Independence in AP Statistics

The campus bookstore at a local university is interested in finding out whether the textbook preference and the class level (freshman, sophomore, junior, senior) of the student are associated. A random sample of 100 students is obtained, and each student in the sample is asked which textbook he or she prefers: new books, used books, or digital books. The students are also asked whether their class level is freshman, sophomore, junior, or senior. Which of the following is the appropriate test for the investigation?

Jana, a high school principal, hosted a movie event at her school. Jana's assistant kept track of the number of students in each grade who attended the event. The distribution shown in the table represents the number of students in each grade that were present. Jana knows that the grade levels are equally distributed across the school of 1,200 students. She would like to use a chi-square test to see if the proportion of individuals in each class at the movie are also equally distributed. How many seniors would be expected at the event?

• 61.3

• 59.5

• 56.4

• 57.9

either stranded or not stranded and additionally noted their age category. The researchers wanted to investigate whether there is convincing evidence of an association between becoming stranded and age. Data from their study are shown in the following table. If becoming stranded and age are independent in these creatures, which of the following is closest to the expected number of young stranded horseshoe crabs?

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

A random survey of 131 high school students was conducted on April 25. The results are shown in the table. Let A = being male and B = have completed ALL DLD assignments for 5 weeks. Are the events independent? Explain.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26

  P(A) x P(B) = 0.26 Since P(A) x P(B) = P(A and B), the events are independent.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26

  P(A) x P(B) = 0.26 Since P(A) x P(B) = P(A and B), the events are not independent.

• This cannot be determined since the number of males surveyed is not equal to the number of females surveyed.

• P(A) = 0.42, P(B) = 0.62, P(A and B) = 0.26 and P(A or B) = 0.78 so the events are independent.

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)

• 1
• 2
• 3
• 4

Use the probabilities in the Venn Diagram to determine if the events A and B are independent.

• A and B are independent because (0.25)(0.6) = 0.15.

• A and B are not independent because (0.25)(0.6) = 0.15.

• A and B are not indepedent because (0.4)(0.75) = 0.3 not 0.15.

• A and B are indepedent because (0.4)(0.75) = 0.3 not 0.15.

Determine if the events are independent or dependent.

• Independent

• Dependent

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