A Survey Of 225 Students Showed The Mean Number Of Hours Spent Studying Per Week Was 20.6, And The Standard Deviation Was 2.7.Assuming A 90 % 90\% 90% Confidence Level, The Margin Of Error Is

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Introduction

In the field of statistics, understanding the margin of error is crucial in making informed decisions and interpreting data. The margin of error is a measure of the amount of random variation in a sample of data. In this article, we will explore how to calculate the margin of error using a given dataset of 225 students who participated in a survey. The survey aimed to determine the mean number of hours spent studying per week, with a reported mean of 20.6 hours and a standard deviation of 2.7 hours. We will assume a confidence level of 90% and calculate the margin of error.

What is Margin of Error?

The margin of error is a statistical measure that represents the amount of uncertainty or random variation in a sample of data. It is a crucial concept in statistics, as it helps to determine the reliability of the results obtained from a sample. The margin of error is typically denoted by the symbol E and is calculated as a percentage of the sample mean.

Formula for Margin of Error

The formula for calculating the margin of error is given by:

E = (Z * σ) / √n

where:

  • E is the margin of error
  • Z is the Z-score corresponding to the desired confidence level
  • σ is the standard deviation of the sample
  • n is the sample size

Calculating the Margin of Error

To calculate the margin of error, we need to determine the Z-score corresponding to the desired confidence level. For a 90% confidence level, the Z-score is typically denoted by Z = 1.645.

Given the standard deviation (σ) of 2.7 hours and the sample size (n) of 225, we can plug these values into the formula:

E = (1.645 * 2.7) / √225

E = 4.42 / 15

E = 0.295

Interpreting the Results

The calculated margin of error is 0.295 hours, which represents a 29.5% of the sample mean. This means that if we were to take multiple samples from the same population, we would expect the sample mean to vary by approximately 0.295 hours from the true population mean.

Implications of the Margin of Error

The margin of error has significant implications for the interpretation of the results. It indicates that the sample mean of 20.6 hours is likely to be within 0.295 hours of the true population mean. This means that if the true population mean is 20.6 hours, we can be 90% confident that the sample mean will be within 0.295 hours of this value.

Conclusion

In conclusion, the margin of error is a crucial concept in statistics that represents the amount of uncertainty or random variation in a sample of data. By calculating the margin of error, we can determine the reliability of the results obtained from a sample. In this article, we calculated the margin of error for a sample of 225 students who participated in a survey, assuming a 90% confidence level. The calculated margin of error was 0.295 hours, which represents a 29.5% of the sample mean.

References

  • [1] Moore, D. S., & McCabe, G. P. (2011). Introduction to the practice of statistics. W.H. Freeman and Company.
  • [2] Larson, R. E., & Farber, B. (2013). Elementary statistics: Picturing the world. Cengage Learning.

Discussion

The margin of error is a critical concept in statistics that has significant implications for the interpretation of results. By understanding the margin of error, researchers and analysts can make informed decisions and draw reliable conclusions from their data. In this article, we explored how to calculate the margin of error using a given dataset of 225 students who participated in a survey. The calculated margin of error was 0.295 hours, which represents a 29.5% of the sample mean.

What do you think about the margin of error?

  • Do you think the margin of error is a useful concept in statistics?
  • How do you think the margin of error can be applied in real-world scenarios?
  • What are some potential limitations of the margin of error?

Share your thoughts and opinions in the comments below!

Related Articles

Leave a comment below and let's discuss!

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Introduction

In our previous article, we explored the concept of margin of error and calculated its value for a sample of 225 students who participated in a survey. The margin of error is a crucial concept in statistics that represents the amount of uncertainty or random variation in a sample of data. In this article, we will address some frequently asked questions (FAQs) related to margin of error and provide additional insights into its application.

Q&A

Q1: What is the purpose of calculating the margin of error?

A1: The primary purpose of calculating the margin of error is to determine the reliability of the results obtained from a sample. By understanding the margin of error, researchers and analysts can make informed decisions and draw reliable conclusions from their data.

Q2: How is the margin of error related to the confidence level?

A2: The margin of error is directly related to the confidence level. A higher confidence level typically results in a larger margin of error. For example, a 90% confidence level will result in a larger margin of error compared to a 95% confidence level.

Q3: Can the margin of error be reduced?

A3: Yes, the margin of error can be reduced by increasing the sample size. A larger sample size will result in a smaller margin of error, as the sample mean will be more representative of the population mean.

Q4: How is the margin of error used in real-world scenarios?

A4: The margin of error is used in a variety of real-world scenarios, including:

  • Polling: Margin of error is used to determine the reliability of poll results.
  • Marketing research: Margin of error is used to determine the effectiveness of marketing campaigns.
  • Medical research: Margin of error is used to determine the reliability of medical study results.

Q5: Can the margin of error be used to make predictions?

A5: Yes, the margin of error can be used to make predictions. By understanding the margin of error, researchers and analysts can make informed predictions about future outcomes.

Q6: How is the margin of error related to the standard deviation?

A6: The margin of error is directly related to the standard deviation. A larger standard deviation will result in a larger margin of error.

Q7: Can the margin of error be used to compare different samples?

A7: Yes, the margin of error can be used to compare different samples. By understanding the margin of error, researchers and analysts can determine whether the differences between samples are statistically significant.

Q8: How is the margin of error used in hypothesis testing?

A8: The margin of error is used in hypothesis testing to determine whether the null hypothesis can be rejected. If the margin of error is large, it may indicate that the null hypothesis cannot be rejected.

Conclusion

In conclusion, the margin of error is a crucial concept in statistics that represents the amount of uncertainty or random variation in a sample of data. By understanding the margin of error, researchers and analysts can make informed decisions and draw reliable conclusions from their data. In this article, we addressed some frequently asked questions related to margin of error and provided additional insights into its application.

References

  • [1] Moore, D. S., & McCabe, G. P. (2011). Introduction to the practice of statistics. W.H. Freeman and Company.
  • [2] Larson, R. E., & Farber, B. (2013). Elementary statistics: Picturing the world. Cengage Learning.

Discussion

The margin of error is a critical concept in statistics that has significant implications for the interpretation of results. By understanding the margin of error, researchers and analysts can make informed decisions and draw reliable conclusions from their data. In this article, we explored some frequently asked questions related to margin of error and provided additional insights into its application.

What do you think about the margin of error?

  • Do you think the margin of error is a useful concept in statistics?
  • How do you think the margin of error can be applied in real-world scenarios?
  • What are some potential limitations of the margin of error?

Share your thoughts and opinions in the comments below!

Related Articles

Leave a comment below and let's discuss!