11.4 Test of Independence
Two categorical traits measured on one sample in a contingency table, with expected counts from row and column totals showing whether the traits move together.
Introductory Business Statistics 2e, 11.4 Test of Independence
19 exercises
11.4 Exercise 1
A sample of 300 students is taken. Of the students surveyed, 50 were music students, while 250 were not. Ninety-seven of the 300 surveyed were on the honor roll, while 203 were not. If we assume being a music student and being on the honor roll are independent events, what is the expected number of music students who are also on the honor roll?
11.4 Exercise 4
a. How many high anxiety level students are expected to have a high need to succeed in school?
11.4 Exercise 5
b. If the two variables are independent, how many students do you expect to have a low need to succeed in school and a med-low level of anxiety?
11.4 Exercise 7
Determine the appropriate test to be used in the next three exercises.
A pharmaceutical company is interested in the relationship between age and presentation of symptoms for a common viral infection. A random sample is taken of 500 people with the infection across different age groups.
11.4 Exercise 9
Determine the appropriate test to be used in the next three exercises.
A marathon runner is interested in the relationship between the brand of shoes runners wear and their run times. They take a random sample of 50 runners and records their run times as well as the brand of shoes they were wearing.
11.4 Exercise 11
df = _______
11.4 Exercise 13
How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?
Smoking Levels by Ethnicity (Observed)
Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Lat…
11.4 Exercise 18
Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Lat…
11.4 Exercise 20
Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Lat…
11.4 Exercise 21
Use the following information to answer the next eight exercises: An article in the New England Journal of Medicine, discussed a study on smokers in California and Hawaii. In one part of the report, the self-reported ethnicity and smoking levels per day were given. Of the people smoking at most ten cigarettes per day, there were 9,886 Black people, 2,745 Native Hawaiian people, 12,831 Hispanic/Lat…
11.4 Exercise 23
State the decision and conclusion (in a complete sentence) for the following preconceived levels of α.
α = 0.05
- Decision: ___________________
- Reason for the decision: ___________________
- Conclusion (write out in a complete sentence): ___________________
11.4 Exercise 26
Car manufacturers are interested in whether there is a relationship between the size of car an individual drives and the number of people in the driver’s family (that is, whether car size and family size are independent). To test this, suppose that 800 car owners were randomly surveyed with the results in the table. Conduct a test of independence.
11.4 Exercise 28
Some travel agents claim that honeymoon hot spots vary according to age of the bride. Suppose that 280 recent brides were interviewed as to where they spent their honeymoons. The information is given in the table. Conduct a test of independence.
11.4 Exercise 30
A major food manufacturer is concerned that the sales for its skinny french fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are shown in the table. Conduct a test of independence.
11.4 Exercise 32
Suppose that 600 thirty-year-olds were surveyed to determine whether or not there is a relationship between the level of education an individual has and salary. Conduct a test of independence.
11.4 Exercise 34
Read the statement and decide whether it is true or false.
The test for independence uses tables of observed and expected data values.
11.4 Exercise 36
Read the statement and decide whether it is true or false.
In a test of independence, the expected number is equal to the row total multiplied by the column total divided by the total surveyed.
11.4 Exercise 38
Read the statement and decide whether it is true or false.
the table provides a recent survey of the youngest online entrepreneurs whose net worth is estimated at one million dollars or more. Their ages range from 17 to 30. Each cell in the table illustrates the number of entrepreneurs who correspond to the specific age group and their net worth. Are the ages and net worth independent? Perform a t…
Adapted from Introductory Business Statistics 2e © 2023 Rice University. Licensed under CC BY 4.0. Source: Introductory Business Statistics 2e. Imported at revision 50ec917.