The employee credit union at State University is planning the allocation of funds for the coming year. The credit union makes four types of loans to its members. In addition, the credit union invests in risk-free securities to stabilize income. The various revenue-producing investments together with annual rates of return are as follows: Type of Loan/Investment Annual Rate of Return (%) Automobile loans 8 Furniture loans 10 Other secured loans 11 Signature loans 12 Risk-free securities 9 The credit union will have $1.8 million available for investment during the coming year. State laws and credit union policies impose the following restrictions on the composition of the loans and investments: • Risk-free securities may not exceed 25% of the total funds available for investment. • Signature loans may not exceed 12% of the funds invested in all loans (automobile, furniture, other secured, and signature loans). • Furniture loans plus other secured loans may not exceed the automobile loans. • Other secured loans plus signature loans may not exceed the funds invested in risk-free securities. How should the $1.8 million be allocated to each of the loan/investment alternatives to maximize total annual return? Type of Loan/Investment Fund Allocation Automobile loans $ Furniture loans $ Other secured loans $ Signature loans $ Risk-free securities $ What is the projected total annual return? Annual Return =

Define ANOVA and fully discuss the F ratio. What information does an ANOVA summary table provide?

There are four numeric columns in R programming language's iris data set. Create a scatter plot between the four numeric columns using R programming language and give answers to the following parts.

1. Calculate the correlation between each pair of the four numeric columns in iris.
2. Which pair of variables has the strongest linear relationship? Interpret their ??.
3. Which pair of variables has the weakest linear relationship? Interpret their ??.
4. Which pair(s) of variables can you conclude have a population correlation different from 0? Use ?? = 0.01.

Answers should be in the form of R code and should include the correct statistical explanation for those that require in in the question. Please be as thorough as possible. Thank you for your time.

3. Using the R data set called warpbreaks (See ?warpbreaks for more info), we want to compare the mean breaks across both the different types of wool and the different levels of tension. In this problem, use ?? = 0.10.

a. Make a boxplot to compare breaks across both wool and tension. Color-code the three different tension levels for easier visibility. Within wool A, describe the relationship between tension and breaks. Within wool B, describe the relationship between tension and breaks.

b. Run a two-way ANOVA to compare breaks across both wool and tension, including their interaction. Is the interaction significant? Which main effects are significant?

c. Regardless of your answer to part b, make an interaction plot (color coding might help, but is not required) and interpret it.

d. Run a one-way ANOVA (or a two-sample ??-test) to compare breaks across just wool. What is the result of the test, and how do you reconcile that with our previous results?

Answers should be in the form of R code on how to accomplish each part and include the correct statistical explanation for those that require it in the question. Please be as thorough as possible. Thank you so much!!!

What is the H₀ rejection region for Z (i.e. standard normal distribution) for a two-tailed test with α/2 = .025?

Select one:

a. Reject H₀ if z < 1.96 or z > -1.96

b. Reject H₀ if z > 1.96 or z < -1.96

c. Reject H₀ if z < 2.58 or z > -2.58

d. Reject H₀ if z > 2.58 or z < -2.58

This week, a very large running race (5K) occured in Denver. The times were normally distributed, with a mean of 24.03 minutes and a standard deviation of 3.04 minutes. a. What percent of runners took 26.614 minutes or less to complete the race? b. What time in minutes is the cutoff for the fastest 99.38 %? c. What percent of runners took more than 31.934 minutes to complete the race?

For the following questions , identify the type of test that should be used. Simply use the corresponding letter: A) One-sample z test (for a mean); B) One-sample t-test; C) One-sample z-test for a proportion (or a chi-squared goodness-of-fit); D) Chi-square goodness of fit (and a z-test is not appropriate); E) Two-sample z-test for a difference between proportions (or a chi-squared test for independence); F) Chi-square test for independence (and a z-test is not appropriate); G) Simple regression; H) Multiple regression; I) Two-independent samples t-test (with homogeneity of variance); J) Two-independent samples t-test (without homogeneity of variance);       K) Two-related samples t-test; L) One-way (independent measures) ANOVA; M) One-way Repeated measures ANOVA; N) Two-way ANOVA (independent, mixed, or repeated measures); O) Mann-Whitney; P) Wilcoxon; Q) Kruskal-Wallis; R) Friedman; If you are going down the interval/ratio branch, it is safe to use parametric measures, unless something is directly stated that clearly indicates otherwise, or unless the data strongly and unambiguously indicates otherwise. Similarly, it is safe to assume homogeneity of variance unless it is clearly indicated otherwise. Do not try to analyze whether or not the experiment is tenable or practical or flawless. This is not your concern right now. Most of the below were written by students in this class.

4.         The manager of a grocery store selected a random sample of 14 customers to investigate the association between the number of customers in a checkout line and the time it takes to checkout. As soon as the selected customer entered the end of the line, data was collected on the number of customers in the line in front of the selected customer and the time, in seconds, until they finished checkout. This store can get very crowded and there can be up to twenty customers in a line.

