Question

At a small high school, 5 students took Mrs. Jones's AP Statistics class last year. The student's names are Ashley, Brayden, Carmen, Dale, and Eve. Ashley, Brayden, and Carmen each got a 5 on the AP Statistics exam. Mrs. Jones would like to use the results of these 5 students to demonstrate how to create a sampling distribution of the sample proportion for simple random samples of size n = 2 for her current students. a) What is the value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam? Explain. b) Using the table provided, list all 10 possible simple random samples of size n = 2, and for each sample calculate the sample proportion of students who got a 5 on the AP Statistics exam. The first one is completed for you. SRS n = 2 А, В P 1 c) Using the number line provided, create a dotplot to display the sampling distribution of p. d) is the sample proportion an unbiased estimator of the population proportion? Explain.

Answer 1

Explanation:

a) The value of p, the population proportion of students in Mrs. Jones's AP Statistics class who got a 5 on the AP Statistics exam, is 3/5. This is because out of the 5 students, 3 (Ashley, Brayden, and Carmen) got a 5 on the AP Statistics exam.

b) The 10 possible simple random samples of size n = 2 are:

Ashley, Brayden; P = 2/2 = 1

Ashley, Carmen; P = 2/2 = 1

Ashley, Dale; P = 1/2 = 0.5

Ashley, Eve; P = 1/2 = 0.5

Brayden, Carmen; P = 2/2 = 1

Brayden, Dale; P = 1/2 = 0.5

Brayden, Eve; P = 1/2 = 0.5

Carmen, Dale; P = 1/2 = 0.5

Carmen, Eve; P = 1/2 = 0.5

Dale, Eve; P = 0/2 = 0

c) To create the dotplot for the sampling distribution of p:

Label the number line with 0, 0.5, 1

For each sample proportion calculated, place a dot above the corresponding value on the number line

Repeat this process for all sample proportions

d) Yes, the sample proportion is an unbiased estimator of the population proportion. This means that on average, the sample proportion will equal the population proportion. In other words, the mean of the sampling distribution of the sample proportion will equal the population proportion.