Chi-Square Tests

Set up a mock ESP experiment by writing the numbers 1 through 10 on ten identical pieces of paper, and placing these in a hat, bag, or other opaque container. Now tell a randomly selected person that you are going to select one of these pieces of paper and concentrate on the number, while the subject tries to read your mind. Be very careful to ensure that the subject cannot see the number on the paper. Record the answer and then tell the subject the selected number. Repeat this experiment with at least 50 different subjects. When you have all of your data, calculate the p -value for a test of the null hypothesis that each number is equally likely to be chosen by the subjects.

After attempting to imitate a popular television character, a young man concluded that whether one is right-handed or left-handed affects how far apart the two middle fingers on each hand can be spread. If a wider "V" is made with the right hand, the person is probably left-handed; if a wider V is made with the left hand or there is no difference, the person is probably right-handed. Ask at least 100 randomly selected students to spread the middle two fingers on each hand to make a "V." Record whether the wider "V" is made with the right hand or the left hand (or no difference), and then ask the person whether he or she is left-handed or right-handed. How well does the wider "V" predict handedness?

Ask at least 100 students, "Do you usually make sure you look good before leaving your room?" Also record the person's sex and year in school. Determine the p-values for a test of these null hypotheses: (a) the responses are unrelated to sex, and (b) the responses are unrelated to year in school.

Ask randomly selected students if they have had a serious romantic relationship in the past 2 years and, if so, to identify the month in which the most recent relationship began. When you have found 120 students who answered yes and identified the month, calculate the p -value for a test of the null hypothesis that each month is equally likely for the beginning of a romantic relationship.

Ask randomly selected students if they have ended a serious romantic relationship in the past 2 years and, if so, to identify the month in which the most recent ended-relationship ended. When you have 120 students who answered yes and identified the month, calculate the p -value for a test of the null hypothesis that each month is equally likely for the end of a romantic relationship.

In the game Roshambo (rock-scissors-paper), two players simultaneously move their fists up and down three times and then show a fist (rock), two fingers (scissors), or an open hand (paper). Rock beats scissors, scissors beats paper, and paper beats rock. Play this game against at least 120 different people, recording the initial move of each opponent. Use these data to test the null hypothesis that rock, scissors, and paper are used equally often on the initial move. Do your results support the adage, "Losers lead with rock," based on the perception that naive players lead with rock more than one-third of the time?

Ask 100 randomly selected students this question and then compare the male and female responses: "You have a coach ticket for a nonstop flight from Los Angeles to New York. Because the flight is overbooked, randomly selected passengers will be allowed to sit in open first-class seats. You are the first person selected. Would you rather sit next to: (a) Bill Clinton; (b) Hillary Clinton; or (c) Michael Jordan? Alternatively, you can choose three other famous people.

Use the obituaries in a book of famous people, The New York Times, or another source to find the birth and death dates of at least 120 persons. Divide these data into four categories: deaths that occurred: during the 14 days preceding the birthday, on the birthday, during the 14 days following the birthday, and on other days. Calculate the p -value for a test of the null hypothesis that a person's death date is not related to his or her birth date.

Make a list of ten well-known books (including one that you feel will be controversial) and ask at least 30 teachers and 30 students to separate these books into two groups of five, based on how important it is that students read these books: most important and least important. Are there statistically persuasive differences between how the students and teachers classified the book you felt would be controversial?

The nine positions on a baseball team can be divided into four categories: pitcher, catcher, the four infielders, and the three outfielders. Collect all the data you can on MLB managers and test the null hypothesis that, among those managers who played baseball, the probabilities of having played in these four categories are 1/9, 1/9, 4/9, and 3/9, respectively.

Follow the instructions for the preceding exercise but for a different sport such as soccer, football, or basketball.

Administer the following four tests to at least 50 subjects, and then apply a chi-square test with the columns right-handed or left-handed and the rows tests $\mathrm{a}, \mathrm{b}$, and c.

Ask a random sample of 100 students to compare themselves to other students in the population the sample was taken from. For example, if you survey a random sample of ABC School students, ask each student to compare himself or herself to other ABC students. Ask the students to rank themselves in their ability to get along with others; top $25 \%$, next $25 \%$, next $25 \%$, bottom $25 \%$. What is the p-value for a test of the null hypothesis that a randomly selected person is equally likely to pick each of these four quartiles?

Ask 100 randomly selected students to tell you their birth order: only child, first-born, second-born, third-born, or other, and compare these to the national percentages.