BEYOND THE NUMBERS 2.8 | LEARNING OUTCOMES 1 TO 3 Random or Representative? Name
ID: 3354230 • Letter: B
Question
BEYOND THE NUMBERS 2.8 | LEARNING OUTCOMES 1 TO 3 Random or Representative? Name: To be graded, all assignments must be completed and submitted on the original book page. Section Number Gulliver Travels 900 people live in Gulliver, a small town in Michigan's Upper Peninsula. You want to know what proportion of Gulliver's population supports legalizing marijuana. Suppose you already know the following demographic information about Gulliver's 900 citizens: Gender 500 are Females 20% make more than $80,000 70% make between $40,000 and $80,000 10% make less than $40,000 Income Political 70% 30% 50% 50% 30% 70% Affilliation Democrat Republican Democrat Republican Democrat Republican Gender 400 are Males 40% make more than $80,000 50% make between $40,000 and $80,000 10% make less than $40,000 Income 4096 50% 40% 60% Political 60% Affilliation Democrat Republican Democrat Republican Democrat Republican 50% Questions You have enough money to interview 90 residents. Working much the way Gallup did in the 1930s you want your sample of 90 to mirror the distribution of subjects in the population exactly 1. (at least along the lines of gender, income, and political affiliation). How many people would your sample place in the groups shown on the next page? If a calculation results in a partial person (e.g., 6.4 persons), leave the number as it is-don't round There really is a Guliver,MI of about this size. The demographics are completely made up, however BEYOND THE NUMBERS 2.8 149Explanation / Answer
1.
Total population = Number of male + Number of females
= 400 + 500
= 900
Percentage of females = (500/900) * 100
= 55.56%
Percentage of males = (400/900) * 100
=44.44%
Number of males and females:
Now, compute the number of males and females in the sample of 90 as follows:
Number of males = 44.44% of 90
= 0.4444 * 90
= 40
Number of females = 55.56% * 90
= 0.5556 * 90
= 50
Males making between $40,000 and $80,000 yearly:
According to the question, 50% of males makes between $40,000 to $80,000. Therefore, number of males earning $40,000 to $80,000 in the sample 90 can be calculated as follows:
Number of males making between $40,000 to $80,000 = 50% of Number of males in sample
= 0.50 * 40
= 20
Females making less than $40,000 per year who are Democrats:
According to the question, 10% of females makes between less than $40,000. Therefore, number of females earning less than $40,000 in the sample 90 can be calculated as follows:
Number of females making less than $40,000 = 10% of Number of females in sample
= 0.10 * 50
= 5
According to the question, 30% of females earning less than $40,000 are Democrats. Therefore, number of females earning less than $40,000 who are Democrats in the sample 90 can be calculated as follows:
Number of females earning less than $40,000 who are Democrats = 30% of Number of females earning less than $40,000
= 0.3 * 5
= 1.5
Males Republicans making over $80,000 per year:
According to the question, 40% of males makes between more than $80,000. Therefore, number of males earning more than $80,000 in the sample 90 can be calculated as follows:
Number of males making more than $80,000 = 40% of Number of males in sample
= 0.40 * 40
= 16
According to the question, 40% of males earning more than $80,000 are Republican. Therefore, number of males earning more than $80,000 who are Republican in the sample 90 can be calculated as follows:
Number of males earning more than $80,000 who are Republican = 40% of Number of males earning more than $80,000
= 0.4 * 16
= 6.4
Tabular form:
The obtained results can be shown in the tabular forms as follows:
Category Number of persons Males 40 Females 50 Males making between $40,000 and $80,000 yearly 20 Females making less than $40,000 per year who are Democrats 1.5 Males Republican making over $80,000 per year 6.4Related Questions
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