Please type responses as it is difficult for me to see written responses. Thank you

1) How does understanding the correlation between variables help us understand regression?

2) Provide two ways on how you might use regression while teaching a classroom of children.

3) What is one easy way to remember the differences between parametric and nonparametric tests? (Note: I'm not asking you to list the differences but HOW you can remember the differences. Feel free to be creative here - you are free to use mnemonics, diagrams, poetry, etc...!)

4) Provide two ways on how you might use chi-square tests in a classroom environment if you were a teacher.

Build a garch model using the following monthly change data for Mexico. Use R

Assume the life of a roller bearing follows a Weibull distribution with parameters β=2 and δ=7,500 hours.

1. Determine the probability that the bearing will last at least 8000 hours.
2. Determine the expect value and the variance.

The statement -- Researchers are interested to compare height of three species of rhino Asian, African, and Sumatran. These species are geographically isolated and believed to be different in their size. Twenty rhinos from each population were selected randomly and their height was measured.

From this statement for the one way ANOVA what is the Hypothesis?

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Alice, Bob, and Chuck are three students who go out for coffee every day. But every day, they randomly determine who pays for the three coffee. If Alice pays for the coffee today, then there is a 25% chance she will also pay tomorrow, a 50% chance Bob will pay tomorrow, and 25% chance Chuck will pay tomorrow. If Bob pays today, there is a 50% chance Alice will pay tomorrow, and 50% chance Chuck will pay tomorrow. If Chuck pays today, there is a 50% chance Alice will pay tomorrow, 25% chance Bob will pay tomorrow, and 25% chance that Chuck will pay again tomorrow. a. This is a Markov chain. What are the three states? b. Calculate what proportion of time each person will pay over the long term

A hobbyist family is making PPE (personal protective equipment) to donate to local health care workers. Let

• T1 ∼ U(1,4) be the amount of time (in hours) to 3D print a face mask and
• T2 be an exponentially distributed random variable with an average of 3 hours to represent the

time (in hours) to cut out and sew a suit.

Describe the distribution of time to complete construction of one suit-and-mask outfit by computing the mean, median, and standard deviation of the sum T1 + T2 assuming independence between T1 and T2. (Hint: there is only one input variable—time—so there is no need for double integrals.)

1. This assignment focuses on the architecture of the Poisson, Negative Binomial, Zero-Inflated Poisson and Zero-Inflated Negative Binomial regression models.

A. In which context Poisson regression can be employed, please provide some examples?

B. What is the main difference between the Poisson regression model and the Negative Binomial regression model? Please explain.

C. Why is it important to use Zero-Inflated models such as the Zero-Inflation Poisson regression model or the Zero-Inflated Negative Binomial regression model in the first place?

D. What is the specific contribution of the Vuong test into the count outcomes regression analysis? Be specific.

Effects of a Pre-workout Energy Drink Supplement on Upper Body Muscular Endurance Performance

The use of pre-workout beverages is becoming an increasingly common method of improving performance during exercise in athletic and recreationally active populations. Therefore, the purpose of this study was to investigate the effects of a commercially available energy drink on exercise performance. Thirty-one healthy males (n=23) and females (n=8) participated in this study and were separated into two groups: supplement (SU; n=16) or placebo (PL; n=15). Subjects visited the laboratory on 2 occasions separated by no more than 7 days. The first visit consisted of completing a push up to fatigue protocol (PUFP) without ingesting the pre-workout energy drink supplement (PWEDS). The second visit consisted of ingesting either a placebo or the PWEDS 30 minutes prior to completing the PUFP. Rate of perceived exertion (RPE) was recorded following each set of pushups on both testing days. Also, participant's height, weight, and body composition were collected. There was no significant differences at baseline in any variable between groups (p = >.05). After the second testing session, both groups significantly improved total push-ups (PL Pre: 133.3 ±39.4, PL Post: 155.3 ± 54.1; SU Pre: 139.3 ± 58.5, SU Post: 161.3 ± 79.4; p=<.001), and push-ups completed in each of the 3 sets (p=<.001), when compared to baseline. Post-testing revealed no significant difference between groups in total push-ups completed or RPE at any time point, when compared to baseline. In conclusion, the commercially available PWEDS offered no additional ergogenic effects when compared to the placebo.

Write the title of the article                                                                                                   

Identify the Null and Alternative Hypothesis

Identify the independent and dependent variables  

Identify if the results of the study were what the authors hypothesized

Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are data on prices paid to coffee growers in Indonesia and the rate of deforestation in a national park that lies in a coffee-producing region for five years: Price(cents per pound) Deforestation (percent) 29 0.49 40 1.59 54 1.69 55 1.82 72 3.10 (a) Make a scatterplot. What is the explanatory variable? What kind of pattern does your plot show? (b) Find the correlation r step-by-step. That is, find the mean and standard deviation of the two variables. Then find the five standardized values for each variable and use the formula for r.

Explain how your value for r matches your graph in (a). (c) Now enter these data into your calculator or Excel and use the correlation function to find r. Check that you get the same result as in (b). PLEASE, GIVE A DETAILED SOLUTION. THANK YOU IN ADVANCE!

Until 2002, hormone replacement therapy (HRT), estrogen and/or progesterone, was commonly prescribed to post-menopausal women. This changed in 2002, when the results of a large clinical trial were published.8506 women were randomized to take HRT, 8102 were randomized to placebo. 166 HRT and 124 placebo women developed invasive breast cancer. Does HRT increase risk of breast cancer? (P value = 0.03)

Define all the parameters of interest

State the null and alternative hypotheses

What is informal description of the strength of evidence against H₀

Are the results statistically significant?

State the formal decision about H₀, using α = 0.05

Conclusion in the context of the question

Calculate the statistics of interest

An urn contains 7 black balls, 4 red balls, 3 white balls and 1 blue ball, and a player is to draw one ball. If it is black, he wins $1, if it is red, he wins $2, if it is white he wins $3 and if it is blue, he pay $25.

a. Set up the empirical probability distribution for the random variable X, the payoff of the game.

b. What is the mathematical expectation of this game?



c. In the long-run, will the player win or lose?

QUESTION 5      

The Layton Tire and Rubber Company wishes to set a minimum mileage guarantee on its new MX100 tire. Tests reveal the mean mileage is 67900 with a standard deviation of 2050 miles and that the distribution of miles follows the normal distribution. They want to set the minimum guarantee mileage so that no more than 4 percent of tires will be replaced. What minimum guaranteed mileage should Layton announce?

Using the data below, test the null hypothesis that the variance in the Close Ratio for the sample of employees is at most 1.5% at 5% significance level.

The (mixed) random variable X has probability density function (pdf) fX (x) given by:

f_x(x)=0.5δ(x−3)+ { c.(4-x²), 0≤x≤2

0, otherwise

where c is a constant.

(a) Sketch fX (x) and find the constant c.

(b) Find P (X > 1).

(c) Suppose that somebody tells you {X > 1} occurred. Find the conditional pdf f_X|{X>1}(x), the pdf of X given that {X > 1}.

(d) Find FX(x), the cumulative distribution function of X.

(e) Let Y = X² . Find fY (y), the probability density function of the random variable Y