5.         Thomas wants to find out if California bees prefer red or yellow flowers. He sets up a camera that faces both a red and a yellow flower. (The red and yellow flowers are next to each other.) He then counts the number of bees that visit the red flower and the number of bees that visit the yellow flower. He has multiple cameras set up throughout California. Thomas does not feel comfortable making parametric assumptions. [Note to the student who wrote this: Obviously I changed your question a little bit, which changes the answer.]

6.         While grading essays, a TA noticed that students who hand-wrote the essay seemed to do worse than those who typed it. The TA also feels that this hypothesis mainly affects female students. She wants to check this, too; thus, she notes if the essay were written by a male or a female. The dependent variable is total point score on the essay and can be assumed to be interval in nature.

1. Using the R built-in data set called Chick Weight, we want to compare the mean weight across the different types of Diet. IMPORTANT: We only want to compare chicks at the final value of Time, 21. In this problem, use ?? = 0.05.
   1. Make a boxplot to compare weight across the different types of Diet. Based on the boxplot, describe any differences (or lack of differences) you see.
   2. Run an ANOVA to compare weight across the different types of Diet. Is there a significant difference in means?
   3. Regardless of your answer to part b, using Tukey’s HSD approach, which pair or pairs of Diet have significantly different means?
   4. Check the assumptions of the ANOVA: Do the variances look similar across groups? And do the residuals look like they could have come from a Normal Distribution?

Answers should be in the form of R code on how to accomplish each part and include the correct statistical explanation for those that require it in the question. Please be as thorough as possible. Thank you so much!!!

Customers arrive at a service center according to a Poisson process with a mean interarrival

time of 15 minutes.

1. If two customers were observed to have arrived in the first hour, what is the probability that at least

   one arrived in the last 10 minutes of that hour?

1. If the original population is normally distributed, will random sample means and random sample percentage have distribution that is also normally distributed? Explain.

2. If the original population is skewed, will random sample means and random sample percentage have a distribution that is also normally distributed? If not, what sample size will ensure that the sampling distribution is normal?

3. State the Central Limit Theorem (one of the most important theorems in statistics.)

4. what are some of the consequences of the central limit theorem and how does it relate to the

A company is interested in the satisfaction of their employees, so they hired a consulting firm to conduct an in-house study. Employees were classified into three categories (support staff, analysts and executives) and asked if they felt the company had a healthy work environment.

The data:

You're interested in whether employee classification has anything to do with attitudes about work environment. For step 1, instead of re-writing this question of interest, instead say whether the appropriate comparison is across columns, or across rows.

Step 2: State the null hypothesis.

Step 3: State the alternative hypothesis.

Step 4: What is the correct level of alpha, and which tails matter? Choose all statments that are correct.

Step 5: Which statistical test are you using?

Step 6: What is the value of the test statistic?

Step 6 continued: How many degrees of freedom in this test?

Step 7: What is the critical value for the test statistic?

Step 8: How does the test statistic compare to the critical value?

Step 9: Based on this comparison, do you accept or reject your null hypothesis?

Step 10: What do you conclude from this analysis?

A nearby park is comprised of 15% pine, 20% elm, 30% alder and 35% cedar. In the spring, the surrounding city is flooded with pollen. You wonder whether these four tree species contribute proportionally to the total pollen count.

Using air traps, you collect pollen samples. After mixing them, you separate out 1000 pollen granules and identify them by species. Here are the data:

The question of interest is whether the tree species contribute proportionally to pollen count.

Step 2: State the null hypothesis.

Step 3: State the alternative hypothesis.

Step 4: What is the correct level of alpha?

Step 5: Which statistical test are you using?

Step 6: What is the value of the test statistic?

Step 6 continued: How many degrees of freedom in this test?

Step 7: What is the critical value for the test statistic?

Step 8: How does the test statistic compare to the critical value?

Step 9: Based on this comparison, do you accept or reject your null hypothesis?

Step 10: What do you conclude from this analysis?

Hermit crabs live in shells, but they don't grow the shells themselves. They find an abandoned snail shell and make it their home. They inhabit shells of different snail species, but it's not clear if the hermit crabs choose shells of different species randomly or if they have a preference for certain snail species.

We can't just collect a bunch of hermit crabs and then conclude that the snail shell with the highest prevalence is the most preferred, because it might be the case that that snail species is simply more common. Instead, it makes more sense to collect a bunch of shells, and determine if they are occupied or unoccupied by a crab. If crabs have no preference, then the ratio of occupied to unoccupied should be the same across snail species.

For three snail species in the area, shells were collected and it was recorded whether they were inhabited by a hermit crab. The data:

The question of interest is: do hermit crabs care about the species of shell they inhabit?

Step 2: State the null hypothesis.

Step 3: State the alternative hypothesis.

Step 4: What is the correct level of alpha?

Step 5: Which statistical test are you using?

Step 6: What is the value of the test statistic?

Step 6 continued: How many degrees of freedom in this test?

Step 7: What is the critical value for the test statistic?

Step 8: How does the test statistic compare to the critical value?

Step 9: Based on this comparison, do you accept or reject your null hypothesis?

Step 10: What do you conclude from this analysis?

