In the late $1980$s, many states and localities passed laws against hate crimes. These laws defined the types of acts that constituted hate crimes and provided criminal penalties for them. St. Paul, Minnesota, was one of many cities to pass such a law. This city's ordinance read as follows: Whoever places on public or private property a symbol... or graffiti, including but not limited to a burning cross or Nazi swastika, which one knows or has reasonable grounds to know arouses anger, alarm, or resentment in others on the basis of race, color, creed, religion, or gender, commits disorderly conduct and shall be guilty of a misdemeanor.

Russell and Laura Jones and their five children were an African American family who had just moved into a mostly white St. Paul neighborhood. Late one night they were awakened by noise outside their bedroom window. When they parted the curtains, they saw a cross burning on their front lawn. St. Paul police arrested an $18$-year-old white male. He was prosecuted and convicted under the local ordinance described above.

When interviewed by a national newspaper, the lawyer for the defendant stated that, "Everybody's gotten real thin-skinned lately, and I'm defending the right to express yourself in that kind of climate... With an ordinance like this, you open up a doctrine that swallows the First Amendment." What did the defendant's lawyer mean by these comments? Do you agree or disagree with these comments? Give the reasons for your answers.

According to a theory in psychology, young female adults show more emotional empathy toward others than do males. The Journal of Moral Education (June 2010) tested this theory by examining the attitudes of a sample of 30 female college students. Each student completed the Ethic of Care interview, which consisted of a series of statements on empathy attitudes. For the statement on emotional empathy (e.g., "l often have tender, concerned feelings for people less fortunate than me"), the sample mean response was 3.28. Assume the population standard deviation for females is .5. [Note: Empathy scores ranged from 0 to 4, where 0 = "never" and 4 = "always".] Suppose it is known that male college students have an average emotional empathy score of $\mu=3$. a. Specify the null and alternative hypotheses for testing whether female college students score higher than 3.0 on the emotional empathy scale. b. Compute the test statistic. c. Find the observed significance level (p-value) of the test. d. At $\alpha=.01$, what is the appropriate conclusion? e. How small of an $\alpha$-value can you choose and still have sufficient evidence to reject the null hypothesis?

From the list below, supply the words needed to complete the paragraph. Some words will not be used.

$$\begin{array}{llll}\text { sapient } & \text { idiosyncrasy } & \text { blanch } & \text { machination } \\ \text { pejorative } & \text { masochist } & \text { nubile } & \text { deride } \\ \text { heterogeneous } & \text { grandiose } & \text { raiment } & \text { finesse }\end{array}$$

Dr. Quade still wore the ______ of a maximum-security prison inmate when he entered an abandoned warehouse to evade the searchlights of police helicopters. Six years of living without sunlight in an underground cell had ______ the color of his face, and the beatings and ______ treatment that he received from guards had left him with a perpetual scowl. Now, he mused, he would be free to carry out the ______ that he had planned during his confinement, but not before using his criminal ______ to steal an automobile from the nearby parking garage. The garage contained a[n] ______ collection of automobiles, but the ______ Dr. Quade chose a very dull, plain car to hotwire; a[n] ______ car could draw unwanted attention that jeopardized the escape.

Even without keys, the mad genius was able to start the car in two minutes; however, he revealed a violent ______ by punching the dashboard when a light indicated that the car was low in fuel. The resulting cuts on his hands would have irritated a normal person, but not a[n] ______ like Dr. Quade. As he drove out of the garage, Dr. Quade allowed himself a chuckle as he ______ the system that had mistakenly thought it could keep him imprisoned.

A study of how eye movement behavior can distort one’s judgment of the location of an object was published in Advances in Cognitive Psychology (Vol. 6, 2010). The medical term for fast voluntary movement of the eyes when focusing on an object is saccadic eye movement . The researchers designed several experiments in which volunteers fixated their eyes on a cross in the middle of a computer screen. A probe was then spatially extended near the cross and each volunteer was asked to judge the location of the probe. Saccadic eye movement was monitored during each session. The researchers used spatial position of the probe (

$$x_1 ,$$

measured in degrees) and position of the cross (

$$x_2 ,$$

degrees) to predict the amplitude ( y ) of saccadic eye movement. The following model was fit to the data:

$$E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 }$$

a. The model yielded R2 = .994 . Interpret this result. b. In the words of the problem, what does it mean to say that

$$“ x_1 \ and \ x_2$$

interact”? c. The least squares prediction equation was determined as:

$$\hat { y } = .91 + .70 x _ { 1 } - .06 x _ { 2 } - .03 x _ { 1 } x _ { 2 }$$

Illustrate interaction by graphing the relationship between predicted amplitude

$$( \hat { y } )$$

and cross position

$$( x_2 )$$

for probe positions

$$x _ { 1 } = 3.5 \text { and } x _ { 1 } = 6.5$$

A psychology professor is studying the relation between overcrowding and violent behavior in a rat colony. Eight colonies with different degrees of overcrowding are being studied. By using a television monitor, lab assistants record incidents of violence. Each colony has been ranked for crowding and violence. A rank of 1 means most crowded or most violent. The results for the eight colonies are given in the following table, with x being the population density rank and y the violence rank.

