Test of Independence

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:

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