Refer to the following. In a random sample of 525 teenagers,...

Name: Problem 6, Chapter 8: AP Statistics with 6 Practice Tests
Uploaded: 2021-06-19T14:47:38-08:00
Duration: 1 min 45 s
Channel: Meredith Kempson
Description: Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses. Which of the following is the expected count of blue-eyed teenagers who choose blue as their favorite color? (A) 6 (B) 21 (C) 23.4 (D) 28.2 (E) 30

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses. Which of the following is the expected count of blue-eyed teenagers who choose blue as their favorite color? (A) 6 (B) 21 (C) 23.4 (D) 28.2 (E) 30

Refer to the following. In a random sample of 525 teenagers, eye colors are cross-classified with favorite colors from among green, red, blue, and purple. Below is a two-way table of the responses.
Which of the following is the expected count of blue-eyed teenagers who choose blue as their favorite color?
(A) 6
(B) 21
(C) 23.4
(D) 28.2
(E) 30

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Key Concepts

Contingency Table

A contingency table is a method used to display the frequency distribution of two categorical variables. It organizes data into rows and columns, allowing researchers to observe the relationship and possible association between these variables, such as eye colors and favorite colors.

Expected Frequency Calculation

The expected frequency of a cell in a contingency table is computed under the assumption of independence between the variables. It is calculated by multiplying the total of the corresponding row by the total of the corresponding column and then dividing by the overall sample size. This calculation provides an expected count for how many observations would fall into that cell if there were no association between the variables.

Independence Assumption

The independence assumption is a key concept in statistics that posits that the occurrence of one event does not affect the occurrence of another. In the context of a contingency table, it allows the use of the expected frequency formula to determine what the cell counts would be if the two categorical variables were statistically independent.

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