$$\scriptstyle\begin{array}{c|cccccccc} \hline \text { Colony } & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline x \text { rank } & 3 & 5 & 6 & 1 & 8 & 7 & 4 & 2 \\ y \text { rank } & 1 & 3 & 5 & 2 & 8 & 6 & 4 & 7 \\ \hline \end{array}$$

Using a 0.05 level of significance, test the claim that lower crowding ranks mean lower violence ranks (i.e., the variables have a monotone-increasing relationship). Compute the sample test statistic.

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 nine 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 is the probability that (b) more than half the students are able to pass the polygraph examination?

The Journal of Economic Psychology (September 2008) published the results of a high-stakes experiment where subjects (university students) were asked how much they would pay to ensure a valuable painting. The painting was threatened by fire and theft, hence, the need for insurance. Of interest was the amount the subject was willing to pay (WTP) for insurance (thousands of dollars). 252 subjects were randomly assigned to one of three groups for one part of the experiment. Group 1 subjects $\left(n_{1}=84\right)$ were informed of the hazards (both fire and theft) but were not told the exact probabilities of the hazards occurring. These subjects provided a different WTP value for fire and theft. Group 2 subjects $\left(n_{2}=84\right)$ were also informed of the hazards (fire/theft) and were not told the exact probabilities of the hazards occurring. However, these subjects provided a single WTP value covering fire and theft. Group 3 subjects $\left(n_{3}=84\right)$ were told of the hazards in sequential order (fire first, then theft). After being given the exact probability of a fire occurring, the subjects provided a WTP value for fire. Then they were given the exact probability of theft and asked to provide a WTP value for theft. The researchers investigated whether the three groups' mean total WTP values differed.

b. Specify the dependent (response) variable and treatments for the design.

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 question s, employing unusual breathing patterns, biting one's tongue at the right time, pressing one's toes hard to the floor, and counting backward 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 nine students (in a psychology laboratory) are told a "secret" and then given instruction s on how to pass the polygraph examination without revealing their knowledge of the secret. What is the probability that all the students fail the polygraph examination?

The grading system known as "grading on the curve" is based on the assumption that grades are often distributed according to the normal curve and that a certain percent of a class should receive each grade, regardless of the performance of the class as a whole. The following is how one professor might grade on the curve.

$$\begin{matrix} \text{Grade} & \text{Total Points}\\ \hline \text{A} & \text{Greater than $\mu+(3 / 2) \sigma$}\\ \text{B} & \text{$\mu+(1 / 2) \sigma \text { to } \mu+(3 / 2) \sigma$}\\ \text{C} & \text{$\mu-(1 / 2) \sigma \text { to } \mu+(1 / 2) \sigma$}\\ \text{D} & \text{$\mu-(3 / 2) \sigma \text { to } \mu-(1 / 2) \sigma$}\\ \text{F} & \text{Below $\mu-(3 / 2) \sigma$}\\ \end{matrix}$$

Do you think this system would be more likely to be fair in a large freshman class in psychology or in a graduate seminar of five students? Why?

The psychologists Amos Tversky and Daniel Kahneman studied the psychology of risk by posing survey questions related to expected value. Consider the following two questions.

Question $1$: Which option would you rather take, A or B?

Option A: $100 \%$ chance of gaining $\$ 240$

Option B: $25 \%$ chance of gaining $\$ 1000 ; 75 \%$ chance of gaining nothing

Question $2$: Which option would you rather take, $C$ or $D$?

Option C: $100 \%$ chance of losing $\$ 750$

Option D: $75 \%$ chance of losing $\$ 1000$ and $25 \%$ chance of losing nothing

a. Before doing calculations, answer both questions based on your own intuition.

b. For each question, find the expected value of each option.

c. Tversky and Kahneman discovered that for Question $1$, a majority of people chose option A, while for Question $2$, a majority of people chose option D. Are the responses given in the surveys consistent with the expected values?

d. Give a possible explanation for the responses in Allais's surveys.

