1) Xi~Bernoulli(p), MLE and MOME of p

2) Xi~Exp(λ), MLE and MOME of λ

3) Xi~Normal(μ, σ² ), MLE and MOME of μ, σ²

9.50. t test and and retail; Many communities worldwide are lamenting the effects of so-called big-box retailers (eg. Walmart) on their local communities, particularly on small, independent owned shops. Do these large stores affect the bottom lines of locally owned retailers? Imagine that you decide to test this premise. You assess earnings at 20 local stores for the month of October, a few month before a big box store opens. you then assess earnings the following October, correcting for inflation.

A. what are the two population?

B. what is the comparison distribution? Explain

C. Which hypothesis test you would you use

D. check the assumption test for this hypothesis test

E. what is one flaw in drawing conclusion from this comparison from this comparison over time?

f. state the null and research hypothesis in both words and symbols.

Thank you.

Human Resource Management researchers examined the impact of environment on employee development. Employees were randomly assigned one of the following four workplace types/conditions: Impoverished (isolated cubicles each with bare minimum equipment - chair, desk & computer), standard (cubicles placed hear each other, equipped with a 'normal level' of office equipment - printer, shelves, manuals, stationery, etc.), enriched (standard cubicles plus regular work-related meetings), super enriched (enriched environment plus regular non-work-related social events).

Employees were also categorized by function they performed for the company (engineering, sales, manufacturing, etc.), because it's possible that functional background may have been a bigger association with test score than working condition.  

After two months, the employees were tested on a variety of work-relevant learning measures. Use the Microsoft Excel "Anova: Two-Factor Without Replication" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

1. What are the two Questions, in context, that we want our ANOVA to answer?
2. What are your two answers? Use the factor confidence levels obtained by way of the Excel ANOVA output table's p-values. State your answers in terms of working condition and employee function.
3. What are your two null hypotheses in this study?
4. What are your two corresponding alternate hypotheses? Use the phrase "at least one" in each of your hypothesis statements.

Students completed a high school senior level standardized algebra exam. Major for students was also recorded. Data in terms of percent correct is recorded below for 32 students. We are interested to see if there is any difference between students' high-school algebra test scores and subsequent declared college major.

These students have now also just completed the same college-level calculus class and received a grade. We are therefore now also interested to see if there is any relationship between the students' algebra test scores and their calculus course grades: On average, did students who tended to score higher on the high-school algebra test also finish the course with higher grades? Conveniently, only one student of each major received the same grade (see table - for example, there is only one Education major who received a grad of A).

Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

1. What are your two null hypotheses in this study?
2. What are your two corresponding alternate hypotheses? Use the phrase "at least one" in each of your hypothesis statements.
3. What level of significance did you choose and why?
4. What are your F_crit values?

Depressed patients were randomly assigned to one of three groups: a placebo group, a group that received a moderate dose of the drug, and a group that received a high dose of the drug. After four weeks of treatment, the patients completed the Beck Depression Inventory. The higher the score, the more depressed the patient.

We are now also interested if a patient's weight has an effect on the drug's effectiveness. Patients were categorized as either underweight, overweight, or 'medium weight'.  These revised data are presented below. Use the Microsoft Excel "Anova Single-Factor" Data Analysis tool to conduct a 2-way ANOVA test for the data in the following table:

1. What are your F_crit values?
2. If there is a significant difference between the weights, where specifically are the differences?
3. Is there a significant interaction between weight and dosage? Why/why not?

Suppose that the total carbohydrates in the listed cereals are approximated by a normal curve with a mean of 30.7931 and a standard deviation of 8.8858. What is the probability that a randomly selected cereal has at most 25 grams of carbohydrates? What is the probability that a randomly selected cereal has at least 45 grams of carbohydrates? What is the probability that a randomly selected Kellogg’s cereal has between 30 and 40 grams of carbohydrates? What amount of carbohydrates would separate the lowest 10% of Kellogg’s cereals? What amount of carbohydrates would separate the highest 5% of Kellogg’s cereals? Show your work or calculator syntax

Suppose that at a large university 30% of students are involved in intramural sports. If we randomly select 12 students from this university, what is the probability that no more than 4 of these students are involved in intramural sports?

Anyone who has been outdoors on a summer evening has probably heard crickets. Did you know that it is possible to use the cricket as a thermometer? Crickets tend to chirp more frequently as temperatures increase. This phenomenon was studied in detail by George W. Pierce, a physics professor at Harvard. In the following data, x is a random variable representing chirps per second and y is a random variable representing temperature (°F).

Complete parts (a) through (e), given Σx = 247.1, Σy = 1198, Σx² = 4107.43, Σy² = 96,302.7, Σxy = 19,855.58, and r ≈ 0.796.

(b) Verify the given sums Σx, Σy, Σx², Σy², Σxy, and the value of the sample correlation coefficient r. (Round your value for r to three decimal places.)

(c) Find x, and y. Then find the equation of the least-squares line  = a + bx. (Round your answers for x and y to two decimal places. Round your answers for a and b to three decimal places.)

(e) Find the value of the coefficient of determination r². What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line? What percentage is unexplained? (Round your answer for r² to three decimal places. Round your answers for the percentages to one decimal place.)

(f) What is the predicted temperature when x = 19.0 chirps per second? (Round your answer to two decimal places.)
°F

If we run a one-way ANOVA on 4th graders, 5th graders, and 6th graders, which of these outcomes are possibly true?

1. A t-test should be used when the standard deviation of the population is known, whereas a z-test should be used when the standard deviation of the population is unknown. True or False?

