26. Calculate each value requested for the following set of scores.

a. ΣX X Y

b. ΣY 1 6

c. ΣXΣY 3 0

d. ΣXY 0 –2

2 –4

27. Use summation notation to express each of the following calculations. a. Add 3 points to each score, then find the sum of the resulting values. b. Find the sum of the scores, then add 10 points to the total. c. Subtract 1 point from each score, then square each of the resulting values. Next, find the sum of the squared numbers. Finally, add 5 points to this sum.

28. Describe the relationships between a sample, a population, a statistic and a parameter.

1. A sample dataset with 25 values was randomly generated from a normally distributed random variable with a mean of 100.  The randomly selected data points are presented in the following table:

1. What kind of sample data do you have? Select the appropriate type of data
   1. One sample
   2. Paired sample
   3. Two samples
2. Based on what you know about the distribution of the data points, what is the preferred method of statistical analysis for the data?  Justify your answer
3. Can you use an alternative equivalent statistical test?  Justify your answer

I need help trying to explain and solve b and c!!

Each applicant has a score. If there are a total of n applicants then each applicant whose score is above sn is accepted, where s1 = .2, s2 = .4, sn = .5,n ≥ 3. Suppose the scores of the applicants are independent uniform (0, 1)random variables and are independent of N, the number of applicants, which is Poisson distributed with mean 2. Let X denote the number of applicants that are accepted. Derive expressions for (a) P(X=0). (b) E[X].

f(x,y)=(xcos(t)−ysin(t),xsin(t)+ycos(t))f(x,y)=(xcos⁡(t)−ysin⁡(t),xsin⁡(t)+ycos⁡(t))

defines rotation around the origin through angle tt in the Cartesian plane R2R2. If one rotates a point (x,y)∈R2(x,y)∈R2 around the origin through angle tt, then f(x,y)f(x,y) is the result.

Let (a,b)∈R2(a,b)∈R2 be an arbitrary point. Find a formula for the function gg that rotates each point (x,y)(x,y) around the point (a,b)(a,b) through angle tt.

IQ scores have a mean of 100 and standard deviation of 15:

a) What percentage of scores fall between 100 & 135?

b) What percentage of scores fall between 88 & 100?

Gentle Ben is a Morgan horse at a Colorado dude ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

The sample mean is x ≈ 94.8. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know from past experience that σ = 12.5. The mean glucose level for horses should be μ = 85 mg/100 ml.† Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use α = 0.05.

(a) What is the level of significance?

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)


(c) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Aldrich Ames is a convicted traitor who leaked American secrets to a foreign power. Yet Ames took routine lie detector tests and each time passed them. How can this be done? Recognizing control questions, employing unusual breathing patterns, biting one's tongue at the right time, pressing one's toes hard to the floor, and counting backwards by 7 are countermeasures that are difficult to detect but can change the results of a polygraph examination†. In fact, it is reported in Professor Ford's book that after only 20 minutes of instruction by "Buzz" Fay (a prison inmate), 85% of those trained were able to pass the polygraph examination even when guilty of a crime. Suppose that a random sample of eleven students (in a psychology laboratory) are told a "secret" and then given instructions on how to pass the polygraph examination without revealing their knowledge of the secret. What are the following probabilities? (Round your answers to three decimal places.)

(a) all the students are able to pass the polygraph examination

(b) more than half the students are able to pass the polygraph examination

(c) no more than half of the students are able to pass the polygraph examination

(d) all the students fail the polygraph examination

In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees.

A.  How many​ four-year colleges and universities were​ surveyed? There were ___​four-year colleges and universities surveyed. Of the​ four-year colleges and universities​ surveyed, how many offered

B.  a liberal arts degree and a nursing​ degree, but not a computer engineering ​degree? There are ____ ​four-year colleges and universities that offer a liberal arts degree and a nursing​ degree, but not a computer engineering degree.

C.  a computer engineering ​degree, but neither a liberal arts degree nor a nursing​ degree? There are ____ ​four-year colleges and universities that offer a computer engineering ​degree, but neither a liberal arts degree nor a nursing degree.

D.  a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree? There are ____ ​four-year colleges and universities that offer a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. Enter your answer in each of the answer boxes.

1. Suppose that the Canadian stock market return, denoted by a random variable X, varies within {−0.2, −0.1, 0, 0.1, 0.2, 0.4, 0.9}, and suppose that P (X = x) = (1 − x)/10 for x < 0.5 and P (X = 0.9) = 0. Determine each of the following:

   (a) The pdf of X. (b) The cdf of X.

   (c) The expected value of X. (d) The variance of X.

   (e) The standard deviation of X.
   (f) Calculate the sample median of X.

   (g) Let Y denote another random variable such that Y = X2, determine the variance of Y .

2. Let Φ(z) represent the cdf of a N(0,1) random variable at some cut-off point, z. Let X denote

   a N(0.5,1.5) random variable.

   1. (a) Calculate P (−1 ≤ X ≤ 2).

