Two-Sample Tests

What percentage of college seniors expect to be married within 5 years of graduation? What percentage expect to have children within 5 years of graduation? How many biological children do college seniors expect to have during their lifetimes? Are the differences between the male and female responses substantial and statistically persuasive?

Do economics majors get better grades in humanities courses or in science courses? (Do not include economics courses.) Is the average difference substantial and statistically persuasive?

Ask 50 males and 50 females this question: "You were engaged to be married to A, but broke off the engagement a month before the wedding when you found A in bed with your best friend. Two years have now passed and you are engaged to be married to someone else. A month before the wedding, A calls you and says 'Let's get drunk tonight for old-time's sake.' Do you say yes or no?" Devise a procedure that will allow each person to respond anonymously, but will still allow you to distinguish male and female responses (e.g., different colored sheets of paper). Are the differences in the male and female responses substantial and statistically persuasive?

Ask 50 males and 50 females to write down a brief answer to this question: "You are engaged to be married to A and while you are both at a party, a former lover who is unknown to A flirts with you outrageously. You rebuff these advances, but afterwards A asks you to identify the person who was flirting with you. What do you say?" Devise a procedure that will allow each person to respond anonymously, but will still allow you to distinguish male and female responses. Now ask someone who is unaware of your system for identifying male and female responses to classify each response as either truthful or deceitful. Are the differences in the male and female responses substantial and statistically persuasive?

In the 1980s Kahneman and Tversky asked students the following question: "Imagine that you have decided to see a play and paid the admission price of $\$ 10$ per ticket. As you enter the theater, you discover that you have lost the ticket. The seat was not marked and the ticket cannot be recovered. Would you pay $\$ 10$ for another ticket?" They asked a different group of students this question: "Imagine that you have decided to see a play where admission is $\$ 10$ per ticket. As you enter the theater, you discover that you have lost a $\$ 10$ bill. Would you still pay $\$ 10$ for a ticket for the play?" Do this experiment with an updated ticket price and see if there is a substantial and statistically persuasive difference in the responses to these two questions.

Ask a random sample of students the following question: "Your favorite singer is performing tonight and you paid $\$ 200$ for a ticket to the concert. Unfortunately, you will have to drive 60 miles through a snowstorm to get to the concert. Will you go?" Ask another random sample of students this question: "Your favorite singer is performing tonight and you were given a free ticket to the concert. Unfortunately, you will have to drive 60 miles through a snowstorm to get to the concert. Will you go?" Is there a substantial and statistically persuasive difference in the responses to these two questions?

Ask a random sample of students the following question: "Your favorite singer is performing tonight and a friend paid $\$ 200$ for a ticket to the concert. Your friend is sick and gave you the ticket for free. Unfortunately, you will have to drive 60 miles through a snowstorm to get to the concert. Will you go?" Ask another random sample of students this question: "Your favorite singer is performing tonight and a friend got a free ticket to the concert. Your friend is sick and gave you the ticket. Unfortunately, you will have to drive 60 miles through a snowstorm to get to the concert. Will you go?" Is there a substantial and statistically persuasive difference in the responses to these two questions?

A stock's dividend yield is its annual dividend divided by its current market price; its earnings yield is the annual earnings divided by the current price. Determine the dividend and earnings yields on some date in the past for each of the 30 stocks in the Dow Jones Industrial Average. Identify the ten stocks with the highest dividend yields and the ten with the lowest dividend yields. Calculate the percentage price increases for these 20 stocks over the next year. Redo these calculations, this time using the earnings yields. In each case, are the observed differences between the two groups substantial and statistically persuasive?

Post a sign on the main entrance to a campus building requesting the use of a less convenient entrance; for example, "Please use the door on the north side of the building." From an inconspicuous location, observe how many people ignore the sign and use the main entrance and how many people do not use the main entrance. Is there a substantial and statistically persuasive difference in the behavior of students and professors? In the behavior of male and female students? Try to pick a building and time when traffic is light, so that large numbers do not enter simultaneously.

Choose a random sample of at least 20 barber shops or beauty salons that cut both men's and women's hair. Do not choose more than one store from a chain. Have a female telephone each store in your sample and find the price of the least expensive female haircut. A few hours later, have a male telephone this store and determine the price of the least expensive male haircut. Are the observed differences substantial and statistically persuasive?

Anchoring is a general human tendency to rely on a reference point when making decisions. For example, a student did a term paper in which randomly selected students were asked one of these two questions:

The population of Bolivia is 5 million. Estimate the population of Bulgaria. The population of Bolivia is 15 million. Estimate the population of Bulgaria. Those who were told that Bolivia's population was 15 million tended to give higher answers than did those told that Bolivia's population was 5 million. Several similar questions confirmed this pattern. People use a known "fact" as an anchor for their guess. Redo this study using questions you make up.