Dermatologists' primary recommendation to prevent skin cancer is minimal exposure to the sun. Yet models used in product advertisements are typically well-tanned. Do such advertisements influence a consumer's attitude toward tanning? University of California and California State University researchers designed an experiment to investigate this phenomenon and published their results in Basic and Applied Social Psychology (May 2010). College student participants were randomly assigned to one of three conditions: (1) view product advertisements featuring models with a tan, (2) view product advertisements featuring models without a tan, or (3) view products advertised with no models (control group). The objective was to determine whether the mean attitude toward tanning differs across the three conditions. A tanning attitude index (measured on a scale of 0 to 5 points) was recorded for each participant. The results are summarized in the accompanying table.

$$\begin{matrix} \text{ } & \text{Tanned Models} & \text{Models with No Tan} & \text{No Models}\\ \text{Sample size} & \text{56} & \text{56} & \text{56}\\ \text{Mean} & \text{2.40} & \text{2.11} & \text{2.50}\\ \text{Standard deviation} & \text{.85} & \text{.73} & \text{.82}\\ \end{matrix}$$

What assumptions are required for the inferences derived from the test to be valid?

Dermatologists' primary recommendation to prevent skin cancer is minimal exposure to the sun. Yet models used in product advertisements are typically well-tanned. Do such advertisements influence a consumer's attitude toward tanning? University of California and California State University researchers designed an experiment to investigate this phenomenon and published their results in Basic and Applied Social Psychology (May 2010). College student participants were randomly assigned to one of three conditions: (1) view product advertisements featuring models with a tan, (2) view product advertisements featuring models without a tan, or (3) view products advertised with no models (control group). The objective was to determine whether the mean attitude toward tanning differs across the three conditions. A tanning attitude index (measured on a scale of 0 to 5 points) was recorded for each participant. The results are summarized in the accompanying table.

$$\begin{matrix} \text{ } & \text{Tanned Models} & \text{Models with No Tan} & \text{No Models}\\ \text{Sample size} & \text{56} & \text{56} & \text{56}\\ \text{Mean} & \text{2.40} & \text{2.11} & \text{2.50}\\ \text{Standard deviation} & \text{.85} & \text{.73} & \text{.82}\\ \end{matrix}$$

The researchers conducted an ANOVA on the data and reported the following results: F = 3.60,p-value = .03. Carry out the test. Use $\alpha=.05$ to draw your conclusion.

Arlen City Police Department is offering special classes for interested high school students this summer. Elsa decides to enroll in an introductory forensic sciences class. On the first day, Dr. Suarez tells Elsa's class that they will perform an experiment at a local driving track. On the day of the experiment, a professional driver conducts multiple trial runs in which the driver drives down a straight track at a certain speed and then quickly applies the brakes. Elsa and her classmates record the length of the skid marks left by the car based on its speed during each trial run.

The table shows the results based on many trial runs.

During another class period, Dr. Suarez takes Elsa's class to the scene of a traffic crime. Police officers are measuring the length of the skid marks.

a. Describe a new function that Elsa can use to determine the car's speed before the criminal stopped and fled the scene. In your description, include information about the independent and dependent variables, and the domain and range of this problem situation. Base your response on the data from the trial runs Elsa's class recorded during their experiment.

b. Predict what you think the graph of the new function will look like and sketch the graph on the grid shown.

c. Use your sketch to estimate the car's speed before stopping if the length of the skid mark is:

• 50 feet.
• 175 feet.
• 350 feet.

In the paper, “Drink and Be Merry? Gender, Life Satisfaction, and Alcohol Consumption Among College Students" (Psychology of Addictive Behaviors, Vol. 19, Issue 2, pp. 184-191), J. Murphy et al. examined the impact of alcohol use and alcohol-related problems on several domains of life satisfaction (LS) in a sample of 353 college students. All LS items were rated on a 7-point Likert scale that ranged from 1 (strongly disagree) to 7 (strongly agree). On the WeissStats site you will find data for dating satisfaction, based on the results of the study. Use the technology of your choice to do the following. a. Obtain normal probability plots, boxplots, and the standard deviations for the two samples. b. Based on your results from part (a), which are preferable here, pooled or nonpooled t-procedures? Explain your-reasoning. c. At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean dating satisfaction of male and female college students? d. Determine a 95% confidence'interval for the difference between mean dating satisfaction of male and female college students. e. Are your procedures in parts (0) and (d) justified? Explain your answer.