1.How do we recognize a correctly stated standardized regression equation?

2.After scores have been standardized, the value of the Y intercept will always be what?

3.What does the coefficient of multiple determination show?

4.Under what condition could the coefficient of multiple determination be lower than the zero order correlation coefficients?

5.What is the coefficient of multiple determination with two independent variables?

Retaking the SAT: Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 50 such students, the score on the second try was, on average, 28 points above the first try with a standard deviation of 13 points. Test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.01 significance level.

(a) The claim is that the mean difference is greater than 25 (μ_d > 25), what type of test is this?

This is a two-tailed test.

This is a right-tailed test.    

This is a left-tailed test.

(b) What is the test statistic? Round your answer to 2 decimal places.
t-<sub>d= ?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = ?

(d) What is the conclusion regarding the null hypothesis?</sub>

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points.    

We reject the claim that retaking the SAT increases the score on average by more than 25 points.

We have proven that retaking the SAT increases the score on average by more than 25 points.

Suppose x has a distribution with a mean of 80 and a standard deviation of 12. Random samples of size n = 64 are drawn.

(a) Describe the x bar distribution. x bar has an approximately normal distribution. x bar has a Poisson distribution. x bar has a binomial distribution. x bar has an unknown distribution. x bar has a normal distribution. x bar has a geometric distribution. Compute the mean and standard deviation of the distribution. (For each answer, enter a number.) mu sub x bar = mu sub x bar = sigma sub x bar = sigma sub x bar =

(b) Find the z value corresponding to x bar = 83. (Enter an exact number.) z =

(c) Find P(x bar < 83). (Enter a number. Round your answer to four decimal places.) P(x bar < 83) = P(x bar < 83)

(d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 83?

Explain.

The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations. Both the quality of management and the reputation of the company were rated on an excellent, good, and fair categorical scale. Assume the sample data for 200 respondents below applies to this study.

Use a 0.05 level of significance and test for independence of the quality of management and the reputation of the company.

A) State the null and alternative hypotheses.

H₀: Quality of management is independent of the reputation of the company.
H_a: Quality of management is not independent of the reputation of the company.

H₀: Quality of management is not independent of the reputation of the company.
H_a: Quality of management is independent of the reputation of the company.    

H₀: Quality of management is not independent of the reputation of the company.
H_a: The proportion of companies with excellent management is not equal across companies with differing reputations.

H₀: Quality of management is independent of the reputation of the company.
H_a: The proportion of companies with excellent management is equal across companies with differing reputations.

B) Find the value of the test statistic. (Round your answer to three decimal places.)

C) Find the p-value. (Round your answer to four decimal places.)

D) State your conclusion.

Do not reject H₀. We cannot conclude that the rating for the quality of management is independent of the rating of the reputation of the company.

Reject H₀. We conclude that the rating for the quality of management is not independent of the rating for the reputation of the company.     

Reject H₀. We conclude that the rating for the quality of management is independent of the rating for the reputation of the company.

Do not reject H₀. We cannot conclude that the ratings for the quality of management and the reputation of the company are not independent.

E) If there is a dependence or association between the two ratings, discuss and use probabilities to justify your answer.

For companies with an excellent reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. For companies with a good reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. For companies with a fair reputation, the largest column probability corresponds to [ EXCELLENT/GOOD/FAIR ] excellent good fair management quality. Since these highest probabilities correspond to [THE SAME/DIFFERENT ] the same different ratings of quality of management and reputation, the two ratings are [ ASSOCIATED/INDEPENDENT ] associated independent.

Use the sample information x¯ ⎯ x¯ = 40, σ = 7, n = 13 to calculate the following confidence intervals for μ assuming the sample is from a normal population.

(a) 90 percent confidence. (Round your answers to 4 decimal places.)
  
The 90% confidence interval is from __to__

(b) 95 percent confidence. (Round your answers to 4 decimal places.)
  
The 95% confidence interval is from __to__

(c) 99 percent confidence. (Round your answers to 4 decimal places.)
  
The 99% confidence interval is from __to__

(d) Describe how the intervals change as you increase the confidence level.
  

A- The interval gets narrower as the confidence level increases.

