/*! 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 2 Do people who work for non-profi... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit organizations revealed that 377 of them were "highly satisfied." From the for-profit companies, 431 out 518 employees reported the same level of satisfaction. Find the standard error of the difference in sample proportions.

Short Answer

Expert verified
The standard error of the difference in sample proportions is approximately 0.022.

Step by step solution

01

Calculate the Proportions

First, calculate the proportion of employees highly satisfied at both types of organizations using the provided numbers. For non-profit organizations, this would be \(p1 = 377/422 = 0.893\) (rounded to three decimal places). For for-profit companies, the proportion \(p2 = 431/518 = 0.832\) (rounded to three decimal places).
02

Apply the Standard Error Formula

Next, substitute these values into the standard error formula: \(SE = \sqrt{p1 * (1-p1) / n1 + p2 * (1-p2) / n2}\). This becomes \(SE = \sqrt{0.893 * (1 - 0.893) / 422 + 0.832 * (1 - 0.832) / 518}\).
03

Calculate the Standard Error

Upon performing the calculation, the standard error will be approximately \(SE = 0.022\).

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.

Sample Proportions
When we talk about sample proportions, we are often looking at the fraction of a group that shares a common characteristic. In our exercise, we are interested in the proportion of employees who are "highly satisfied" with their jobs.

Calculating sample proportions is straightforward. For non-profit organizations, 377 out of 422 employees reported high job satisfaction. This gives us a proportion of 0.893, which means 89.3% of the sample is highly satisfied.

For for-profit companies, 431 of 518 employees reported the same satisfaction level, translating into a proportion of 0.832. This indicates that 83.2% of the sample is highly satisfied.
  • The numerator in our formula represents the number of 'success' cases—in this scenario, employees who are highly satisfied.
  • The denominator reflects the total sample size.
These proportions help us compare satisfaction levels between the two types of organizations.

Next, we use these sample proportions to delve into understanding the standard error and its role in statistical analysis.
Job Satisfaction
Job satisfaction is an important factor that contributes to the overall well-being of employees. It reflects how content individuals are with their work environment, roles, and relationships within the company. This concept is assessed through various measures, often involving surveys like the one conducted in our exercise.

High job satisfaction is beneficial for both the employee and the organization, as it can lead to better performance, lower turnover rates, and a more positive workplace culture. In our specific context, we're comparing how job satisfaction differs between employees at non-profit organizations versus those at for-profit companies.

Understanding job satisfaction levels across different types of organizations can provide insights for human resources departments to enhance work environments. Some common factors impacting job satisfaction include:
  • Compensation and benefits
  • Work-life balance
  • Opportunities for advancement
  • Company culture and values
Each of these can vary significantly between non-profit and for-profit sectors, which makes analyzing satisfaction levels important for strategic improvements.
Non-Profit Organizations
Non-profit organizations operate primarily to serve public or social interests rather than to earn profits for owners or investors. Common examples include charities, educational institutions, and healthcare organizations.

Employees in non-profits often value mission-driven work, which can lead to high job satisfaction. The sense of contributing to a greater cause can be a significant motivator.

However, these organizations might not excel in other areas, like offering competitive salaries, which can affect satisfaction. Our exercise showed that a large proportion of non-profit employees were highly satisfied with their jobs, demonstrating a possible strong alignment with their organization's goals.
  • Mission alignment can increase employee motivation and satisfaction.
  • Lack of resources could be a challenge in enhancing job satisfaction further.
For many non-profit workers, the intrinsic rewards of their work often surpass some of the financial limitations inherent in this sector.
For-Profit Companies
For-profit companies are businesses that aim to make money for their owners and shareholders. They can range from small businesses to large multinational corporations. The primary goal is financial growth and profit maximization.

When examining job satisfaction in for-profit companies, monetary incentives and various benefits often play a significant role. These companies may offer competitive salaries, bonuses, and career development opportunities to attract and retain talent.

However, this focus on profit can sometimes create highly demanding work environments, which might negatively impact job satisfaction despite good compensation. In the exercise, a significant number of employees in for-profit organizations reported high job satisfaction, suggesting that other positive factors balance these demands.
  • Higher financial resources allow better compensation packages.
  • Profit-oriented strategies could lead to performance pressure.
These distinct differences from non-profits make for-profit companies an interesting subject of study regarding employee satisfaction.

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

A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They'll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can't know this, but suppose the candidate has a positive image with \(59 \%\) of males but with only \(53 \%\) of females. a. What kind of sampling design is his staff planning to use? b. What difference would you expect the poll to show? c. Of course, sampling error means the poll won't reflect the difference perfectly. What's the standard deviation for the difference in the proportions? d. Sketch a sampling model for the size difference in proportions of men and women with favorable impressions of this candidate that might appear in a poll like this. e. Could the campaign be misled by the poll, concluding that there really is no gender gap? Explain.

Political pundits talk about the "bounce" that a presidential candidate gets after his party's convention. In the past 40 years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voters at random and found that \(47 \%\) favored John Kerry. Just afterward, they took another random sample of 1500 likely voters and found that \(49 \%\) favored Kerry. That's a two percentage point increase, but the pollsters claimed that there was no bounce. Explain.

Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves. \({ }^{12}\) At an "ice cream social," people were randomly given either a 17 -oz or a 34 -oz bowl (both large enough that they would not be filled to capacity). They were then invited to scoop as much ice cream as they liked. Did the bowl size change the selected portion size? Here are the summaries: 12Brian Wansink, Koert van Ittersum, and James E. Painter, "Ice Cream Illusions: Bowls, Spoons, and Self-Served Portion Sizes," Am. J. Prev. Med. 2006 . Test an appropriate hypothesis and state your conclusions. For assumptions and conditions that you cannot test, you may assume that they are sufficiently satisfied to proceed.

In 2001 , the conclusion of the study outlined in Exercise 41 was questioned. A new \(9-\) year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared to 66 deaths among the control group. (The New York Times, Dec. 9,2001 ) a. Do these results support the effectiveness of regular mammograms in preventing deaths from breast cancer? b. If your conclusion is incorrect, what kind of error have you committed?

A Time magazine article about a survey of men's attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded "Yes" to the question "Are you a stay-at-home dad?" How big is the difference in proportions in the two populations? a. Construct and interpret an appropriate confidence interval. b. Overall, the survey contacted 1302 men and claims a margin of error of \(\pm 2.9 \%\). Why is the margin of error different for your confidence interval?

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.