Follow the instructions for the preceding project but use an unrelated "fact;" for example,

Annual per capita income in Bulgaria is $4,000. Estimate the population of Bulgaria.

Annual per capita income in Bulgaria is $20,000. Estimate the population of Bulgaria.

Ask at least 50 students to participate in this experiment. Tell each volunteer that you are going to ask two brief questions. Then ask the first question: "Guess the number that you will pull from a bag containing 100 slips of paper, numbered 1 to 100." (In fact, 50 slips have 10 written on them; the other 50 slips have the number 65.) After the number is revealed, ask the second question: "Estimate the percentage of total United Nations membership made up of countries in Africa." Test whether there is a substantial and statistically persuasive difference between the Africa guesses made by those who picked 10 and those who selected 65.

Arrange 16 facial photos in a $4 \times 4$ grid, with 3 of the faces smiling and the other 13 faces neutral. Ask a random sample of people to pick out the three smiling faces and record how long it takes each person to do so. Repeat the same experiment with three angry faces and 13 neutral faces. Does it take longer, on average, for people to recognize smiling faces or angry faces?

Ask someone to shoot ten basketball free throws, then ask them to shoot two free throws blind-folded, and then ten more free throws not blindfolded. Repeat this experiment with several different people, but don't let anyone in your sample see your experiment with other people. For half the people in your sample, loudly cheer after each blindfolded shot and tell the person that they made the shot; for the other half, groan after each blindfolded shot and say they missed badly. Does the negative/positive reinforcement during the blindfolded shots have any effect on their performance when not blindfolded?

Ask 50 female students these four questions: "Among female students at this school, is your height above average or below average?" "Is your weight above average or below average?" "Is your intelligence above average or below average?" "Is your physical attractiveness above average or below average?" Ask 50 male students these same questions (in comparison to male students). Try to design a survey procedure that will ensure candid answers. For each sex and each question, test the null hypothesis that $\mathrm{p}=.5$. Also, compare the male and female answers to each question.

Ask 50 male and 50 female students these two questions: "Compared to all male students nationwide, is the intelligence of the average male student at your school above average or below average?" "Compared to all male students nationwide, is the physical attractiveness of the average male student at your school above average or below average?" Repeat the survey with a new sample, asking 50 male and 50 female students these two questions: "Compared to all female students nationwide, is the intelligence of the average female student at your school above average or below average?" "Compared to all female students nationwide, is the physical attractiveness of the average female student at your school above average or below average?" Try to design a survey procedure that will ensure candid answers. For each survey question, are there substantial and statistically persuasive differences in the male and female answers?

Stand in a place where a reasonable number of people walk by. Stare at the sky and have a friend record the percentage of the people walking by who look up at the sky, too, and the percentage who do not. Now repeat this experiment at the same place with 5, 10, or 15 of your friends staring at the sky. Again, have a friend record the percentage of people walking by who look up at the sky and the number who do not. Is the difference substantial and statistically persuasive? (Choose a location where people do not walk by in large groups.)

Have ten or more friends stand in a line outside a closed door, with you stationed as the last person in line. Tell your friends standing in line that if anyone asks why they are waiting in line, they should say, "I don't know. I just saw this line and figured it must be something good." Is there a substantial and statistically persuasive difference in the propensity of male and female students to join the line?

Ask at least 20 people this question: "A bag contains 10 red balls and 10 blue balls. You randomly pick a ball from the bag and win $\$ 10$ if the ball is blue. What is the maximum amount you would pay to play this game once?" Ask another group of at least 20 people this question: "There are an unknown number of red and blue balls in a bag. You pick a color, red or blue, and then randomly pick a ball from the bag and win $\$ 10$ if the ball is the color you picked. What is the maximum amount you would pay to play this game once?" Is there a substantial and statistically persuasive difference in the responses to these two questions?

Find a crosswalk at an intersection with traffic lights that has a walk button that pedestrians can use to signal that they are waiting to cross the street. Record several observations on how long it takes the light to turn green after having turned red: (a) when no one pushes the pedestrian walk button; and (b) when you push the pedestrian walk button shortly after the light turns red. Is the average difference substantial and statistically persuasive?

Select two NCAA basketball tournaments-one recent and the other several years ago-and tabulate the number of three-point shots and the total number of shots taken by each team in each game. Compare the fraction of the shots taken that were three-point shots (a) in total in each tournament; (b) by the favorite and underdog teams in the recent tournament; and (c) by the favorite and underdog teams in the distant tournament. Are these various differences substantial and statistically persuasive?