A large pond contains f fish, of which t have been tagged. Biologist A takes a simple random sample of nA fish from the pond. Biologist B takes a simple random sample of nB fish from the fish that remain in the pond after Biologist A has drawn her sample. You can assume that nA+nB<t.

a) Fill in the blank with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish in Biologist A's sample has expectation _____________.

b) Fill in the blank (carefully!) with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish in Biologist B's sample has expectation __________.

c) Fill in the blank with a math expression involving any or all of f, t, nA, and nB. Explain your answer.

The number of tagged fish that don't get into the samples has expectation_________.

A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is correct. Four points are awarded for each correct answer. To discourage guessing, one point is taken away for every answer that is not correct (this includes answers that are missing).

The company that creates the test has to understand how well a student could do just by random guessing. Suppose a student answers each question by picking one of the five choices at random independently of the choices on all other questions. Let S be the student's score on the test.

a) Find ?(S).

b) Find P(S>10). Write your answer as a math expression, then use the code cell below to find its numerical value and provide it along with your math expression.

1. A researcher is interested to learn if there is a linear relationship between the hours in a week spent exercising and a person’s life satisfaction. The researchers collected the following data from a random sample, which included the number of hours spent exercising in a week and a ranking of life satisfaction from 1 to 10 ( 1 being the lowest and 10 the highest). PLEASE help in SPSS.

1. Find the mean hours of exercise per week by the participants.
2. Find the variance and standard deviation of the hours of exercise per week by the participants.
3. Run a bivariate correlation to determine if there is a linear relationship between the hours of exercise per week and the life satisfaction. Report the results of the test statistic using correct APA formatting.
4. Run a linear regression on the data. Report the results, using correct APA formatting. Identify the amount of variation in the life satisfaction ranking that is due to the relationship between the hours of exercise per week and the life satisfaction (Hint: the R² value)
5. Report a model of the linear relationship between the two variables using the regression line formula.

Case Study: Project Communications Management: Best Practices in Practice As part of a large IT systems integration project for the State of California, I witnessed the Project Management Office (PMO) do an excellent job of ensuring that the project stakeholders were properly informed of the project’s progress, outstanding issues, risks, and change requests. Information was gathered from multiple sources (for example, Project Schedule, Issue and Risk Repositories, Testing Tool Data Metrics, Change Request Log, and so on) and compiled into a comprehensive weekly status report that was shared with the stakeholders. In addition, detailed risk and issue status reports were prepared and shared in the weekly risk and issue management meetings. Also, the overall project performance status was communicated to the control agencies (for example, California Department of Technology, Department of Finance, and so on) via a monthly Project Status Report (aka PSR) containing a variety of performance tracking metrics. All questions were responded to, and all ambiguities were clarified in a timely manner to ensure that the information was clearly understood by the recipients as intended and everyone was on the same page. The project director was a strong proponent of information quality who took a keen interest in monitoring the quality of the content and delivery of the status reports and suggested improvements when necessary. Case Study Questions 1. What project communications best practices did the project practice? 2. How was the project performance status communicated to the control agencies? 3. What role did the project director play in enhancing the project communications management? 4. What are the lessons learned from this case?

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 31% contain one defective component, and 20% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions? (Round your answers to four decimal places.)

(a) Neither tested component is defective.

(b) One of the two tested components is defective. [Hint: Draw a tree diagram with three first-generation branches for the three different types of batches.]

Evaluate the differences between dependent and independent samples. Provide an example of each type of sample.

I am curious as to how the "descriptive and inferential statistics physically mean and how they are used in a simulated "real-world" problem" portion should be answered. I spent a long time trying to come up with a way to solve this. Don't be shy. All ideas are welcome.

Discuss the challenges a researcher would encounter in transforming an area probability face-to-face survey into an Online survey when attempting to estimate the same statistics.

How does the likelihood function change for Random Vectors vs Random Variables?

