STA100: Relationship Between the Two Variables in Terms of Direction - Statistics Assessment Answer

STA100

Statistics Assessment Task

1. As of the seventh generation of Pókemon, there are 809 Pókemon recorded in the Pókedex. Pókemon can have up to two "types", such as fire, water, electric, etc. Professor Oak is interested in the probabilities of Pókemon being fire and fighting types. He categorizes all 809 according to whether they are those types or not in the following table:

2. A random variable X describes the number of hairs Ben finds in his hairbrush each morning after brushing. X has the probability distribution given below

Select one of the 809 Pókemon at random.

(a) What is the probability of the Pókemon having the Fire type?

(b) What is the probability of the Pókemon having the Fighting type?

(c) What is the probability of the Pókemon having both the Fire and Fighting types?

(d) What is the probability of the Pókemon having the Fighting type, given that they have the Fire type?

(e) Is being a Fire-type Pókemon independent of being a Fighting-type Pókemon?

(f) If I select 10 Pókemon at random, how many will have the Fire type? What is the distribution of this count? Assume we sample with replacement.

(g) Out of 20 Pókemon selected at random, how many can I expect to have the Fighting type?

2. A random variable X describes the number of hairs Ben finds in his hairbrush each morning after brushing. X has the probability distribution given below.

(a) How many hairs can Ben expect to lose on a given morning? What is the standard deviation?

(b) Over 10 days, what is the probability that Ben loses at least 2 hairs per day? Assume each of the days are independent.

(c) Over those 10 days, what is the probability that Ben loses 5 hairs on at least on day? Hint: Setup a binomial random variable.

3. ** R is necessary for the remaining questions. The movie Moneyball is about how proper use of statistics in baseball (called "sabermetrics") can bring unexpected success to a low-ranked, low-budget team. In it, the manager of the Oakland A’s believes that (then) unpopular statistics, like a player’s ability to get on base, can predict the team’s ability to score runs better than traditional statistics, such as homerun counts and batting averages. By recruiting players who scored high in these underused statistics, he was able to improve the record of the team without needing to spend exorbitant amounts of money on the more mainstream players. We will examine the data from the 30 MLB teams during the 2009 season. We will search for linear relationships between potential explanatory variables and the response variable: the number of runs scored in a season, which we treat as a measure of "success" for this data analysis. You don’t need to know the rules of baseball to understand this question, but if you would like a refresher you can check out Wikipedia: https://en.wikipedia.org/wiki/Baseball_rules#Gameplay In addition to runs scored, there are seven traditionally-used variables in the data set: at-bats, hits, homeruns, batting average, strikeouts, walks and stolen bases. The last three variables in the data set are "nontraditional": on-base percentage, slugging percentage, and on base plus slugging. (a) Import the 2009 MLB dataset into R Studio using read.csv() or read.table(). The dataset can be found on Canvas in the file "mlb09.csv". Make sure the data file is placed in your current working directory.

(b) Plot at_bats on the x-axis and runs on the y-axis. Describe the relationship between the two variables in terms of direction (positively or negatively correlated). (c) How confident would you rate your ability to predict a team’s season runs scored, if you just knew the team’s at-bats?

(d) Find the slope and intercept of the regression line through the dataset. Plot the corresponding line over the scatterplot in (b).

(e) Suppose the manager of a team comes and asks you to predict how many runs his team will score if they get 5000 at-bats, 5500 at-bats, and 6000 at-bats. What would you predict for each case?

This STA100 Statistics Assessment has been solved by our Statistics experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.

Be it a used or new solution, the quality of the work submitted by our assignment experts remains unhampered. You may continue to expect the same or even better quality with the used and new assignment solution files respectively. There’s one thing to be noticed that you could choose one between the two and acquire an HD either way. You could choose a new assignment solution file to get yourself an exclusive, plagiarism (with free Turnitin file), expert quality assignment or order an old solution file that was considered worthy of the highest distinction.