/*! 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 3 Consumption of fast food is a to... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Consumption of fast food is a topic of interest to researchers in the field of nutrition. The article "Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children" (Pediatrics [2004]: \(112-118\) ) reported that 1720 of those in a random sample of 6212 U.S. children indicated that on a typical day, they ate fast food. Estimate \(p\), the proportion of children in the United States who eat fast food on a typical day.

Short Answer

Expert verified
The proportion, \(p\), of children in the United States who eat fast food on a typical day is calculated as \(\frac{1720}{6212} = 0.2767\). This implies that approximately 27.67% of children eat fast food on a typical day.

Step by step solution

01

Identification of Sample and Successful Outcomes

The exercise mentions a sample size of 6212 children, with 1720 among these children eating fast food on a typical day. We need these figures to calculate the proportion of children who eat fast food on a typical day. Learning to identify the necessary components of the proportion calculation is crucial.
02

Calculation of Proportion

The proportion, \(p\), can be calculated using the formula: \[p = \frac{Number\:of\:successful\:outcomes}{Total\:number\:of\:outcomes}\] In this case, the successful outcomes are the children who eat fast food on a typical day. Thus, \[p = \frac{1720}{6212}\]
03

Simplification and Solution

Carrying out the division will give us a decimal version of the proportion. It's acceptable to express the proportion as a fraction, a decimal or a percentage, depending on the specific task requirements. But normally we represent it in the decimal form.

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 91Ó°ÊÓ!

Key Concepts

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

Understanding Statistics in Proportion Calculation
Statistics play a crucial role in analyzing data collected from surveys and studies. When researchers aim to understand behaviors or trends, they often rely on statistical methods to process the information. In this exercise, the primary statistical concept is the proportion, which represents a part of a whole. The proportion calculation helps determine how many children, out of a given sample, are engaging in fast food consumption.
The formula for the proportion is straightforward:
  • Identify the total number of subjects in the study.
  • Determine the number of subjects exhibiting the behavior of interest – in this case, eating fast food.
By applying the proportion formula, we can derive meaningful insights into the dietary habits of children. Statistics, in this context, are not just numbers. They are a tool that translates raw data into easily understandable patterns, assisting in public health decisions and research.
The Importance of Sample Size
When conducting research, the sample size is a critical factor that influences the reliability of the results. A sample size of 6212 U.S. children provides a robust base for estimating the proportion of fast food eaters among children. Larger sample sizes typically lead to more accurate and reliable statistical outcomes because they tend to reduce the impact of variability.
Sample size affects the level of confidence researchers have in their findings. A larger sample size increases the confidence that the sample proportion closely estimates the actual proportion in the entire population. Smaller samples might not capture all the variability within the population, which can lead to less reliable conclusions. Therefore, choosing an appropriate sample size in nutritional research or any field is crucial for generating valid and generalizable results.
Nutrition Research and Its Impact
Nutrition research aims to understand how dietary habits affect health. It encompasses a wide range of studies on food consumption patterns, nutritional status, and health outcomes. Research in this area helps identify risk factors for health issues and guides dietary recommendations.
One significant element of nutrition research is examining fast food consumption. By studying such trends, researchers can identify potential links between fast food intake and nutritional deficiencies, obesity, or other health problems.
  • Studies like the one mentioned in the exercise are fundamental in shaping public health guidelines.
  • They provide valuable data that can influence policies on food labeling, children's diets, and more.
Through nutrition research, we can better understand the balance required in our diets and how certain consumption patterns affect long-term well-being, particularly among vulnerable groups like children.
Fast Food Consumption: A Snapshot
Fast food consumption among children is a growing concern in nutrition research due to its potential impact on energy intake and diet quality. The exercise provides us with data indicating that a notable proportion of children consume fast food on a typical day. This data highlights a trend that could influence children's long-term health outcomes. Fast foods are often high in calories, fats, sugars, and sodium but low in essential nutrients. This type of diet can lead to various health issues if consumed excessively over time.
  • Understanding the typical dietary patterns of children allows for more targeted health interventions.
  • The data aids in educating parents and guardians about healthier dietary choices.
  • It can also inform public policy on food marketing and availability.
By analyzing fast food consumption data, we can start to address these concerns and develop strategies to promote healthier eating habits among children, ultimately aiming for a healthier future generation.

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 June 2009, Harris Interactive conducted its Great Schools Survey. In this survey, the sample consisted of 1086 adults who were parents of school-aged children. The sample was selected in a way that makes it reasonable to regard it as representative of the population of parents of school-aged children. One question on the survey asked respondents how much time (in hours) per month they spent volunteering at their children's school during the previous school year. The following summary statistics for time volunteered per month were given: $$n=1086 \quad \bar{x}=5.6 \quad \text { median }=1$$ a. What does the fact that the mean is so much larger than the median tell you about the distribution of time spent volunteering per month? b. Based on your answer to Part (a), explain why it is not reasonable to assume that the population distribution of time spent volunteering is approximately normal. c. Explain why it is appropriate to use the \(t\) confidence interval to estimate the mean time spent volunteering for the population of parents of school-aged children even though the population distribution is not approximately normal. d. Suppose that the sample standard deviation was \(s=\) 5.2. Compute and interpret a \(98 \%\) confidence interval for \(\mu\), the mean time spent volunteering for the population of parents of school-aged children.

Based on a representative sample of 511 U.S. teenagers age 12 to 17 , International Communications Research estimated that the proportion of teens who support keeping the legal drinking age at 21 is \(\hat{p}=0.64\) \((64 \%)\). The press release titled "Majority of Teens (Still) Favor the Legal Drinking Age" (www.icrsurvey.com. January 21, 2009) also reported a margin of error of \(0.04(4 \%)\) for this estimate. Show how the reported value for the margin of error was computed.

Authors of the news release titled "Major Gaps Still Exist Between the Perception and the Reality of Americans' Internet Security Protections, Study Finds" (The National Cyber Security Alliance) estimated the proportion of Americans who claim to have a firewall installed on their computer to protect them from computer hackers to be \(.80\) based on a survey conducted by the Zogby market research firm. They also estimated the proportion of those who actually have a firewall installed to be .42, based on checkups performed by Norton's \(\mathrm{PC}\) Help software. The following quote is from the news release: For the study, NCSA commissioned a Zogby survey of more than 3000 Americans and Symantec conducted checkups of 400 Americans' personal computers performed by PC Help by Norton (www.norton.com/tuneup). The Zogby poll has a margin of error of \(+/-1.6 \%\) and the checkup has a margin of error of \(+/-5 \%\). Explain why the margins of error for the two estimated proportions are different.

Suppose that each of 935 smokers received a nicotine patch, which delivers nicotine to the bloodstream but at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12 -week period. Suppose that 245 of the subjects were still not smoking 6 months after treatment. Assuming it is reasonable to regard this sample as representative of all smokers, estimate the percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months.

The article "Career Expert Provides DOs and DON'Ts for Job Seekers on Social Networking" (CareerBuilder.com, August 19, 2009) included data from a survey of 2667 hiring managers and human resource professionals. The article noted that many employers are using social networks to screen job applicants and that this practice is becoming more common. Of the 2667 people who participated in the survey, 1200 indicated that they use social networking sites (such as Facebook, MySpace, and LinkedIn) to research job applicants. For the purposes of this exercise, assume that the sample is representative of hiring managers and human resource professionals. Construct and interpret a \(95 \%\) confidence interval for the proportion of hiring managers and human resource professionals who use social networking sites to research job applicants.

See all solutions

Recommended explanations on Math Textbooks

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.