Suppose that each student in a sample had been categorized with respect to political views, marijuana usage, and religious preference, with the categories of this latter factor being Protestant, Catholic, and other. The data could be displayed in three different two-way tables, one corresponding to each category of the third factor. With pijk = P(political category i, marijuana category j, and religious category k), the null hypothesis of independence of all three factors states that
Let nijk denote the observed frequency in cell (i, j, k). Show how to estimate the expected cell counts assuming that H0 is true (
In 1912 the Titanic struck an iceberg and sank on its first voyage. Some passengers got off the ship in lifeboats, but many died. The following two-way table gives information about adult passengers who survived and who died, by class of travel.
Suppose we randomly select one of the adult passengers who rode on the Titanic. Define event D as getting a person who died and event F as getting a passenger in first class. Find P (not a passenger in first class and survived).
Do male and female students have different favorite seasons? The two-way table shows the favorite season and gender for a simple random sample of 89 high school juniors and seniors in the United States from the Census At School database. Is there convincing evidence of an association between gender and favorite season for students like those who participated in the Census At School survey?
A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-50s.
Suppose we choose one of these players at random. What is the probability that the player has arthritis?
A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-fifties:
What percent of the elite soccer players developed arthritis? What percent of those who got arthritis were elite soccer players?
Mutually exclusive versus independent. The two-way table summarizes data on the gender and eye color of students in a college statistics class. Imagine choosing a student from the class at random. Define event A: student is male, and event B: student has blue eyes.
Copy and complete the two-way table so that events A and B are mutually exclusive.
Is there a relationship between gender and relative finger length? To investigate, a random sample of 452 U.S. high school students was selected. The two-way table shows the gender of each student and which finger was longer on his or her left hand (index finger or ring finger). State the hypotheses for a test of the relationship between gender and relative finger length for U.S. high school students.
A random sample of 1200 U.S. college students was asked, "What is your perception of your own body? Do you feel that you are overweight, underweight, or about right?" The two-way table summarizes the data on perceived body image by gender.
What percent of respondents feel that their body weight is about right?
A survey was designed to study how business operations vary according to their size. Companies were classified as small, medium, or large. Questionnaires were sent to 200 randomly selected businesses of each size. Because not all questionnaires were returned, researchers decided to investigate the relationship between the response rate and the size of the business. The data are given in the two-way table.
Which variable should be used as the explanatory variable? Explain.