Question

Instructions: Show your work in steps by including the names of the probability or rule, the formula, your calculation, and the correct results. Do Americans prefer name-brand milk or store-brand milk? A survey was conducted by Harris Poll Interactive, Inc. in November 2014. Suppose the results, based on 1138 females and 1138 males, 319 males, and 341 females prefer name brand milk, 717 males and 649 females prefer store brand milk, and 102 males and 148 females prefer something else. 1) Construct the contingency table. 2) If an American is selected at random, what is the probability that he or she: a. Prefers store-brand milk? b. Is female and prefers store-brand milk? c. Is female or prefers store-brand milk? 3) Given that an American is a female, what is the probability that she prefers store brand milk?

Answer 1

To address the student's question, we would create a contingency table, sum up preferences for store-brand milk, calculate the probability of being female and preferring store-brand milk, and determine the conditional probability for females preferring store-brand milk.

Step-by-step explanation:

Contingency Table and Probability Calculations

To answer the student's question, we need to perform several steps including constructing a contingency table, calculating probabilities, and understanding the concept of conditional probability:

1. Construct the contingency table with rows for gender (female, male) and columns for milk preference (name-brand, store-brand, something else).
2. Calculate the probabilities of preference for store-brand milk, being a female and preferring store-brand milk, and being a female or preferring store-brand milk.
3. Determine conditional probability of a female preferring store-brand milk, given that the person is known to be a female.

For the first part of the question, the student can create a contingency table by categorizing each group (males and females) by their preference (name-brand, store-brand, something else) based on the numbers provided in the survey.

To calculate the probabilities (Part 2):

• a. The probability that an American prefers store-brand milk is calculated by adding the number of males and females that prefer store-brand milk and dividing by the total number of respondents.
• c. The probability that an American is female or prefers store-brand milk requires adding the probability of being female to the probability of preferring store-brand milk minus the probability of being a female who prefers store-brand milk, to avoid double counting the overlap.

For the third part of the question, given that an American is a female, the probability that she prefers store brand milk is the number of females who prefer store-brand milk divided by the total number of females.