   2. (b) Let Y be a N(0,2) random variable that is independent of X defined above. Calculate P(−0.5≤X+Y ≤3).

3. At the points, x = 0,1,...,6, the cdf for the discrete random variable, X, has the value F(x) = x(x + 1)/42. Find the pdf for X.

The following frequency distribution shows the number of customers who had an oil change at a particular Jiffy Lube franchise for the past 40 days.

Use this data to construct a relative frequency and cumulative relative frequency distribution. Report all of your answers in the table above to 3 decimal places, using conventional rounding rules.

What percent of the days are there less than 45 customers who had an oil change at this Jiffy Lube? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:          %

What proportion of the days were there 65 – 74 customers at this Jiffy Lube for an oil change? Report your final answer to 4 decimal places, using conventional rounding rules.

ANSWER:         

What percent of the days were there at least 55 customers at this Jiffy Lube for an oil change? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:          %

What is the approximate mean number of customers at this Jiffy Lube for an oil change? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

What is the approximate standard deviation of the number of customers at this Jiffy Lube for an oil change? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

What is the midpoint of the class interval with the largest frequency? Report your final answer to 2 decimal places, using conventional rounding rules.

ANSWER:         

True or False

_____I. If a negative correlation exists between X and Y, and a new data point is added whose Z_X = -2.5 and Z_Y = 2.5, |r| will decrease.

_____J. If a positive correlation exists between X and Y, and a new data point is added whose Z_X = 2.5 and Z_Y = 2.5, |r| will decrease.

_____K. In simple linear regression predicting Y from X, the unstandardized coefficient of the X variable will always equal the Pearson r between X and Y. (Assume X and Y are not measured as z scores.)

_____L. In simple linear regression predicting Y from X, the standardized coefficient of the X variable will always equal the Pearson r between X and Y.

_____M. In multiple regression predicting Y from two X variables, the standardized coefficient for the first X variable will always equal the Pearson r between that X and Y.

Compare the coefficients of determination (r-squared values) from the three linear regressions: simple linear regression from Module 3 Case, multivariate regression from Module 4 Case, and the second multivariate regression with the logged values from Module 4 Case. Which model had the “best fit”? Calculate the residual for the first observation from the simple linear regression model. Recall, the Residual = Observed value - Predicted value or e = y – ŷ. What happens to the overall distance between the best fit line and the coordinates in the scatterplot when the residuals shrink? What happens to the coefficient of determination when the residuals shrink? Consider the r-squared from the linear regression model and the r-squared from the first multivariate regression model. Why did the coefficient of determination change when more variables were added to the model? Annual Amount Spent on Organic Food Age Annual Income Number of People in Household Gender

Module 4

Module 3

A) Body mass index (BMI) in children is approximately normally distributed with a mean of 24.5 and a standard deviation of 6.2. A BMI between 25 and 30 is considered overweight. What proportion of children are overweight? (Hint: p[25<x<30]. Answer in 0.0000 format, NOT in percentage format. Round to 4 decimal places)

B) If BMI larger than 30 is considered obese, what proportion of children are obese? (Answer in 0.0000 format, NOT in percentage format. Round to 4 decimal places).

C)Based on information provided in Question 42, in a random sample of 10 children, what is the probability that their mean BMI exceeds 25? (Hint: Central Limit Theorem. Answer in 0.0000 format, NOT in percentage format. Round to 4 decimal places)

Annual Amount Spent on Organic Food = α + b₁Age + b₂AnnualIncome
+ b₃Number of People in Household + b₄Gender

After you have reviewed the results from the estimation, write a report to your boss that interprets the results that you obtained. Please include the following in your report:

1. The regression output you generated in Excel.
2. Your interpretation of the coefficient of determination (r-squared).
3. Your interpretation of the global test for statistical significance (the F-test).
4. Your interpretation of the coefficient estimates for all the independent variables.
5. Your interpretation of the statistical significance of the coefficient estimates for all the independent variables.
6. The regression equation with estimates substituted into the equation. (Note: Once the estimates are substituted into the regression equation, it should take a form similar to this: y = 10 +2x₁ +1x₂ +4x₃ +0.9x₄)
7. An estimate of “Annual Amount Spent on Organic Food” for the average consumer. (Note: You will need to substitute the averages for all the independent variables into the regression equation for x, the intercept for α, and solve for y.)
8. A discussion of whether or not the coefficient estimate on the Age variable in this estimation is different than it was in the simple linear regression model from Module 3 Case. Be sure to explain why it did/did not change.
9. You decide you want to generate an elasticity coefficient, so you log the following variables in Excel: Annual Amount Spent on Organic Food, Annual Income.
10. Using Excel, generate regression estimates for the following model:

Log(Annual Amount Spent on Organic Food) = α +b₁Age + b₂Log(AnnualIncome)
+ b₃Number of People in Household + b₄Gender

11. Your interpretation of the coefficient estimate for Log(AnnualIncome).
12. Your interpretation of the coefficient of determination (r-squared) for this new model.