When two targets are presented close together in a rapid visual stream, the second target is often missed. Psychologists call this phenomenon the attentional blink (AB). A study published in Advances in Cognitive Psychology (July 2013) investigated whether simultaneous or preceding sounds could reduce AB. Twenty subjects were presented a rapid visual stream of symbols and letters on a computer screen and asked to identify the first and second letters (the targets). After several trials, the subject's AB magnitude was measured as the difference between the percentages of first target and second target letters correctly identified. Each subject performed the task under each of three conditions. In the Simultaneous condition, a sound (tone) was presented simultaneously with the second target; in the Alert condition, a sound was presented prior to the coming of the second target; and in the No-Tone condition, no sound was presented with the second target. Scatterplots of AB magnitude for each possible pair of conditions are shown below as well as the least squares line for each.

a. Which pair of conditions produces the least squares line with the steepest estimated slope?

b. Which pair of conditions produces the least squares line with the largest SSE?

c. Which pair of conditions produces the least squares line with the smallest estimate of \(\sigma\)?

Do men and women differ in their attitudes toward public corruption and tax evasion? This was the question of interest in a study published in Contemporary Economic Policy (Oct. 2010). The data for the analysis were obtained from a representative sample of over 30,000 Europeans. Each person was asked how justifiable it is for someone to (1) accept a bribe in the course of their duties and (2) cheat on their taxes. Responses were measured as 0, 1, 2, or 3, where O = "always justified" and 3 = "never justified." The large-sample Wilcoxon rank sum test was applied in order to compare the response distributions of men and women.

a. Give the null hypothesis for the test in the words of the problem.

b. An analysis of the "justifiability of corruption" responses yielded a large-sample test statistic of \(z = -14.10\) with a corresponding p-value of approximately 0. Interpret this result.

c. Refer to part b. Women had a larger rank sum statistic than men. What does this imply about gender attitudes. toward corruption?

d. An analysis of the "justifiability of tax evasion" responses yielded a large-sample test statistic of \(z = -18.12\) with a corresponding p-value of approximately 0. Interpret this result.

e. Refer to part d. Again, women had a larger rank sum statistic than men. What does this imply about gender attitudes toward tax evasion?

The following definition is discussed in advanced mathematics courses. \($f(x)=\begin{cases}\ 0 & \text{if xx is a rational number}\\ 1 & \text{if xx is an irrational number}\\ \end{cases}$\)
Evaluate \(f(−34), f(−2–\sqrt )\), and \(\displaystyle{f{{\left(\pi\right)}}}\).

Make a scatterplot of the data. Use 87 for 1987

.\(\begin{array}{|c|c|} \hline \text{ Year } & \text{ Sales (millions of dollars)} \\ \hline 1987 & 300 \\ \hline 1988 & 345 \\ \hline 1989 & 397 \\ \hline 1990 & 457\\ \hline 1991 & 510 \\ \hline 1992 & 578 \\ \hline 1993 & 664 \\ \hline 1994 & 700 \\ \hline 1995 & 770 \\ \hline 1996 & 792 \\ \hline 1997 & 830 \\ \hline 1998 & 872 \\ \hline 1999 & 915 \\ \hline \end{array}\)

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 \(u_{n−1}\).

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. At the end of 2 years, Lester receives a raise and decides to save $250 each month. Maurice receives a $5000 graduation gift from his parents and deposits this amount into his money market account. Maurice goes to work and saves $500 each month. Complete the equations below for the money market account balance for each twin. Let the initial balance u0 be the account balance at the end of 2 years. Write an expression for this month's account balance un in terms of un−1. Recall that the interest rate for the account is 3 percent, compounded monthly. Maurice: \(u_{0}=$ 5248.47, u_{n}=?\ Lester: u_{0}=?, u_{n}=?\).

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. \($$\begin{matrix} \text{Majoring in a science field}\ \quad & \quad & \text{Yes} & \text{No}\ \text{Class} & \text{Junior} & \text{150} & \text{210}\ \quad & \text{Senior} & \text{112} & \text{200}\ \end{matrix}$$\)

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 \(time^2\)

(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 \(\log(time)\)