You are a creating a portfolio of investments for a retiring person. The portfolio consists of ten securities. Three of them must be stocks, and seven of them must be bonds. You can choose among ten stocks, and twenty bonds. Answer the following-

1. If you randomly choose ten securities, what is the probability that the portfolio specification will be met, i.e., you would have three stocks and seven bonds in the portfolio?

2. Suppose that you are told that two stocks, GM and GE must be in the portfolio. Also, you are told that bonds of ATT and Verizon must be in the portfolio. These are already in the specified set of ten stocks and twenty bonds. How likely is it that a randomly formulated portfolio of ten securities will contain these stocks and bonds, and also satisfy the requirements for containing three stocks and seven bonds?

   (Note: the values in this problem are rather large to compute manually. You will be better off using Excel functions such as =permut or =combin for your analysis. If you do use them, write down the exact expressions you used as part of your analysis).

A factory produces metal links for building long chains used in the shipping and construction industry. The factory’s R&D unit models the length of an individual metal link (in ?m) by a random variable ?? with expectation ?0 m and variance ?. ?4 ??^?. The length of a chain is equal to the sum of the lengths of individual links that comprise the chain. The factory sells ?0 ? long chains as its final product, which it makes by combining ?002 individual metal links together. The factory guarantees that the chain length is not shorter than ?0 ? − if by chance a chain is too short, the customer is reimbursed and a new chain is issued for free.

a. For what percentage of chains would the factory need to reimburse clients and deliver new chains free of cost?

b. The sales team notices that the factory has been handing out a much larger fraction of free chains than expected as per your answer above. After further probing, the research lab reports that the exact expectation is ?. ?? ?m and not ? ?m as was previously reported based on rounding-off approximation. Do you think the research team committed a serious mistake by rounding off to the nearest whole number instead of using the exact value for expectation? Why?

Many people purchase SUV because they think they are sturdier and hence safer than regular cars. However data have indicated that the costs of repair of SUV are higher that midsize cars when both cars are in an accident. A random sample of 8 new SUV and midsize cars is tested for front impact resistance. The amount of damage in hundreds of dollars to the vehicles when crashed at 20mph are recorded below. Questions: 1. Is this an independent data or paired? 2. which non-parametric test will be appropriate. rank the data using table 3. test to determine if there is a difference in the distribution of cost of repairs for the cars. use nonparametric test.- critical region=0.05 car 1 2 3 4 5 6 7 8 SUv 14.23 12.47 14.00 13.17 27.48 12.42 32.58 12.98 midsize 11.97 11.42 13. 27 9.87 10.12 10.36 12.65 25.23

Suppose you wanted to evaluate the performance of the three judges in Smallville, Texas: Judge Adams, Judge Brown, and Judge Carter. Over a three-year period in Smallville, Judge Adams saw 26% of the cases, Judge Brown saw 34% of the cases, and Judge Carter saw the remainder of the cases. 3% of Judge Adams’ cases were appealed, 6% of Judge Brown’s cases were appealed, and 9% of Judge Carter’s cases were appealed. Given the judge in a case from this three-year period was not Judge Brown, what is the probability the case was not appealed?

a.) According to a recent​ report, 46% of college student internships are unpaid. A recent survey of 120 college interns at a local university found that 57 had unpaid internships. 1.)Use the​ five-step p-value approach to hypothesis testing and a 0.05 level of significance to determine whether the proportion of college interns that had unpaid internships is different from 0.46. 2.) Assume that the study found that 70 of the 120 college interns had unpaid internships and repeat​ (1). Are the conclusions the​ same? Let π be the population proportion. Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1. ​(Type integers or decimals. Do not​ round.)

b.) ​Recently, a large academic medical center determined that 9 of 23 employees in a particular position were male​, whereas 55​% of the employees for this position in the general workforce were male. At the 0.05 level of​ significance, is there evidence that the proportion of males in this position at this medical center is different from what would be expected in the general​ workforce? What are the correct hypotheses to test to determine if the proportion is​ different?

c.) A consulting group recently conducted a global survey of product teams with the goal of better understanding the dynamics of product team performance and uncovering the practices that make these teams successful. One of the survey findings was that 36​% of organizations have a coherent business strategy that they stick to and effectively communicate. Suppose another study is conducted to check the validity of this​result, with the goal of proving that the percentage is less than 36​%. State the null and research hypotheses. Identify the null and alternative hypotheses.

Question 1 (1 point)

The Kellogg Company periodically compares sales across departments. In one particular instance, they would like to determine if sales of snacks are different from sales of frozen foods. If snacks are group 1 and frozen foods are group 2, what are the hypotheses for this test?

Question 1 options:

Question 2 (1 point)

Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants different from the average stock price for fast food restaurants? If sit down restaurants are considered group 1 and fast food restaurants are group 2, what are the hypotheses of this scenario?

Question 2 options:

Question 3 (1 point)

Does the amount of hazardous material absorbed by the bodies of hazardous waste workers depend on gender? You want to test the hypotheses that the amount absorbed by men (group 1) is different from the amount absorbed by women (group 2). A random sample of 195 male workers and 199 female workers showed an average lead absorption in the blood of 12.13 (SD = 1.281) and 11.84 (SD = 0.821), respectively (measured in micrograms/deciliter). Assuming that the population standard deviations are the same, perform a two independent samples t-test on the hypotheses Null Hypothesis: μ₁ = μ₂, Alternative Hypothesis: μ₁ ≠ μ₂. What is the test statistic and p-value of this test?

