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.

The Centers for Disease Control reported the percentage of people 18 years of age and older who smoke (CDC website, December 14, 2014). Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of .29.

a. How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of .02 (rounded up to the next whole number)? Use 95% confidence.

b. Assume that the study uses your sample size recommendation in part (a) and finds 520 smokers. What is the point estimate of the proportion of smokers in the population (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of smokers in the population (to 4 decimals)?

The effectiveness of birth control is measured by comparing what percentage of women of childbearing age become pregnant in a year, while using the method. The table below gives the data from a clinical trial for a new birth control pill.

a. Given that a woman uses birth control, find the conditional probability that she becomes pregnant within one year. Round your answer to 4 decimal places.

b. Given that a woman does not use birth control, find the conditional probability that she becomes pregnant within one year. Round your answer to 4 decimal places.

c. Are the events "a randomly selected woman uses birth control" and "a randomly selected woman becomes pregnant within one year" independent? Why or why not?

Select your answer from one of the following options.

• a.No. A woman can still become pregnant while on birth control.
• b.No. Using birth control significantly decreases the probability that a woman will become pregnant within one year.
• c.Yes. A woman can still become pregnant while on birth control.
• d.Yes. Using birth control significantly decreases the probability that a woman will become pregnant within one year.

d. Are the events "a randomly selected woman uses birth control" and "a randomly selected woman becomes pregnant within one year" mutually exclusive? Why or why not?

Select your answer from one of the following options.

• a.No. A woman can still become pregnant while on birth control.
• b.No. Using birth control significantly decreases the probability that a woman will become pregnant within one year.
• c.Yes. A woman can still become pregnant while on birth control.
• d.Yes. Using birth control significantly decreases the probability that a woman will become pregnant within one year.

3) A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene.

The researcher collect a random sample of 529 people from across the country, and tests them for the gene. The gene was present in 57 of the 529 people tested.

a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene.

b) Provide the right endpoint of the interval as your answer.

Round your answer to 4 decimal places.

4) A medical researcher is interested in knowing what percentage of the U.S. population has a certain gene.

The researcher collect a random sample of 515 people from across the country, and tests them for the gene. The gene was present in 78 of the 515 people tested.

a) Find a 90% confidence interval for the true proportion of people in the U.S. with the gene.

b) Provide the margin of error of the interval as your answer.

Round your answer to 4 decimal places.

You are a quality control officer for a hair-dryer company. If the percentage of defective hairdryers that you test is statistically greater than 5%, then you have to get rid of the batch. You collect a simple random sample of 157 hair dryers and find that 9 of them are defective. Conduct a hypothesis test with a ?? =.05 level of significance to determine if greater than 5% of the hair dryers are defective. Write all non-calculation answers in complete sentences.

a. Which test would you use and why?

b. Write the null and alternative hypothesis in complete sentences. (Make sure you mark which is the null and which is the alternative.)

c. Write the null and alternative hypothesis as symbols.

d. State the requirements that have been met to run the test.

e.What is the test statistic and the p-value? (Make sure you use the right notation.)

f. Should you reject or fail to reject the null hypothesis?

g. State the conclusion for the test.

h. According to the results of your hypothesis test, should you get rid of the batch. Explain your reasoning based upon the hypothesis test.

29. In multiple regression, the adjusted R-square can be interpreted as a. the percentage of variance accounted for in the dependent variable by the set of independent variables b. the percentage of variance accounted for in the dependent variable by a single independent variable c. the strength of the relationship between the dependent variable and the set of independent variables d. the percentage of variance accounted for in the dependent variable by the set of independent variables minus an estimate penalty

30.In multiple regression, the ANOVA table tells us whether the three main regression coefficients (R, R-square, adjusted R-square) are significantly different from a. zero b. 1.00 c. .50 d. 1.50 31. In a multiple regression analysis, the final section of the output contains the coefficients. Which of these coefficients is of primary concern? a. unstandardized B b. standard error of B c. standardized coefficient beta d. standard error of beta

32. The ____________ correlation gives an estimate of the degree of relationship between two dichotomous variables. a. Pearson b. Spearman c. point-biserial d. phi

2. What are the four major categories of mortgages and what percentage of the overall market does each entail?

18. Describe a collateralized mortgage obligation. How is a CMO created?

4. You plan to purchase a $150,000 house using a 15-year mortgage obtained from your local credit union. The mortgage page 238rate offered to you is 5.25 percent. You will make a down payment of 20 percent of the purchase price.

1. Calculate your monthly payments on this mortgage.

2. Construct the amortization schedule for the first six payments.

8. A particular poll tracks daily the percentage of Americans who approve or disapprove of the performance by President 1. Daily results are based on random telephone interviews with approximately 1300 national adults. The poll reports that 49% of adults approve of President 1. The same poll reported an approval rating of 50​% for President 2. A news anchor remarks that​ "President 1​ doesn't even get as much approval as President 2​ did." Is there evidence that this difference is​ real? State and test the appropriate hypotheses. Check conditions.

A. What is the value of the test​ statistic? (Round to two decimal places as​ needed.)

9. It the​ 1980s, it was generally believed that congenital abnormalities affected about 8​% of a large​ nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 366 randomly selected children and found that 37 of them showed signs of an abnormality. Is this strong evidence that the risk has​ increased? (Consider a​ P-value of around 0.05 to represent reasonable​ evidence.)

A. What is the​ P-value? (Round to three decimal places as​ needed)

10. A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it is convinced that more than 20​% of current readers would subscribe. The magazine contacted a simple random sample of 500 current​ subscribers, and 108 of those surveyed expressed interest. What should the magazine​ do?

A. What is the​ P-value of the test​ statistic? (Round to three decimal places as​ needed.)

Can we say that prices of bonds are equally sensitive to the same percentage increases or decreases of the market interest rate (YTM)? Explain. (i.e. Market interest rate increases, say, from 5% to 6% or decreases from 5% to 4%)