Say: If you have Random Variables A1...An with a normal distribution, with mean mu_A and Variance and another Random Variable, B1...Bn, with mean mu_B and Variance...

If there's a random vector C, which equals (a1, ... an, b1, ... bn), and you wanted the likelihood function, would you have two likelihood functions likelihood(a) & likelihood (b) or just one likelihood(a, b)?

Question 1 The coffee shop A coffee shop knows from past records that its weekly takings (sales) are normally distributed with a mean of $10,500 and a standard deviation of $478. Answer the following questions:

a. Find the probability that in a given week the coffee shop would have takings of more than $10,700

b. Find the probability that in a given week the takings are between $9,800 and $11,000.

c. Calculate the inter-quartile range of weekly takings.

d. What are the maximum weekly takings for the worst 5% of weeks?

Question 2 Normal model

a. A cut-off score of 79 has been established for a sample of scores in which the mean is 67. If the corresponding z-score is 1.4 and the scores are normally distributed, what is the standard deviation?

b. The standard deviation of a normal distribution is 12 and 95% of the values are greater than 6. What is the value of the mean?

c. The mean of a normal distribution is 130, and only 3% of the values are greater than 155. What is the standard deviation?

You conduct a study to determine the impact that varying the amount of noise in an office has on worker productivity (0 – 25). You obtain the following productivity scores:

For each condition, determine the sample mean and the sample (unbiased) standard deviation. Report the means and standard deviations in a bar graph (include the whiskers on the bars). Write an interpretation of these data including the means and standard deviation.

3. Testing for equal proportions

Imagine that you are contracted by a local news provider to study consumer demographics in relation to three different types of news media: print (newspaper), Internet, and television. In prior market research, the company has classified each of its customers as receiving news content primarily from only one of these three sources, and as either urban or rural residents. In order to help design effective marketing strategies, you are asked to perform a test for equality of proportions to determine whether there is a significant difference in the proportion of consumers who live in urban versus rural areas for the three media types that are offered.

The three population proportions that you are interested in are:

You conduct a hypothesis test with a 0.05 level of significance to determine whether the proportion of urban consumers is the same for all three news sources. The null and alternate hypotheses for your test are:

New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backen and Hayes LLC is an accounting firm in New York state. The accounting firms believe that it may have to hire additional accountants to assist with the increased demand in tax advice for the upcoming tax season. Backen and Hayes LLC has developed the following probability distribution for x= number of new clients seeking tax advice.

a. Is this a valid probability distribution? Explain.

b. What is the probability that Backens and Hayes LLC will obtain 40 or more new clients?

c. What is the probability that Backens and Hayes LLC will obtain fewer than 35 new clients?

d. Compute the expected value, variance, and standard deviation of x.

Using Baynesian estimation. 1. Let X is Poi(Ꝋ). Let Ꝋ be Γ(α, β). Show that the marginal pmf of X (the compound distribution) is k1(x) = (Γ (α + x) β^x) / (Γ(α) x! (1 + β)^(α+x ); x = 0, 1, 2, 3, …, which is a generalization of the negative binomial distribution.

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 400 current​ subscribers, and 102 of those surveyed expressed interest. What should the company​ do? Test appropriate hypotheses and state your conclusion.

Are the assumptions and the conditions to perform a​ one-proportion z-test​ met?

Yes or No

State the null and alternative hypotheses. Choose the correct answer below.

A. H0​: p equals=0.20.2

HA​: p not equals≠0.20.2

B. H0​:p equals=0.20.2

HA​:p less than<0.20.2

C. H0​:p equals=0.20.2

HA​: p greater than>0.20.2

D.The assumptions and conditions are not​ met, so the test cannot proceed.

Determine the​ z-test statistic. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. z equals=nothing

​(Round to two decimal places as​ needed.)

B. The assumptions and conditions are not​ met, so the test cannot proceed.

Find the​ P-value. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A. ​P-value equals=nothing

​(Round to four decimal places as​ needed.)

B. The assumptions and conditions are not​ met, so the test cannot proceed.