/*! 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 1 According to the Bureau of Labor... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 1

According to the Bureau of Labor Statistics, the official unemployment rate was \(15.5 \%\) among Blacks and \(7.9 \%\) among Whites as of March 2011 . During the recession of \(2009-2011,\) the Black levels of unemployment have been similar or in many locations higher than those during the Great Depression era (www .bls.gov/news.release/empsit.t02.htm). a. Identify the response variable and the explanatory variable. b. Identify the two groups that are the categories of the explanatory variable. c. The unemployment statistics are based on a sample of individuals. Were the samples of white individuals and black individuals independent samples, or dependent samples? Explain.

Short Answer

Expert verified
a. Unemployment rate is the response variable; race is the explanatory variable. b. Blacks and Whites are the categories. c. The samples are independent.

Step by step solution

01

Identify the Response Variable

A response variable is the outcome of interest that we are analyzing. In this exercise, the response variable is the unemployment rate, as it is the main outcome we are looking at for both Blacks and Whites.
02

Identify the Explanatory Variable

An explanatory variable is the one that is thought to influence or explain changes in the response variable. Here, the explanatory variable is the race of the individuals being studied, as this characteristic is used to categorize the unemployment rates.
03

Identify the Categories of the Explanatory Variable

The two categories of the explanatory variable (race) in this context are Blacks and Whites. This categorization is used to determine and compare the unemployment rates between these two groups.
04

Determine the Type of Samples

Independent samples are used when the samples are selected from different populations and have no influence on each other. In this study, the unemployment rates for Blacks and Whites are based on samples of different racial groups taken from the general population. Hence, they are independent samples, as the selection of individuals in one group does not affect the selection in the other group.

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.

Understanding the Response Variable
The concept of a response variable is central in statistical analysis, especially when we aim to understand how different factors influence an outcome. In our scenario, the response variable is the unemployment rate. This is because the core of our analysis centers around observing how unemployment rates vary between different racial groups during a specific period. The response variable, sometimes called the dependent variable, is what researchers seek to explain through their studies.
  • The response variable is the primary measurement of interest.
  • In our example, it represents the proportion of unemployed individuals within each racial group.
  • Analysis focuses on changes or differences in this variable in relation to another factor.
By focusing on unemployment rates as the response variable, we can analyze external influences, such as race, that might be contributing to shifts or disparities in employment statistics.
Role of the Explanatory Variable
The explanatory variable is a key piece of the puzzle in statistical studies as it provides the context or factor that potentially influences the response variable. In this exercise, the explanatory variable is race. This variable aims to categorize and potentially explain the differences observed in unemployment rates.
  • An explanatory variable, sometimes called an independent variable, is used to uncover patterns or causal relationships.
  • Race provides distinct categories: Blacks and Whites.
  • These categories are crucial for examining disparities between them regarding unemployment rates.
A clear understanding of the explanatory variable is essential, as it forms the basis for analyzing how it affects the unemployment rate, providing insights into socio-economic challenges and disparities present during the recession.
Independent Samples in Statistical Analysis
In statistical research, understanding whether samples are independent or dependent greatly affects the interpretation of the results. Independent samples refer to samples drawn from distinct populations that have no effect on each other. In this exercise, the unemployment rates for Blacks and Whites are derived from independent samples.
  • Independent samples mean selection in one group doesn't influence selection in another.
  • This characteristic ensures that the analysis of unemployment rates for Blacks and Whites does not overlap.
  • The independence of samples allows for a more unbiased comparison between the two groups.
By using independent samples, we ensure that the analysis of unemployment across different racial groups is robust and that the comparisons are valid, reflecting true population behaviors without one group's data affecting the other.

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

Last month a random sample of 1000 subjects was interviewed and asked whether they thought the president was doing a good job. This month the same subjects were asked this again. The results are: 450 said yes each time, 450 said no each time, 60 said yes on the first survey and no on the second survey, and 40 said no on the first survey and yes on the second survey. a. Form a contingency table showing these results. b. Estimate the proportion giving a favorable rating (i) last month and (ii) this month. c. Show how each of the proportions in part b can be obtained as a sample mean. d. Find the test statistic and P-value for applying McNemar's test that the population proportion was the same each month. Interpret.

Two TV commercials are developed for marketing a new product. A volunteer test sample of 200 people is randomly split into two groups of 100 each. In a controlled setting, Group \(\mathrm{A}\) watches commercial A and Group B watches commercial B. In Group A, 25 say they would buy the product. In group B, 20 say they would buy the product. The marketing manager who devised this experiment concludes that commercial A is better. Is this conclusion justified? Analyze the data. If you prefer, use software (such as MINITAB) for which you can enter summary counts. a. Show all steps of your analysis, including assumptions. b. Comment on the manager's conclusion, and indicate limitations of the experiment.

Living poorly A survey of residents of several Western countries estimated the percentage in each country who reported going without food or without health care or without adequate clothing sometime in the past year. For example, the estimated percentage was \(33 \%\) in the United States (the highest in the survey) and \(9 \%\) in Japan. Are the samples from the United States and Japan independent samples or dependent samples? Why?

As part of a class exercise, an instructor at a major university asks her students how many hours per week they spend on social networks. She wants to investigate if time spent on social networks differs for male and female students at this university. The results for those age 21 or under were: \(\begin{array}{ll}\text { Males: } & 5,7,9,10,12,12,12,13,13,15,15,20 \\\ \text { Females: } & 5,7,7,8,10,10,11,12,12,14,14,14,16,18, \\ & 20,20,20,22,23,25,40\end{array}\) a. Using software or a calculator, find the sample mean and standard deviation for each group. Interpret. b. Find the standard error for the difference between the sample means. c. Find and interpret a \(90 \%\) confidence interval comparing the population means.

Bulimia CI A study of bulimia among college women (J. Kern and T. Hastings, Journal of Clinical Psychology, vol. \(51,1995,\) p. 499 ) studied the connection between childhood sexual abuse and a measure of family cohesion (the higher the score, the greater the cohesion). The sample mean on the family cohesion scale was 2.0 for 13 sexually abused students \((s=2.1)\) and 4.8 for 17 nonabused students \((s=3.2)\) a. Find the standard error for comparing the means. b. Construct a \(95 \%\) confidence interval for the difference between the mean family cohesion for sexually abused students and non-abused students. Interpret.
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Statistics

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Decision Maths

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.