2. If r = 0.72, what proportion of the variance in Y is accounted for by it's relationship with X?

A. .72

b. .52

c. .36

d. .85

3.Jane conducts a Pearson correlation to assess the relationship between years of marriage and happiness from data collected from 100 individuals. What's df in this study?

a.98

b. 99.

C. 100

d. Not enough information

4.A study with 46 participants investigated whether there was a relationship between one’s attitude toward giving blood and the number of times one has given blood in a year. The correlation coefficient was r = +0.56. Thus, the rcritrcrit is ±0.288±0.288 True or False?

In a state, 50,000 students graduated from four-year not for profit colleges in 2019. Out of these 50,000 graduates, 20,000 students graduated from private colleges, and 30,000 students graduated from public colleges. You have selected a stratified sample from the population of 2019 graduates in this state with graduates from private and public colleges as the two strata. For each graduate in your sample, you recorded how much student debt, if any, the graduate carried at graduation. The results are as follows: (1) Private college graduates: n1 = 400, X-bar-1 = 33,000, s1 = 15,000 (2) Public college graduates: n2 = 100, X-bar-2 = 26,400, s2 = 6000 2(a) At a 99% level of confidence, test the null hypothesis that the total debt of the 20,000 private college graduates, combined, did not exceed $600,000,000. 2(b) At a 99% level of confidence, test the null hypothesis that the average debt of a private college graduate did not exceed the average debt of a public college graduate by more than $5000.

For what type of dependent variable are poisson and negative binomial regressions appropriate? Give an example of such a variable. In what metric are these regression coefficients? What can we do to them to make them more interpretable, and how would we interpret the resulting translated coefficients?

(Understanding and Using Statistics for Criminology and Criminal Justice)

In the book Advanced Managerial Accounting, Robert P. Magee discusses monitoring cost variances. A cost variance is the difference between a budgeted cost and an actual cost. Magee describes the following situation:

Michael Bitner has responsibility for control of two manufacturing processes. Every week he receives a cost variance report for each of the two processes, broken down by labor costs, materials costs, and so on. One of the two processes, which we'll call process A , involves a stable, easily controlled production process with a little fluctuation in variances. Process B involves more random events: the equipment is more sensitive and prone to breakdown, the raw material prices fluctuate more, and so on.

     "It seems like I'm spending more of my time with process B than with process A," says Michael Bitner. "Yet I know that the probability of an inefficiency developing and the expected costs of inefficiencies are the same for the two processes. It's just the magnitude of random fluctuations that differs between the two, as you can see in the information below."

     "At present, I investigate variances if they exceed $2,789, regardless of whether it was process A or B. I suspect that such a policy is not the most efficient. I should probably set a higher limit for process B."

The means and standard deviations of the cost variances of processes A and B, when these processes are in control, are as follows: (Round your z value to 2 decimal places and final answers to 4 decimal places.):

Furthermore, the means and standard deviations of the cost variances of processes A and B, when these processes are out of control, are as follows:

(a) Recall that the current policy is to investigate a cost variance if it exceeds $2,789 for either process. Assume that cost variances are normally distributed and that both Process A and Process B cost variances are in control. Find the probability that a cost variance for Process A will be investigated. Find the probability that a cost variance for Process B will be investigated. Which in-control process will be investigated more often.

Process A = ___

Process B = ___

_(A or B)__ Process is investigated more often

(b) Assume that cost variances are normally distributed and that both Process A and Process B cost variances are out of control. Find the probability that a cost variance for Process A will be investigated. Find the probability that a cost variance for Process B will be investigated. Which out-of-control process will be investigated more often.

Process A = ___

Process B = ___

_(A or B)__ Process is investigated more often

(c) If both Processes A and B are almost always in control, which process will be investigated more often.

_(A or B)__ Process is investigated more often

(d) Suppose that we wish to reduce the probability that Process B will be investigated (when it is in control) to .2912. What cost variance investigation policy should be used? That is, how large a cost variance should trigger an investigation? Using this new policy, what is the probability that an out-of-control cost variance for Process B will be investigated?

Process A = ___

Process B = ___

. Consider the following table. You need to find out if there is an association between

educational attainment and annual income.

(b) State the research question.

(c) State both hypotheses.

(d) Calculate the degrees of freedom.

(e) Calculate the expected frequencies.

(f) Calculate the test statistic.

(g) State a decision regarding the null hypothesis.

(h) Calculate the p-value.

(i) Interpret the results using the p-value. Be very detailed and specific here

A company produces refrigerator motors. These engines have a life expectancy of 19.4 years with a standard deviation of 4.8 years. Assume that the service life of the motors is normally distributed.

a) Calculate the probability of an engine operating for less than 12 years.
Calculate the probability of an engine operating for more than 25 years.
Calculate the probability that the life of an engine is between 10 and 20 years.

In order to promote the sale of their engines, the company wants to issue a guarantee on the engines which means that the customer can replace the engine free of charge if it breaks before a certain time.

b) How many years of warranty can the company expire if they do not want to replace more than 2.5% of the engines? (That is, the warranty period should be such that the probability that an engine's service life is less than the warranty period is 0.025)
The company has a profit of NOK 1200 on a motor that does not fail before the warranty period, while it has a loss of NOK 4500 (ie a profit of -4500 kroner) on a motor that fails before the warranty period. If the company uses the warranty period calculated, what is the expected profit from the sale of an engine?
Briefly explain what this expected profit in practice tells us.