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Chapter 5: Problem 105

Construct a two-way table with 80 men and 100 women in which both groups show an equal percentage of right-handedness.

Short Answer

Expert verified
The two-way table where the percentage of right-handedness is equal for 80 men and 100 women shows 100% right-handedness in both genders.

Step by step solution

01

Understand the Problem

The goal is to create a two-way table that depicts the same percentage of right-handedness in two different groups: 80 men and 100 women. We can denote 'M' for men, 'W' for women, 'R' for right-handed, 'L' for left handed. To obtain an equal percentage of right-handedness the ratio between right-handed men to total men should equal to the ratio of right-handed women to total women.
02

Define the Variables

Let's denote the number of right-handed men as \(x\) and the number of right-handed women as \(y\). So, \(x\) belongs to men, \(80-x\) belongs to left-handed men. Similarly, \(y\) belongs to right-handed women, \(100-y\) belongs to left-handed women.
03

Set up the Equation

As both groups need to have the same percentage of right-handedness, it means that the ratio of the number of right-handed men to the total number of men should be equal to the ratio of the number of right-handed women to the total number of women. This can be expressed as: \(\frac{x}{80} = \frac{y}{100}\)
04

Solving the Equation

From Step 3, we can simplify the equation to obtain a relation between \(x\) and \(y\). Multiplying both sides of the equation by 80, we find that \(x = 0.8y\). That means for every right-handed woman, we should have 80% of a man right-handed.
05

Constructing the Table

We can now construct our table. Since it is not specified the number of right-handed individuals, we can choose a number that can be scaled down for men. We can set \(y = 100\) (all women are right-handed) hence, \(x = 0.8 * y = 80\), So men are also all right-handed. R | L | Total--|--|--80 | 0 | 80 (men)100| 0 | 100 (women)We see that 100% of both genders are right-handed in this case.

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Most popular questions from this chapter

Refer to exercise \(5.11\) for information about cards. If you draw one card randomly from a standard 52-card playing deck, what is the probability that it will be the following: a. A black card b. A diamond c. A face card (jack, queen, or king) d. A nine e. A king or queen

A 2017 Pew Research poll found that \(72 \%\) of Democrats and \(36 \%\) of Republicans felt that colleges and universities have a positive effect on the way things are going in the United States. If 1500 Democrats and 1500 Republicans were surveyed, how many from each group felt that colleges and universities have a positive effect on the country?

A true/false test has 20 questions. Each question has two choices (true or false), and only one choice is correct. Which of the following methods is a valid simulation of a student who guesses randomly on each question. Explain. (Note: there might be more than one valid method.) a. Twenty digits are selected using a row from a random number table. Each digit represents one question on the test. If the number is even the answer is correct. If the number is odd, the answer is incorrect. b. A die is rolled 20 times. Each roll represents one question on the test. If the die lands on a 6 , the answer is correct; otherwise the answer is incorrect. c. A die is rolled 20 times. Each roll represents one question on the test. If the die lands on an odd number, the answer is correct. If the die lands on an even number, the answer is incorrect.

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