/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Texting While Driving According ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 12

Texting While Driving According to the 2015 High School Youth Risk Behavior Survey, \(41.5 \%\) of high school students reported they had texted or emailed while driving a car or other vehicle. Suppose you randomly sample 80 high school students and ask if they have texted or emailed while driving. Suppose 38 say yes and 42 say no. Calculate the observed value of the chi-square statistic for testing the hypothesis that \(41.5 \%\) of high school students engage in this behavior.

Short Answer

Expert verified
The observed value of the chi-square statistic for testing this hypothesis is 1.17.

Step by step solution

01

Calculate the expected frequencies

Based on the survey data, the expected frequency of students who have texted or emailed while driving is \(80*0.415 = 33.2\). Consequently, the expected frequency for those who have not is \(80-33.2=46.8\).
02

Use the chi-square formula

The formula for the chi-square statistic is \(\chi^{2} = \sum \frac{(Observed-Expected)^{2}}{Expected}\). Apply this formula to each category (yes and no).
03

Calculate the chi-square for yes

First, calculate the chi-square for the 'yes' category as \(\frac{(38-33.2)^{2}}{33.2} = 0.69\).
04

Calculate the chi-square for no

Next, calculate the chi-square for the 'no' category as \(\frac{(42-46.8)^{2}}{46.8} = 0.48\).
05

Add up the chi-square values

Sum up the chi-square values for both categories to obtain the total chi-square statistic: \(0.69 + 0.48 = 1.17\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

High School Statistics
High school statistics is a branch of mathematics that deals with the collection, analysis, interpretation, and presentation of masses of numerical data. An essential part of high school statistics is understanding how to analyze data sets and determine whether they follow a specific pattern or trend.

For instance, knowing that 41.5% of high school students report texting while driving, as observed in a survey, provides a basis for further investigation. If we wish to examine this claim with a new group of students, we can collect data, such as asking 80 high school students about their texting-while-driving behavior, and then use statistical methods to analyze our findings.

Statistics empower students not only to assess the validity of data-driven claims but also to make informed decisions based on their analysis of data. It's about turning data into knowledge and understanding the world through numbers.
Hypothesis Testing
Hypothesis testing is a critical component of statistics that allows us to make decisions about a population parameter based on sample data. In high school statistics, students learn to use sample data to test claims (hypotheses) about population parameters.

In our scenario, we're examining the hypothesis that 41.5% of high school students engage in texting while driving. Hypothesis testing involves several steps: stating the null hypothesis, which in this case is the percentage reported by the survey, collecting data, calculating an appropriate statistic, and then making a decision about the null hypothesis based on that statistic.

It is important to understand that the outcome of a hypothesis test does not prove a hypothesis absolutely; instead, it indicates whether there is enough statistical evidence to either accept or reject the hypothesis within a certain confidence level.
Observed vs Expected Frequency
The concepts of observed and expected frequencies are pivotal when it comes to statistical tests like the chi-square test. In any experiment or survey, the 'observed frequency' refers to the actual data collected 鈥� for example, out of 80 students surveyed, 38 said yes and 42 said no to texting while driving.

Contrastingly, the 'expected frequency' is the frequency we would expect to observe if the null hypothesis were true. It is calculated based on the proportions stated in the hypothesis, and with our sample of 80 students, if 41.5% of them text while driving as the hypothesis suggests, we would expect about 33.2 'yes' responses and 46.8 'no' responses.

The chi-square statistic then measures how much the observed frequencies diverge from the expected frequencies. If they are sufficiently close, we may conclude that our observed data aligns with the expectations under our null hypothesis; if not, we may doubt the null hypothesis.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Chapter 9 , you learned some tests of means. Are tests of means used for numerical or categorical data?

The following table shows the average number of vehicles sold in the United States monthly (in millions) for the years 2001 through 2018 . Data on all monthly vehicle sales for these years were obtained and the average number per month was calculated. Would it be appropriate to do a chi-square analysis of this data set to see if vehicle sales are distributed equally among the months of the year? If so, do the analysis. If not, explain why it would be inappropriate to do so. (Source: www.fred.stlouisfed.org) $$ \begin{array}{|l|l|} \hline \text { Month } & \text { Avg Sales per Month (in millions) } \\ \hline \text { Jan } & 15.7 \\ \hline \text { Feb } & 15.7 \\ \hline \text { Mar } & 15.8 \\ \hline \text { Apr } & 15.8 \\ \hline \text { May } & 15.8 \\ \hline \text { June } & 15.7 \\ \hline \text { July } & 16.1 \\ \hline \text { Aug } & 16.1 \\ \hline \text { Sept } & 15.8 \\ \hline \text { Oct } & 15.9 \\ \hline \text { Nov } & 15.9 \\ \hline \text { Dec } & 15.9 \\ \hline \end{array} $$

Breakfast Habits (Example \(1 \&\) 2) In a 2015 study by Nanney et al. and published in the Journal of American College Health. a random sample of community college students was asked whether they ate breakfast 3 or more times weekly. The data are reported by gender in the table. $$ \begin{array}{|lcc|} \hline \text { Eat breakfast at least } 3 \times \text { weekly } & \text { Females } & \text { Males } \\ \hline \text { Yes } & 206 & 94 \\ \hline \text { No } & 92 & 49 \\ \hline \end{array} $$ a. Find the row, column, and grand totals, and prepare a table showing these values as well as the counts given. b. Find the percentage of students overall who eat breakfast at least three times weekly. Round off to one decimal place. c. Find the expected number who eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. d. Find the expected number who did not eat breakfast at least three times weekly for each gender. Round to two decimal places as needed. e. Calculate the observed value of the chi-square statistic.

You flip a coin 100 times and get 58 heads and 42 tails. Calculate the chi- square statistic by hand, showing your work, assuming the coin is fair.

In a 2015 study reported in the New England Journal of Medicine, Du Toit et al. randomly assigned infants who were likely to develop a peanut allergy (as measured by having eczema, egg allergies, or both) to either consume or avoid peanuts until 60 months of age. The infants in this cohort did not previously show any preexisting sensitivity to peanut extract. The numbers in each group developing a peanut allergy by 60 months of age are shown in the following table. $$ \begin{array}{lcc} & \text { Treatment Group } \\ \hline \begin{array}{l} \text { Peanut allergy at age } \\ \mathbf{6 0} \text { mos. } \end{array} & \text { Consume peanuts } & \text { Avoid peanuts } \\ \hline \text { Yes } & 5 & 37 \\ \hline \text { No } & 267 & 233 \\ \hline \end{array} $$ a. Compare the percentages in each group that developed a peanut allergy by age 60 months. b. Test the hypothesis that treatment group and peanut allergy are associated using the chi-square statistic. Use a significance level of \(0.05\). c. Do a Fisher's Exact Test for the data with the same significance level. Report the two-tailed p-value and your conclusion. (Use technology to run the test.) d. Compare the p-valucs for parts \(\mathrm{b}\) and \(\mathrm{c}\). Which is morc accurate? Explain.
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.