91Ó°ÊÓ

Common Sense Media surveyed 1,000 teens and 1,000 parents of teens to learn about how teens are using social networking sites such as Facebook and MySpace ("Teens Show, Tell Too Much Online," San Francisco Chronicle, August 10,2009 ). The two samples were independently selected and were chosen in a way that makes it reasonable to regard them as representative of American teens and parents of American teens. When asked if they check their online social networking sites more than 10 times a day, 220 of the teens surveyed said yes. When parents of teens were asked if their teen checks his or her site more than 10 times a day, 40 said yes. The researchers used these data to conclude that there was evidence that the proportion of all parents who think their teen checks a social networking site more than 10 times a day is less than the proportion of all teens who report that they check the sites more than 10 times a day.

Step by step solution

01

Calculate the Proportions

First, calculate the two proportions. For teens, the proportion is \(220/1000 = 0.22\) meaning 22% of teens reported frequently checking their social networking sites. Similarly for parents, the proportion is \(40/1000 = 0.04\) representing 4% of parents believe their child frequently checks their social sites.

02

Compare the Proportions

After calculating the two proportions, compare them. Here, the proportion of teens is 0.22 and the proportion of parents is 0.04. Thus, it can be observed that the proportion of teens reporting frequent use of social networking sites exceeds that of the parents' perception.

03

Conclude the Results

After the comparison, it becomes clear that the proportion of all parents who believe their teen checks a social networking site more than 10 times a day is less than the proportion of all teens who report that they check their social sites more than 10 times a day. This aligns with the researchers' conclusion, meaning the researchers' conclusion was accurate.

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Key Concepts

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

Proportion Calculation

Proportion calculation is a foundational concept in statistics that helps you compare parts of a whole.
In this exercise, proportions are used to make sense of survey data collected from teens and their parents. To compute a proportion, you must divide the number of favorable responses by the total number of respondents.
For example:

• From 1,000 surveyed teens, 220 reported they check their social networking sites more than ten times a day. Hence, the proportion is calculated as \(\frac{220}{1000} = 0.22\), or 22%.
• Similarly, 40 out of 1,000 parents believed their teen checks these sites more than ten times daily. The proportion here is \(\frac{40}{1000} = 0.04\), or 4%.

Calculating these proportions helps to transform raw survey results into meaningful metrics that can be more easily understood and compared.

Survey Analysis

Survey analysis involves interpreting data gathered from respondents to draw meaningful conclusions.
It is crucial in transforming numerical data into insights about people's behaviors and perceptions. In the exercise:

• Two distinct groups (teens and parents) were surveyed, allowing researchers to compare results across different perspectives.
• Each group's response is analyzed by calculating the proportion of affirmative answers to total surveyed individuals in that group.
• The disparity in teens' self-reported site usage versus parents' perceptions illustrates variances in behavior awareness.

By applying survey analysis, we discern patterns and derive conclusions that validate or refute preconceived notions or hypotheses.

Data Interpretation

Data interpretation comes after calculations and comparison and helps us understand what these numbers say about real-world behaviors and attitudes.
For example, in this exercise:

• What we see is a noticeable gap between teens' self-reported use of social networking sites and what parents perceive it to be. This hints at a communication or awareness gap.
• The interpretation suggests that teens might engage in social media usage more than their parents would expect.
• This interpretation can be the foundation for further research or actions, like strategies to bridge the understanding gap between parents and teens.

Effective data interpretation helps translate statistical results into actionable insights or further research questions, fueling informed decision-making.