Question 3 options:

Question 4 (1 point)

The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is greater than the average age of females. If the owner conducts a hypothesis test for two independent samples and calculates a p-value of 0.862, what is the appropriate conclusion? Label males as group 1 and females as group 2.

Question 4 options:

A child counts the number of cracks in the sidewalk along the block she lives in (about 1/8 mile of sidewalk). Suppose the expected number of cracks in a block of sidewalk is 2.

a) Which distribution would be best to use to model this situation? Explain.

b) What is the probability that she observes three or more cracks?

c) What is the probability that she observed exactly two cracks in 1/2 of the block?

Find the indicated probability using the standard normal distribution. ​P(z < -0.39​)

a.) Many consumer groups feel that the Country A drug approval process is too easy​ and, as a​ result, too many drugs are approved that are later found to be unsafe. On the other​ hand, a number of industry lobbyists have pushed for a more lenient approval process so that pharmaceutical companies can get new drugs approved more easily and quickly. Consider a null hypothesis that a​ new, unapproved drug is unsafe and an alternative hypothesis that a​ new, unapproved drug is safe. Explain the risks of committing a Type I or Type II error.

b.) A magazine reported that at the top 50 business schools in a​ region, students studied an average of 16.8 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 16.8 hour benchmark. State the null and alternative hypotheses.

c.) The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7,491 hours. The population standard deviation is 900 hours. A random sample of 81 light bulbs indicates a sample mean life of 7,241 hours.

1.) At the 0.05 level of​ significance, is there evidence that the mean life is different from 7 comma 491 hours question mark 7,491 hours? Let μ be the population mean. Determine the null​ hypothesis, H0​, and the alternative​ hypothesis, H1.

2.) Compute the​ p-value and interpret its meaning.

3.) Construct a 95​% confidence interval estimate of the population mean life of the light bulbs.

4.) Compare the results of​ (a) and​ (c). What conclusions do you​ reach?

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. The probability that Z is less than 1.15 is

A population consists of the following amounts: 9, 9, 10, 11, 11

1. Indicate total number possible samples of size 3

2. Compute the sampling distribution of sample means

3. Compare the population mean with the mean of the sampling

   distribution of sample means

4. Compare the dispersion in the population with that of the sample

   means.

Specifically only need help with f-h.

1. Refer to the Excel “Dixie” data posted on eLearning: (18)
   1. Develop an estimated regression equation with the Revenue serving as the dependent variable and Paper Ads and TV Ads serving as explanatory variables. Write out this estimated equation (use the estimate values!) to explain Revenue.
   2. Show the residual plots where residuals are plotted against each explanatory variable separately. Comment on whether you can proceed with statistical inference based on what you see in the plots. (Hint: Don’t go looking for trouble!)
   3. Provide an interpretation for the three coefficient estimates that you calculated in part “a”. (don’t forget the intercept).
   4. What would your regression model predict the revenue amount to be in a market with 0 TV Ads and 0 Paper Ads? Is this a meaningful prediction? Answer, in a sentence, why or why not.
   5. Provide a 90% confidence interval for your estimate of the Paper Ads Coefficient. Interpret exactly what this 90% confidence interval means.
   6. What statistic and p-value would you use to test the specific null hypothesis that:

Ho: b _{Paper Ads} = b _{TV Ads} = 0

      Do you reject or fail to reject this null hypothesis?

1. g. If I asked you to consider a “backward selection” approach which only included predictors to the model that were significant at a 99% level, then would your answer to part “a” change? If so, what would it change to?
2. h. What percentage of the variation in Revenue can be explained by the model you developed on part “a”? How much more variation does this model explain than a model which uses only TV Ads to help predict Revenue?

x 3, 4, 5, 7, 8 y 3, 7, 6, 13, 14 (a) Find the estimates of Bo and B1. Bo=bo= _____ (Round to three decimal places as needed.) B1=b1= ______(Round to four decimal places as needed.)

(b) Compute the standard error the point estimate for se= ____

(c) Assuming the residuals are normally distributed, determine Sb1=____ (Round to four decimal places as needed.)

(d) Assuming the residuals are normally distributed, test HoB1=0 versus H1:B1/=0 at the a=0.05 level of significance. Use the P-value approach. The P-value for this test is _____. (Round to three decimal places as needed.) Make a statement regarding the null hypothesis and draw a conclusion for this test. Choose the correct answer below. A. Reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y. B. Reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y. C. Do not reject Ho. There is not sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y. D. Do not reject Ho. There is sufficient evidence at the a= 0.05 level of significance to conclude that a linear relation exists between x and y.

Indicate the mean and the standard deviation of the distribution of means for each of the following situations.

    Population Sample Size

Mean Variance N

​(a)80 80 5

(b) 80 15 5

​(c) 80 10 5

(d) 80 50 25

​(e) 80 5 25

Question 11 (1 point)

In situation (a) above, the mean of the distribution of means is _____ and the standard deviation of the distribution of means is ______.

In situation (b) above, the mean of the distribution of means is _____ and the standard deviation of the distribution of means is ______.

In situation (c) above, the mean of the distribution of means is _____ and the standard deviation of the distribution of means is ______.

In situation (d) above, the mean of the distribution of means is _____ and the standard deviation of the distribution of means is ______.

In situation (e) above, the mean of the distribution of means is _____ and the standard deviation of the distribution of means is ______.

A biologist is sampling randomly from a population of 1000 birds of which 22-percent are red birds, 18-percent are blue birds, 15-percent are yellow birds, and 14-percent are hawks-

In statistics What is P(third largest yellow bird | yellow bird) and P (red birds | red birds or blue birds)? Give answer in the form of 0.xx