AP Statistics Practice Free Response Test – Chapter 5 - ANSWERS

1. Suppose there are 500 students in your school.

a) What are the two requirements for a Simple Random Sample (SRS)

1. Each individual must have an equal chance of being chosen

2. Each group of n individuals must have an equal chance of being chosen (or put another way: each individual is selected independently of all other individuals)

b) Using Line 125 of the Random Digit Table (RDT), select the first 5 students in an SRS of 30 students.

Numbering the students 001-500, we get 461, 214, 235, 119, and 033

c) Suppose further, that there are 300 girls and 200 boys at your school. Explain how you might use the RDT to perform a stratified random sample so that there are a representative number of girls and boys in your sample of 30 students.

Since the school population is 60% girls and 40% boys, with a straitified random sample, we could ensure that the sample matches those percentages. So we would want .6(30) = 18 girls and .4(30) = 12 boys in our sample. We would then number the girls 001-300 and select an SRS of 18 using the RDT. Lastly, we number the boys 001-200 and select an SRS of 12 using the RDT.

2. Turkeys raised commercially for food are often fed the antibiotic salinomycin to prevent infections from spreading among the birds. However, salinomycin can damage the birds' internal organs, especially the pancreas. A researcher believes that a combination of selenium and vitamin E in the birds' diet may prevent injury. He wants to explore the effects of two different dosages of selenium (call them S1, S2) in combination with any of three different dosages of vitamin E (call them E1, E2, E3) added to the turkeys' diets. There are 48 turkeys available for the study. At the end of the study, the birds will be killed and the condition of their pancreas examined with a microscope.

a) How many treatments are there in this experiment?

There are 6 because we need all combinations of the levels of each variable. Since there are two levels of salinomycin and 3 of vitamin E, we have 3 x 2 = 6 treatments.

b) Outline in diagram form an appropriate design for this experiment. In your diagram, indicate how many turkeys are assigned to each treatment group.

3. Joey is interested in investigating so-called hot streaks in foul shooting among basketball players. He’s a fan of Carla, who has been making approximately 80% of her free throws. Specifically Joey wants to use simulation methods to determine Carla’s longest run of baskets on average, for 20 consecutive free throws.

a) Describe a correspondence between random digits from the RDT and outcomes.

Let make = 0-7 and miss = 8, 9

b) What will constitute one repetition in this simulation?

“Shoot” 20 shots by looking at 20 random digits and count the longest run of makes.

c) Starting with line 101 in the random digit table, carry out 10 repetitions and record the longest run for each repetition.

Starting at Line 101, we have the following random digits for the first repetition of 20 shots:

19223    95034   05756   28713

Note that the digits colored in red represent made shots. So, we see that the longest streak of made shots is 10.

Continuing in that fashion, we get longest runs as follows: 10, 10, 10, 9, 9, 4, 9, 8, 5 and 4

d) What is the mean run length for the 10 repetitions?

The mean of the 10 results from part (c) is 7.8