A random sample of 1,496 respondents of a major metropolitan area was questioned about a number of issues. When asked to agree or disagree with the statement “Hand guns should be outlawed”, 650 respondents agreed. Researchers could thus construct a confidence interval for the proportion of the residents of this metropolitan area who support banning hand guns (use the 95% confidence level). Use this example to answer questions 19 to 23.
19. What’s the proportion of respondents in the sample who agreed “Hand guns should be outlawed”?

20. What would be the Z score(s) associated with the confidence level used in this example?

21. Based on the sample information, what’s the standard error?

22. Using the sample information to estimate the population proportion in the example, what’s the margin of error?

23. What conclusion can we make for this example?

According to data from the 2018 General Social Survey (GSS 2018), the average number of years of education of the 2345 adults in the U.S. sample is 13.73, with a standard deviation of 2.974. Compared to the national average of 13.26 years of education in 2000, researchers are wondering if the national education level had increased during these years. Do a hypothesis testing with α=0.05. Use this example to answer questions 24 to 27.
24. What’s the null hypothesis in this case?
A. The average number of years of education in the U.S. adult population did not change much from 2000 to 2018.
B. The average number of years of education in the U.S. adult population was equal to 13.73 in 2018.
C. The average number of years of education for the GSS 2018 sample is no different from 13.26, the national average in 2000.
D. The average number of years of education in the U.S. adult population had increased from 2000 to 2018.

25. What’s the alternative hypothesis in this case?
A. The average number of years of education in the U.S. adult population had changed since 2000.
B. The average number of years of education for the GSS 2018 sample is different from 13.26, the national average in 2000.
C. The average number of years of education in the U.S. adult population in 2018 was higher than that in 2000.
D. The average number of years of education in the U.S. adult population had decreased from 2000 to 2018.

26. Which of the following statements about this example is correct?
A. This is a two-tailed test and you have two rejection regions.
B. Since the sample size is large, we cannot use the normal distribution as the sampling distribution.
C. This is a one-tailed test and the rejection region is on the left side of the sampling distribution.
D. The rejection region is on the right side of the sampling distribution.

27. What conclusion can we draw for this example?
A. There is no enough evidence to reject the null hypothesis.
B. We can be 90% confident that the average number of years of education in the U.S. adult population had increased since 2000.
C. The average number of years of education in the U.S. adult population had increased since 2000.
D. There is a significant difference between 2018 and 2000 in terms of the national education level in the U.S. adult population.

Are U-Albany students more likely to approve gun control than adults in the U.S.? According to a research report, on a scale from 1 to 10, the mean approval of gun control in the U.S. is 7.8. The mean approval of gun control in a random sample of 26 U-Albany students is 8.3, with the standard deviation of 2.2. Use α = 0.01 for the hypothesis testing. Questions 28 to 32 are based on this example.
28. What would be the H0 for the example?
A. U-Albany students are equally likely to approve gun control than adults in the U.S.
B. The likelihood of approving gun control among U-Albany students is different from that of the U.S. adults.
C. There is no difference between the 26 U-Albany students and all U.S. adults in terms of their attitudes toward gun control.
D. U-Albany students are less likely to approve gun control than adults in the U.S.

29. What would be the t critical value(s)?

30. What’s the standard error based on the sample information?

31. What is the t obtained value?

32. What conclusion can we make for this example?
A. We cannot reject the null hypothesis that the mean approval of gun control among the 26 U-Albany students is 8.3.
B. There is no enough evidence to reject the null hypothesis that the mean approval of gun control among U-Albany students is 8.3.
C. We cannot reject the null hypothesis that the mean approval of gun control among all U-Albany students is 7.8.
D. We can reject H0 and accept H1 that the mean approval of gun control among all U-Albany students is larger than 7.8.

In an election exit poll (N = 1,768), 898 respondents said they voted for Candidate A. Is Candidate A going to win the election (more than 50% of votes needed to win)? Use α = 0.1 for a hypothesis testing. Questions 33 to 38 are based on this example.

33. What’s the proportion of respondents in the poll voted for Candidate A?

34. What would be the H1 for the example?
A. The percentage of respondents in the poll voted for Candidate A is different from 50%.
B. The proportion of all voters in the election who would vote for Candidate A is more than 0.5.
C. The percentage of respondents in the poll voted for Candidate A is different from 50.8%.
D. The proportion of all voters in the election who would vote for Candidate A is more than 0.51.

35. What would be the Z critical value(s)?

36. What’s the standard error based on the sample information?

37. What is the Z obtained value?

38. What conclusion can we make for this example?

(Optional) Using the International Social Survey Program data we find women in the U.S. (N = 654) spend, on average, 3.53 hours per day doing housework, with the standard deviation of 1.91, and women in Sweden (N = 639) spend, on average, 2.87 hours per day doing housework, with the standard deviation of 1.85. Researchers want to test whether American women spend more time than Swedish women on housework? Questions 39 to 42 are based on this example.
39. What is the null hypothesis?

40. What would be the critical value(s) for α = 0.05?

41. What would be the z-obtained value?

42. What conclusion can you make for this example? Briefly explain with statements and numbers.

kindly, I need them done.

Some say that optimal estimators should be preferred while others advocate the use of more robust estimators. What is your opinion? (250 words)