WorksheetsTest of Independence
Total questions: 20
Worksheet time: 20mins
Which test would you use to see if gender is a factor choosing a person’s favorite fruit? 900 college students were surveyed and their favorite fruit recorded.
Chi-square Goodness of Fit Test
Chi-Square Test for Homogeneity
Chi-Square Test for Independence/Association
Not a Chi-square test
Is nationality related to favorite drink? 300 people were observed.
Chi-square Goodness of Fit Test
Chi-Square Test for Homogeneity
Chi-Square Test for Independence/Association
Not a Chi-square test
Is the type of television show that a person chooses to watch related to the brand of deodorant that a person uses? 1500 people were surveyed.
Chi-square Goodness of Fit Test
Chi-Square Test for Homogeneity
Chi-Square Test for Independence/Association
Not a Chi-square test
An economist was interested in whether the public's approval of government economic policy depended on whether they were self-employed or a paid employee. A survey of randomly selected members of the public gave the results in the table. Is type of employment related to economic policy preference? ANSWER by completing the following questions. The null and alternative hypotheses are:
H0: Not related, H1: Are related.
H0: Are related, H1: Not related.
H0: Economic Policy Groups Unrelated, H1: Economic Policy Groups Related.
H0: Employment Groups Unrelated, H1: Employment Groups Related.
Determine if the events are independent or dependent.
Independent
Dependent
If event A and event B are independent, then which of the following is true?
P(A) = P(B)
P(A | B) = P(B)
P(A | B) = P(A)
P(A and B) = P(A) + P(B)
Two Events A and B are independent in relation if and only if...
P(A) = P(B)
P(B|A) = P(B)
P(A|B) = P(B)
P(A|B)=P(B|A)
If two events A and B are INDEPENDENT....
the result of A happening DOES NOT change the probability of B occuring
A and B have the same chance of happening
If A happens, B will also happen
the result of A happening will change the probability of B occuring
Determine if the events are independent or dependent.
Independent
Dependent
Suppose a person is chosen at random from all of the people in the US. Which of the following pairs of Events in the resulting sample space are most likely to be independent in relation to each other?
Being over 6 ft. tall and playing basketball
Being a Canadian immigrant and playing hockey
Having blue eyes and playing soccer
Being male and playing football
Find the degrees of freedom.
4
5
6
7
What are the expected counts of a female who likes Pepsi?
10.5
11
14.5
6.3
What are the degrees of freedom for the following χ² test?
6
2
5
36
If we are testing at a 5% significance level and our p-value is 0.00453, what is the conclusion?
Accept Ho
Reject Ho
We need to know chi-squared
You cannot do this problem without a calculator
The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following school year. She wants to know if each type of food will be equally popular so she can start ordering supplies. To find out, she selects a random sample of 100 students and asks them, "Which type of food do you prefer: Asian food, Mexican food, pizza, or hamburgers?" Here are the data in the table provided. Identify the p-value and decide which of the following is the most appropriate conclusion?
Because 0.0129 is less than α = 0.05, fail to reject H0. There is convincing evidence that the food choices are equally popular.
Because 0.0129 is less than α = 0.05, reject H0. There is convincing evidence that the food choices are not equally popular.
Because 0.0289 is less than α = 0.05, reject H0. There is convincing evidence that the food choices are not equally popular.
Because 0.0289 is less than α = 0.05, fail to reject H0. There is not convincing evidence that the food choices are equally popular.
Recent revenue shortfalls in a midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are in the table provided. Why hypotheses would be appropriate for performing a chi-square test?
The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.
The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years. The alternative is that the mean is different for at least 2 of the 4 years.
The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university. The alternative is that the distribution is different for at least 2 of the 4 years.
The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. We compute the value of the χ² statistic to be 6.58. Assuming that the conditions for inference are met, the P-value of our test is
Between 0.10 and 0.20.
Between 0.05 and 0.10.
Between 0.01 and 0.05.
Less than 0.01.
The table shows the number or babies born on each day of the week. Is there evidence that births are more likely on specific days of the week?
yes, the p value is greater than .05
no, the p value is less than .05
yes, the p value is less than .05
no, the p value is greater than .05
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. Assuming H0 is true, the expected number of Hispanic drivers who would receive a ticket is
10.36
11
11.84
12
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race of the driver. The results are summarized in the table provided. The category that contributes the largest component to the χ² statistic is
White.
Black.
Hispanic.
Other.
