Is a sample correlation coefficient ρ = 0.83 significant at the α = 0.01 level based on a sample size of n = 6 data pairs? What about n = 14 data pairs? (Select all that apply.)

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 6 and α = 0.01.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 6 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 14 and α = 0.01.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 6 and α = 0.01.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 6 and α = 0.01.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 14 and α = 0.01.

(b) Is a sample correlation coefficient ρ = 0.41 significant at the α = 0.05 level based on a sample size of n = 20 data pairs? What about n = 26 data pairs? (Select all that apply.)

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 20 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05.

No, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 26 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 26 and α = 0.05.

Yes, because the absolute value of the given correlation coefficient is greater than or equal to that for a sample size of n = 20 and α = 0.05.

No, because the absolute value of the given correlation coefficient is smaller than that for a sample size of n = 20 and α = 0.05.

(c) Is it true that in order to be significant, a ρ value must be larger than 0.90? larger than 0.70? larger than 0.50? What does sample size have to do with the significance of ρ? Explain your answer.

No, a larger sample size means that a smaller absolute value of the correlation coefficient might be significant.

Yes, a larger correlation coefficient of 0.90 means that the data will be significant.

Yes, a larger correlation coefficient of 0.50 means that the data will be significant.

Yes, a larger correlation coefficient of 0.70 means that the data will be significant.

No, sample size has no bearing on whether or not the correlation coefficient might be significant

Both X and S2 are unbiased for the Poisson λ. Which is better? Use the following steps to answer this question.

a) Generate 200000 random numbers from the Poisson(λ = 2) distribution and arrange them in a matrix with 20 rows. Thus you have 10000 samples of size 20.
b) Compute the 10000 sample means and sample variances and store them in objects means and vars, respectively.

c) Compute the average of the 10000 sample means and the average of the 10000 sample variances. Report the two averages. Do they support the claim that they are unbiased for λ = 2?
d) Compute the sample variance of the 10000 sample means and the sample variance of the 10000 sample variances. Report the two variances. Which estimator of λ is preferable.

The exponential distribution with rate λ has mean μ = 1/λ. Thus the method of moments estimator of λ is 1/X. Use the following steps to verify that X is unbiased, but 1/X is biased.

a) Generate 10000 samples of size n = 5 from the standard exponential distribution (i.e. λ = 1) using rexp(50000) and arranging the 50000 random numbers in a matrix with 5 rows.

b) Use the apply() function to compute the 10000 sample means and store them in the object means. The 10000 estimators of λ can be stored in the object lambdas by lambdas = 1/means

c) Compute the sample mean of the object means, and sample mean of the object lambdas. What can you say about the bias of X and of 1/X?

d) Repeat with a sample of size n = 10, using rexp(100000), and report your estimate of the bias of 1/X. Has the bias decreased?

#4
**Below are two samples of test scores from two different calculus classes. It is believed that class 1 performed better than class two. From previous tests, it is known that the test scores for both classes are normally distributed and the population standard deviation of class 1 is 10 points and the population standard deviation of class 2 is 8 points. Do the data support that class 1 performed better.**
```{r}
class1<-c(100, 86, 98, 72, 66, 95, 93, 82)
class2<-c(98, 82, 99, 99, 70, 71, 94, 79)

```

##5
**A teaching assistant in Florida collected a sample to see if the average number of hours students put into studying depending on if they were in graduate school or not. The data below represents these two samples.**

**Perform a test to determine if the time graduate students spend studying is greater than that of undergraduate students. Be sure to identify your hypotheses and explain your conclusion in the context of the question. Assume the time spend studying for both graduate and undergraduate is normally distributed.**

grad<-c(15,7,15,10,5,5,2,3,12,16,15,37,8,14,10,18,3,25,15,5,5)
undergrad<-c(6,8,15,6,5,14,10,10,12,5)

Please Solve using R studio codes with explanation

Rework problem 35 from the Chapter 2 review exercises in your text, involving auditioning for a play. For this problem, assume 11 males audition, one of them being Seamus, 4 females audition, one of them being Nisha, and 5 children audition. The casting director has 4 male roles available, 2 female roles available, and 2 child roles available.

(1) How many different ways can these roles be filled from these auditioners?

(2) How many different ways can these roles be filled if exactly one of Seamus and Nisha gets a part?

(3) What is the probability (if the roles are filled at random) of both Seamus and Nisha getting a part

Suppose x has a normal distribution with mean μ = 52 and standard deviation σ = 9.

Describe the distribution of x values for sample size n = 4. (Round σ_x to two decimal places.)

Describe the distribution of x values for sample size n = 16. (Round σ_x to two decimal places.)

Describe the distribution of x values for sample size n = 100. (Round σ_x to two decimal places.)

How do the x distributions compare for the various samples sizes?

The standard deviations are the same, but the means are increasing with increasing sample size.The standard deviations are the same, but the means are decreasing with increasing sample size.    The means are the same, but the standard deviations are increasing with increasing sample size.The means are the same, but the standard deviations are decreasing with increasing sample size.The means and standard deviations are the same regardless of sample size.