B- The interval gets wider as the confidence level decreases.

C- The interval gets wider as the confidence level increases.

D- The interval stays the same as the confidence level increases.

1.What elements define the position of the least squares regression line?

2.What are the parts of the regression equation? How do you interpret each?

3.What are the functions of the least squares regression equation?

4.Why is the slope an awkward measure of the strength of a relationship?

5.If the slope is zero, what is the value of r?

If x(overbar) =103 and sigma=8 and n=65 construct a 95% confidence interval estimate of the population mean, u

X is a binomial random variable.

n= 100 p= .4

Use the binomial approach and normal approximation to calculate the follwowing: 1. P(x>=38) 2. P(x=45) 3. P(X>45) 4. P(x <45)

The data below are for 30 people. The independent variable is “age” and the dependent variable is “systolic blood pressure.” Also, note that the variables are presented in the form of vectors that can be used in R. age=c(39,47,45,47,65,46,67,42,67,56,64,56,59,34,42,48,45,17,20,19,36,50,39,21,44,53,63,29,25,69) systolic.BP=c(144,20,138,145,162,142,170,124,158,154,162,150,140,110,128,130,135,114,116,124,136,142,120,120,160,158,144,130,125,175) a) Using R, develop and show a scatterplot of systolic blood pressure (dependent variable) by age (independent variable), and calculate the correlation between these two variables. b) Assume that these data are “straight enough” to model using a linear regression line. Develop and show that model (write out the model in the terms of the problem), and also show in a plot the line that best fits these data. c) Plot the residuals and comment on what you see as to how appropriate the model is. d) Using a boxplot, determine if there are any outliers in systolic blood pressure. If so, point out which points are outliers, if any. e) Assuming there is at least one outlier in systolic blood pressure, remove that outlier and re-do parts a) through c) again using the remaining data without the outlier(s). State and comment on this second model. f) In your second model, explain in the context of age and systolic blood pressure what the slope of your fitted line means. Also, for your second model, calculate R2 (the coefficient of determination), and explain what that means in the context of your second model.

Define the term “Historical Control” and explain its relevance to issues surrounding the differences between a “Randomized Controlled Experiment” and an “Observational Study”.

Explain the difference between a “quantitative variable” and a “qualitative variable” and give an example of each.

In the Ponderosa Development Corp. (PDC) example, if the land for each house costs $108,100 and lumber, supplies, and other materials cost another $41,200 per house. The company leases office and manufacturing space for $3,100 per month and their monthly salaries total to $65,250. Assume that total labor costs are approximately $26,800 per house. The cost of supplies, utilities, and leased equipment is $6,650 per month. The one salesperson of PDC is paid a commission of $3,900 on the sale of each house. The selling price of each house is $195,000.
(1) Identify all costs and revenue for each house.

(2) Write the monthly cost function c (x), revenue function r (x), and profit function p (x).

(3) What is the breakeven point (BEP) for monthly sales of the houses based on the cost, revenue and profit functions specified in (2)?

(4) What is the monthly profit if 13 houses per month are built and sold?

(5) What is the monthly profit if the variable cost per house = $160,500 and PDC built and sold 10 houses per month?

(4) What is the monthly profit if 13 houses per month are built and sold?

Suppose that 51% of all adults regularly consume coffee, 63% regularly consume carbonated soda, and 72% regularly consume coffee OR carbonated soda.

Note: Your answer must have both side of probability definition . Hint P (?) =?

(a) (5 points) What is the probability that a randomly selected adult regularly consumes both coffee and soda? Draw Venn diagram and label (with probability) each portion of the diagram to answer this question.

(b) (2 points) What is the probability that a randomly selected adult regularly consume at most one of these two products?

(c) (2 points) What is the probability that a randomly selected adult consume none these two products?

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 10% of voters are Independent. A survey asked 22 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent? Probability =

B. What is the probability that fewer than 5 are Independent? Probability =

C. What is the probability that more than 17 people are Independent? Probability =

Suppose that 100 items are drawn from a population f manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a right skewed probability distibution with mean=150 oz and standard deviation=30 oz. Find the value of X-bar for which P(X-bar > ?) = 0.75.