/*! 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 Guns in School. Researchers surv... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 15: Problem 3

Guns in School. Researchers surveyed 15,624 Amercian high school students (grades 9-12) and found that \(27.2 \%\) of those surveyed were in grade 9 . The percent of all American high school students who are in grade 9 is \(27.5 \%\). The percent of those surveyed who were in grade 9 and had carried a gun to school was \(4.5 \%\). Is each of the boldface numbers a parameter or a staristic?

Short Answer

Expert verified
27.2% is a statistic, 27.5% is a parameter, 4.5% is a statistic.

Step by step solution

01

Understanding Parameters and Statistics

First, we need to differentiate between a parameter and a statistic. A parameter is a number that describes a characteristic of a population, while a statistic is a number that describes a characteristic of a sample.
02

Identify the Sample size

The given survey is conducted on 15,624 American high school students, which indicates this is the sample size. Thus, any numerical data derived from these surveyed students would be considered a statistic.
03

Examine the Survey Result for Grade 9 Students

From the surveyed students, 27.2% were found to be in grade 9. Since this percentage is derived from the sample (15,624 students), this 27.2% is a statistic.
04

Examine the Population Proportion for Grade 9

The problem states that 27.5% of all American high school students (the population) are in grade 9. Since this percentage describes the entire population, it is a parameter.
05

Analyze the Data on Gun Carriers in Grade 9

The problem states that 4.5% of the surveyed students who were in grade 9 had carried a gun to school. Since this percentage is derived from the surveyed sample, it is a statistic.

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.

Parameter
In statistics, a parameter is an essential concept. It refers to a measurable attribute that defines a characteristic of an entire population. This could be the average age, the percentage of a population possessing a certain trait, or other similar metrics. Unlike statistics that come from sample data, parameters aim to represent the true nature of the whole group without extrapolations or estimates.

Parameters are often uncertain because obtaining precise measurements of entire populations is usually impractical. Therefore, parameters are usually estimated using samples and resulting statistics. In the exercise example, the percentage of all American high school students in grade 9 (27.5%) is a parameter. It describes the characteristic of the entire population, not just the surveyed students.
Sample size
Sample size is a fundamental idea in statistics, as it sets the scope for data collection and analysis. It refers to the number of individual observations or data points collected from a larger group. This sample is used to infer information about the entire population.

Choosing an appropriate sample size is crucial. It determines the reliability of the results and how well they can mimic the population. A larger sample size typically offers more accurate estimates of the population parameters. In the exercise, the sample size is 15,624 American high school students, which is used to analyze certain behaviors like carrying guns to school.
Population
A population in statistical terms refers to the entire group of individuals or items that a researcher is interested in studying. Unlike a sample, which only includes a small part of the population, the population encompasses everyone or everything pertaining to the subject matter of the study.

Studying a population gives a comprehensive view of a subject. However, it can often be impractical due to constraints like time, cost, and accessibility. Instead, samples are used to draw conclusions about the larger population. In the given exercise, the population consists of all American high school students across grades 9 to 12.
Grade 9
The term "Grade 9" in this context refers to the specific academic grade where the study is interested in gathering statistics or parameters. Understanding how certain behaviors or attributes manifest in Grade 9 students can provide valuable insights.

In the exercise described, Grade 9 students are the primary subgroup of interest. Two separate statistics are derived involving them: the percentage of Grade 9 students in the sample and those who had carried a gun to school. By focusing on Grade 9, researchers can better target educational reforms or policy changes to address the needs of this age group.

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

Playing the numbers: A gambler gets chance outcomes. The law of large numbers tells us what happens in the long run. Like many games of chance, the numbers racket has outcomes that vary considerably-one three-digit number wins \(\$ 600\) and all others win nothing - that gamblers never reach "the long run." Even after many bets, their average winnings may not be close to the mean. For the numbers racket, the mean payout for single bets is \(\$ 0.60\) (60 cents) and the standard deviation of payouts is about \(\$ 18.96\). If Joe plays 350 days a year for 40 years, he makes 14,000 bets. (a) What are the mean and standard deviation of the average payout \(\mathrm{x}^{-} \bar{x}\) that Joe receives from his 14,000 bets? (b) The central limit theorem says that his average payout is approximately Nomal with the mean and standard deviation you found in part (a). What is the approximate probability that Joe's average payout per bet is between \(\$ 0.50\) and \(\$ 0.70\) ? You see that Joe's average may not be very close to the mean \(\$ 0.60\) even after 14,000 bets.

Measurements in the Lab. Juan makes a measurement in a chemistry laboratory and records the result in his lab report. Suppose that if Juan makes this measurement repeatedly, the standard deviation of his measurements will be \(\sigma=\) 10 milligrams. Juan repeats the measurement four times and records the mean \(x^{-}=\) of his four measurements. (a) What is the standard deviation of Juan's mean result? (That is, if Juan kept on making four measurements and averaging them, what would be the standard deviation of all his \(x^{-} \bar{x}^{\text {'s}} \mathrm{s}\) ?) (b) How many times must Juan repeat the measurement to reduce the standard deviation of \(x^{-} x\) to 2 ? Explain to someone who knows no statistics the advantage of reporting the average of several measurements rather than the result of a single measurement.

The number of hours a battery lasts before failing varies from battery to battery. The distribution of failure times follows an exponential distribution (see Example \(15.7\) ), which is strongly skewed to the right. The central limit theorem says that (a) as we look at more and more batteries, their average failure time gets ever closer to the mean \(\mu\) for all batteries of this type. (b) the average failure time of a large number of batteries has a distribution of the same shape (strongly skewed) as the distribution for individual batteries. (c) the average failure time of a large number of batteries has a distribution that is close to Normal.

The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sample of 60,000 households; \(4.9 \%\) of the people interviewed were unemployed. The boldface number is a (a) sampling distribution. (b) statistic. (c) parameter.

Statistics anxiety. What can teachers do to alleviate statistics anxiety in their students? To explore this question, statistics anxiety for students in two classes was compared. In one class, the instructor lectured in a formal manner, including dressing formally. In the other, the instructor was less formal, dressed informally, was more personal, used humor, and called on students by their first names. Anxiety was measured using a questionnaire. Higher scores indicate a greater level of anxiety. The mean anxiety score for students in the formal lecture class was \(25.40\); in the informal class the mean was 20.41. For each of the boldface numbers, indicate whether it is a parameter or a statistic. Explain your answer.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

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.