Anonymous
Jan 29
By using examples, explain and differentiate between Margin error and interval estimate?
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ChatGPT
Jan 29
Margin of error and interval estimate are both statistical concepts used to quantify the uncertainty or variability associated with a sample estimate. However, they differ in terms of their interpretation and calculation.
1. Margin of Error:
The margin of error is a measure of the maximum expected difference between the sample estimate and the true population parameter. It is typically used in the context of estimating population proportions or percentages. The margin of error is expressed as a range around the sample estimate, within which the true population parameter is likely to fall.
Example: Suppose a survey is conducted to estimate the proportion of people in a city who support a particular political candidate. The survey finds that 55% of the respondents support the candidate, with a margin of error of +/- 3%. This means that the true proportion of people in the city who support the candidate is likely to be between 52% and 58% (55% +/- 3%).
2. Interval Estimate:
An interval estimate, also known as a confidence interval, provides a range of values within which the true population parameter is likely to lie. It is commonly used in estimating population means or averages. The interval estimate is calculated based on the sample data and the desired level of confidence.
Example: Consider a study to estimate the average height of adult males in a country. A random sample of 1000 adult males is taken, and their heights are measured. The resulting interval estimate might be 170 cm to 175 cm, with a 95% confidence level. This means that we can be 95% confident that the true average height of adult males in the country falls within this range.
In summary, the margin of error is a measure of the expected difference between a sample estimate and the true population parameter, while the interval estimate provides a range of values within which the true population parameter is likely to lie. The margin of error is typically used for proportions or percentages, while the interval estimate is used for means or averages.
1. Margin of Error:
The margin of error is a measure of the maximum expected difference between the sample estimate and the true population parameter. It is typically used in the context of estimating population proportions or percentages. The margin of error is expressed as a range around the sample estimate, within which the true population parameter is likely to fall.
Example: Suppose a survey is conducted to estimate the proportion of people in a city who support a particular political candidate. The survey finds that 55% of the respondents support the candidate, with a margin of error of +/- 3%. This means that the true proportion of people in the city who support the candidate is likely to be between 52% and 58% (55% +/- 3%).
2. Interval Estimate:
An interval estimate, also known as a confidence interval, provides a range of values within which the true population parameter is likely to lie. It is commonly used in estimating population means or averages. The interval estimate is calculated based on the sample data and the desired level of confidence.
Example: Consider a study to estimate the average height of adult males in a country. A random sample of 1000 adult males is taken, and their heights are measured. The resulting interval estimate might be 170 cm to 175 cm, with a 95% confidence level. This means that we can be 95% confident that the true average height of adult males in the country falls within this range.
In summary, the margin of error is a measure of the expected difference between a sample estimate and the true population parameter, while the interval estimate provides a range of values within which the true population parameter is likely to lie. The margin of error is typically used for proportions or percentages, while the interval estimate is used for means or averages.
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