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Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyI using the file format of your choice for the version of the text you are using. The data represent the results of a survey conducted by the author. The variable "Text while Driving" represents the response to the question, "Have you ever texted while driving?" The variable "Tickets" represents the response to the question, "How many speeding tickets have you received in the past 12 months?" Treat the individuals in the survey as a random sample of all U.S. drivers. (a) Build a contingency table treating "Text while Driving" as the row variable and "Tickets" as the column variable. (b) Determine the marginal relative frequency distribution for both the row and column variable. (c) What is the probability a randomly selected U.S. driver texts while driving? (d) What is the probability a randomly selected U.S. driver received three speeding tickets in the past 12 months? (e) What is the probability a randomly selected U.S. driver texts while driving or received three speeding tickets in the past 12 months?

Step by step solution

01

- Download the Data File

Go to www.pearsonhighered.com/sullivanstats and download the data file named SullivanStatsSurveyI. Select the file format that works best for your statistical software or analysis needs.

02

- Load Data into Software

Load the downloaded data file into your preferred statistical software (e.g., Excel, SPSS, R). Make sure all the data is correctly imported and the columns are appropriately named as 'Text while Driving' and 'Tickets'.

03

- Create Contingency Table

Using your statistical software, create a contingency table. Set 'Text while Driving' as the row variable and 'Tickets' as the column variable. This table should show the frequency of respondents for each combination of 'Text while Driving' and 'Tickets' categories.

04

- Calculate Marginal Relative Frequencies

From the contingency table, calculate the marginal relative frequency for the 'Text while Driving' variable by dividing the row totals by the grand total. Similarly, calculate the marginal relative frequency for the 'Tickets' variable by dividing the column totals by the grand total.

05

- Determine Probability of Texting While Driving

To find the probability that a randomly selected U.S. driver texts while driving, use the marginal relative frequency for the 'Text while Driving' row total. This value represents the proportion of people who have texted while driving.

06

- Determine Probability of Receiving Three Speeding Tickets

To find the probability that a randomly selected U.S. driver received three speeding tickets in the past 12 months, use the marginal relative frequency for the '3 Tickets' column total. This value represents the proportion of people who received three speeding tickets.

07

- Determine Combined Probability

To calculate the probability that a randomly selected U.S. driver texts while driving or received three speeding tickets, add the probabilities found in Steps 5 and 6, then subtract the joint probability of both events to avoid double-counting.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Marginal Relative Frequency

Marginal relative frequency is a crucial concept when analyzing survey data, especially when working with contingency tables.
It represents the proportion of individuals that fall into a particular category of one variable, regardless of the other variable.
For example, in our contingency table, we consider two variables: 'Text while Driving' and 'Tickets.'
Marginal relative frequency for the 'Text while Driving' variable can be calculated by dividing the row totals by the grand total.
This tells us the proportion of respondents who have texted while driving out of the total survey sample.
Similarly, for the 'Tickets' variable, the column totals divided by the grand total give the marginal relative frequency for each ticket category.
Understanding and calculating these frequencies help in summarizing the data and identifying trends.

Probability

Probability is another key concept in data analysis. It quantifies the likelihood of a specific event happening.
In the context of our survey, we are interested in several probabilities:

• The probability that a randomly selected U.S. driver has texted while driving.
• The probability that a driver received three speeding tickets in the past 12 months.
• The probability that a driver either has texted while driving or received three tickets.

To find these probabilities, use the marginal relative frequencies calculated earlier.
For instance, the probability that a driver texts while driving is the marginal relative frequency for the 'Text while Driving' variable.
Combined probabilities involve adding the individual probabilities and subtracting any joint probabilities to avoid double-counting.

Survey Data Analysis

Survey data analysis allows researchers to understand and interpret the behavior and characteristics of a studied population.
In our case, the survey data involves U.S. drivers and their texting habits while driving, as well as the number of speeding tickets received.
Using survey data, we create contingency tables to summarize the frequency distribution of respondents across different categories.
Once we have the contingency table, we can calculate marginal relative frequencies and probabilities, which provide insightful summaries about the population.
Survey data analysis is valuable in drawing conclusions and making decisions based on the findings from the sample.

Statistical Software Usage

Using statistical software is essential for efficiently managing and analyzing large sets of data.
There are several popular options to choose from, including Excel, SPSS, and R.
These tools help in easily importing data, creating contingency tables, conducting frequency analysis, and more.
For this exercise, follow these steps:

• Import the survey data file into your chosen software.
• Create a contingency table, designating 'Text while Driving' as the row variable and 'Tickets' as the column variable.
• Use functions in the software to calculate marginal relative frequencies and probabilities.

Leveraging statistical software not only saves time but also reduces the chance for manual errors, leading to more accurate and reliable results.