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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 \(SE = 0.022\).

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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.

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Most popular questions from this chapter

A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did not. During the following year, only 333 of 2455 vaccinated children had ear infections, compared to 499 of 2452 unvaccinated children in the control group. a. Are the conditions for inference satisfied? b. Find a \(95 \%\) confidence interval for the difference in rates of ear infection. c. Use your confidence interval to explain whether you think the vaccine is effective.

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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.

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