Case Problem 1: Stock Market a. Using the dataset “Stock Market”, build a table with the descriptive statistics (N, Mean, Standard Deviation, Minimum, Median and Maximum) (10 points) • Which companies had a higher mean monthly return than the market (as measured by the S&P 500)? (5 points) • Which one was the most volatile (has the largest standard deviation)? Why is the S&P Index the less volatile? (5 points) b. Find the estimated regression equation relating each of the individual stocks to the S&P 500 and the value of R-Sq for each equation. (25 points) c. Find the betas (slope of estimated regression equation) for the individual stocks from the regression output. (10 points) • What does a stock with a beta greater than 1 indicate? And less than 1? What is the stock that benefits most from a rising market? Why? (25 points) d. What dp the R-Sq values indicate? (20 points)

Listed below are the 25 players on the opening-day roster of the 2016 New York Yankees Major League Baseball team, their salaries, and fielding positions.

Sort the players into two groups, all pitchers (relief and starting) and position players (all others). Assume equal population standard deviations for the pitchers and the position players. Test the hypothesis that mean salaries of pitchers and position players are equal using the 0.01 significance level.

1. State the null and alternative hypothesis.

2. What is the decision rule? (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

3. Calculate the test statistic. (Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

4. What is your decision regarding H₀?

• Do not reject H₀

• Reject H₀

5. Is there a difference in the mean salaries of pitchers and position players?

• Yes

• No

In studies for a​ medication, 77 percent of patients gained weight as a side effect. Suppose 615 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 44 patients will gain weight as a side effect.

​(b) no more than 44 patients will gain weight as a side effect.

​(c) at least 56 patients will gain weight as a side effect. What does this result​ suggest?

1. What is the difference between the “Between Treatment” sources in the One-Way ANOVA compared to the Two-Way ANOVA?

2. Explain how and why the numerators changes when calculating different F-statistics in a Two-Way ANOVA..

3. Explain why the denominator does not change when calculating different F-statistics in a Two-Way ANOVA.

A certain flight arrives on time 86 percent of the time. Suppose 178 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

​(a) exactly 161 flights are on time.

​(b) at least 161 flights are on time.

​(c) fewer than 147 flights are on time.

​(d) between 147 and 160​, inclusive are on time.

Problem 1. A drug company tested three formulations of a pain relief medicine for migraine headache sufferers. For the experiment 27 volunteers were selected and 9 were randomly assigned to one of three drug formulations. The subjects were instructed to take the drug during their next migraine headache episode and to report their pain on a scale of 1 to 10 (10 being most pain).

             Drug A 4 5 4 3 2 4 3 4 4

             Drug B 6 8 4 5 4 6 5 8 6

             Drug C 6 7 6 6 7 5 6 5 5

You can read in data into R by the following R code.

pain = c(4, 5, 4, 3, 2, 4, 3, 4, 4, 6, 8, 4, 5, 4, 6, 5, 8, 6, 6, 7, 6, 6, 7, 5, 6, 5, 5)

drug = c(rep("A",9), rep("B",9), rep("C",9))

migraine = data.frame(pain,drug)

a). Make a boxplot to have a visual check.

b). Compute SST, SSG. SSE directly by definition

c). Compute F value directly by definition

d). Find p-value directly by definition

e). Conduct ANOVA test by R function aov.

f). Make your conclusion.

Applied stats 2 r code questions

Based on historical data, your manager believes that 29% of the company's orders come from first-time customers. A random sample of 52 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is greater than than 0.37?

Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.

A mechanical workshop has registered that three cars with electrical problems arrive in the morning, eight with mechanical problems and three with sheet metal problems, and in the afternoon two with electrical problems, three with mechanical problems and one with sheet metal problems.
a) Construct the contingency table with the previous data.
b) Calculate the percentage of those who come in the afternoon.
c) Calculate the percentage of those who attend due to mechanical problems.
d) Calculate the probability that a car with electrical problems will come in the morning.

Based on past​ experience, a bank believes that

88​%

of the people who receive loans will not make payments on time. The bank has recently approved

300

loans. Answer the following questions.

​a) What are the mean and standard deviation of the proportion of clients in this group who may not make timely​ payments?

mu left parenthesis ModifyingAbove p with caret right parenthesisμpequals=

SD left parenthesis ModifyingAbove p with caret right parenthesisSDpequals=

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

​b) What assumptions underlie your​ model? Are the conditions​ met?

A.

With reasonable assumptions about the​ sample, all the conditions are met.

B.

The randomization and​ success/failure conditions are not met.

C.

The randomization and​ 10% conditions are not met.

D.

The randomization condition is not met.

E.

The​ 10% condition is not met.

F.

The​ 10% and​ success/failure conditions are not met.

G.

The​ success/failure condition is not met.

H.

Without unreasonable​ assumptions, none of the conditions are met.

​c) What is the probability that over

10​%

of these clients will not make timely​ payments?

Upper P left parenthesis ModifyingAbove p with caret greater than 0.1 right parenthesisPp>0.1equals=nothing