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Use a scatterplot and the linear correlation coefficient r to determine whether there is a correlation between the two variables. x y 1 3 0 1 15 5 2 6 3 8

Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance. In addition to $x_1=$ conscientiousness score and $x_2=\{1\text{if highly complex job, 0 if not}\}$, the researchers also used $x_3=$ emotional stability score, $x_4=$ organizational citizenship behavior score, and $x_5=$ counterproductive work behavior score to model y = task performance score. One of their concerns is the level of multicollinearity in the data. A matrix of correlations for all possible pairs of independent variables follows. Based on this information, do you detect a moderate or high level of multicollinearity? If so, what are your recommendations?

$x_1{x}_2{x}_3{x}_4$

Conscientiousness $(x_1)$

Job Complexity $(x_2).13$

Emotional Stability $(x_3).62.14$

Organizational Citizenship $(x_4).24.03.24$

Counterproductive Work $(x_5)-.23-.23-.02-.62$

Maurice and Lester are twins who have just graduated from college. They have both been offered jobs where their take-home pay would be $2500 per month. Their parents have given Maurice and Lester two options for a graduation gift. Option 1: If they choose to pursue a graduate degree, their parents will give each of them a gift of $35,000. However, they must pay for their tuition and living expenses out of the gift. Option 2: If they choose to go directly into the workforce, their parents will give each of them a gift of $5000. Maurice decides to go to graduate school for 2 years. He locks in a tuition rate by paying $11,500 for the 2 years in advance, and he figures that his monthly expenses will be $1000. Lester decides to go straight into the workforce. Lester finds that after paying his rent, utilities, and other living expenses, he will be able to save $200 per month. Their parents deposit the appropriate amount of money in a money market account for each twin. The money market accounts are currently paying a nominal interest rate of 3 percent, compounded monthly. Lester works during the time that Maurice attends graduate school. Each month, Lester saves $200 and deposits this amount into the $5000 money market account that his parents set up for him when he graduated. If Lester's initial balance is $u_0=5000,u_n$ is the current month's balance, and $u_{n-1}$ is last month's balance, write an expression for un in terms of $u_{n-1}$.

Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, you probably know that the theoretical relationship between the variables is distance $=490(time{)}^2.$ Which of the following scatter-plots would not approximately follow a straight line?

(a) A plot of distance versus $tim{e}^2$

(b) A plot of radic distance versus time

(c) A plot of distance versus radic time

(d) A plot of $\ln$(distance) versus $\ln (time)$

(e) A plot of $\log$(distance) versus $\log (time)$

A group of students were polled to find out how many were planning to major in a scientific field of study in college. The results of the poll are shown in the two-way table. Which of the following statements is true? A. Three hundred sixty students were polled in all. B. A student in the senior class is more likely to be planning on a scientific major than a nonscientific major. C. A student planning on a scientific major is more likely to be a junior than a senior. D. More seniors than juniors plan to enter a scientific field of study. $\$\$\begin{array}{cccccccccc}\text{Majoring in a science field}& & \text{Yes}& \text{No}\text{Class}& \text{Junior}& \text{150}& \text{210}& \text{Senior}& \text{112}& \text{200}\end{array}\$\$$

A researcher randomly surveys people with a medical condition about whether they received a treatment and whether their condition improved. The results are shown. Make a two-way table that includes the marginal frequencies. Treatment Improved: 34 Did not improve: 10 Not Treatment Improved: 12 Did not improve: 29

Which set of ordered pairs could be generated by an exponential function? a. (0, 0), (1, 1), (2, 8), (3, 27) b. (0, 1), (1, 2), (2, 5), (3, 10) c. (0, 0), (1, 3), (2, 6), (3, 9) d. (0, 1), (1, 3), (2, 9), (3, 27)

An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. Paxton devises a complicated formula based on game statistics for rating quarterbacks. He applies it to all NFL quarterbacks who played in the league between 1950 and 2000 and concludes that the quarterbacks from the 1970s were the best overall.

Match each verbal statement with the value o fQCR U best matches. Drawing sample scatter plots might help you decide QCR values: -1 0 0.33 0.81 1. a. Mrs. A Every student who was below average on test 1 was also below average on test 2. Every student who was above average on test 1 was also above average on test 2." b. Ms. B: "Most of the students who were below average on test 1 were below average on test 2. Similarly, most of the students scoring above average on test 1 were also above average on test 2. There were a few exceptions, but the trend was clear." c. Mr. C: "Wow, there was really no correlation between test 1 and test 2! half the students who were below average on the first test were also below average on the second test, but half were above average! The same was true for the above average students!" d. Mr. D: "This is so weird. Every student who was below average on test 1 was above average on test 2, and vice versa." e. Mr. E: "Of those scoring above average on test 1, about 60% were above average on test 2, but 40$ were below average."

For each topic, decide which type of association a scatterplot of the data would likely show. Explain your choice. Outdoor temperature and layers of clothing

When would you use a two-way table to display data?

Find a real-life data set that can be represented by a two-way table. Then make a two-way table for the data set.

Students and teachers at a school were polled to see if they were in favor of extending the parking lot into part of the athletic fields. The results of the poll are shown in the two-way table. Which of the following statements is false? A. Thirty-nine students were polled in all. B. Fourteen teachers were polled in all. C. Twenty-three students are not in favor of extending the parking lot. D. Nine teachers are in favor of extending the parking lot. In FavorNot in Favor Students1623 Teachers914

How can you use two way-frequency tables to analyze data?

Describe in your own words the process you use to write marginal relative frequencies for data given in a two-way table.

The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115

The ___________ relative frequencies are the sums of each row and column in a two-way table. (joint, marginal, or conditional)

Complete the table.
$\begin{array}{|ccc|}\hline \text{Grade}& \text{Frequency}& \text{Relative frequency}\\ A& 5\\ B& 11\\ C& 16\\ D& 5\\ F& 1\\ \hline\end{array}$
(Round to two decimal places as needed.)

What type of a variation is displayed by the scatterplot?

Anthony has added a line of best fit to the scatterplot. Do you agree with where he put the line? Explain your reasoning.