.

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games won

(f) The team mentioned in part (e) won 91 out of 162 games. Find the residual, using two decimals in your answer.

XYZ Company has 40% debt 60% equity as optimal capital structure. The nominal interest rate for the company is 12% up to $5 million debt, above which interest rate rises to 14%. Expected net income for the year is $17,5 million, dividend payout ratio is 45%, last dividend distributed was $4,5/share, P0 = $37, g=5%, flotation costs 10% and corporate tax rate is 40%.

a. Find the break points

b. Calculate component costs (cost of each financing source)

c. Calculate WACCs.

d. Two projects are available: 1 st. Project requires 15 million initial investments, IRR=18% 2 nd. Project requires 10 million initial investments, IRR=12%

Please find the optimal capital budget. (Project(s) to be invested in)

Kevin and Kira are in a history competition.

(i) In each round, every child still in the contest faces one question. A child is out as soon as he or she misses one question. The contest will last at least 7 rounds.

(ii) For each question, Kevin's probability and Kira's probability of answering that question correctly are each 0.8; their answers are independent.

Calculate the conditional probability that both Kevin and Kira are out by the start of round 7, given that at least one of them participates in round 3.

According to Food Consumption, Prices, and Expenditures, published by the U.S. Department of Agriculture, the mean consumption of beef per person in the year 2000 was 64 lbs. (boneless, trimmed weight). A sample of 40 people taken this year yielded the data provided in the attached data file named Assessment 10 Data. Analyze the data to answer the following question. 1. Construct an appropriate graph of the provided data. Someone has claimed that there are outliers in the data set. Is this true? 2. Two colleagues argue whether to include or exclude the outliers. Person A claims that if we are interested in learning how much meat is eaten by people who eat meat, the outliers should be omitted. Person B claims that if we want to learn how much meat is eaten on average by Americans, we much include Americans who might be vegetarians. 3. A point estimate of the mean meat consumption is? 4. Does the 95% Confidence Interval for the Mean contain the hypothesized value of 64.0? 5. What is the p-value associated with the hypothesis test of μ = 64 using α=0.05? 6. Should you reject the null hypothesis that the mean meat consumption is 64 lbs.? 7. Suppose the true meat consumption was 58 lbs. Calculate the power of the hypothesis test you just completed (e.g., the probability of rejecting the null hypothesis that μ=64 given the true mean is 58) 8. In general, as the sample size increases the power

Most Company has an opportunity to invest in one of two new projects. Project Y requires a $325,000 investment for new machinery with a six-year life and no salvage value. Project Z requires a $325,000 investment for new machinery with a five-year life and no salvage value. The two projects yield the following predicted annual results. The company uses straight-line depreciation, and cash flows occur evenly throughout each year. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

4. Determine each project’s net present value using 7% as the discount rate. Assume that cash flows occur at each year-end. (Round your intermediate calculations.)

Assignment #3: Inferential Statistics Analysis and Writeup

Part A: Inferential Statistics Data Analysis Plan and Computation

Introduction: I chose to imagine I am a 36 year old married individual with a large family. (UniqueID#30)

Variables Selected:

Table 1: Variables Selected for Analysis

Data Analysis:

1. Confidence Interval Analysis: For one expenditure variable, select and run the appropriate method for estimating a parameter, based on a statistic (i.e., confidence interval method) and complete the following table (Note: Format follows Kozak outline):

Table 2: Confidence Interval Information and Results

2. Hypothesis Testing: Using the second expenditure variable (with socioeconomic variable as the grouping variable for making two groups), select and run the appropriate method for making decisions about two parameters relative to observed statistics (i.e., two sample hypothesis testing method) and complete the following table (Note: Format follows Kozak outline):

Table 3: Two Sample Hypothesis Test Analysis

Part B: Results Write Up

Confidence Interval Analysis:

Two Sample Hypothesis Test Analysis:

Discussion:

Data Set:

One year​ ago, your company purchased a machine used in manufacturing for $ 95 000 . You have learned that a new machine is available that offers many​ advantages; you can purchase it for $ 140000 today. It will be depreciated on a​ straight-line basis over ten​ years, after which it has no salvage value. You expect that the new machine will contribute EBITDA​ (earnings before​ interest, taxes,​ depreciation, and​ amortization) of $ 50 000 per year for the next ten years. The current machine is expected to produce EBITDA of $ 20 000 per year. The current machine is being depreciated on a​ straight-line basis over a useful life of 11​ years, after which it will have no salvage​ value, so depreciation expense for the current machine is $ 8 comma 636 per year. All other expenses of the two machines are identical. The market value today of the current machine is $ 50 000 . Your​ company's tax rate is 45 % ​, and the opportunity cost of capital for this type of equipment is 10 % . Is it profitable to replace the​ year-old machine?

4. Bayes Theorem - One way of thinking about Bayes theorem is that it converts a-priori probability to a-posteriori probability meaning that the probability of an event gets changed based upon actual observation or upon experimental data. Suppose you know that there are two plants that produce helicopter doors: Plant 1 produces 1000 helicopter doors per day and Plant 2 produces 4000 helicopter doors per day. The overall percentage of defective helicopter doors is 0.01%, and of all defective helicopter doors, it is observed that 50% come from Plant 1 and 50% come from Plant 2. [8 points]

(i) The a-posteriori probability of defective helicopter doors produced by Plant 1 is:

a. 0.0025

b. 0.025%

c. 0.25%

d. 0.015%

Clustering [4 Points]   

(ii)K-Means clustering algorithm

a. Needs K-means++ to know the optimal location of the centroids

b. Needs K-means++ to know the optimal number of clusters

c. Is a supervised algorithm

d. Provides the optimal clustering of points even if the initialization is bad