Point Estimate, Margin of Error and Confidence Level

In summary, a point estimate is a single value used to estimate a population parameter, while the margin of error is the range of values likely to include the true parameter with a given level of confidence. The confidence level is the probability that the true parameter falls within the margin of error. These three concepts are related and are used together to make inferences about a population. The margin of error and confidence level can be affected by factors such as sample size, data variability, and desired level of confidence.
  • #1
bunnypatotie
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1. One of the few negative effects of quitting smoking is weight gain. The data below shows the weight gain (in pounds) of 18 respondents 12 months after they quit. If the mean gain follows a normal distribution with a standard deviation of 9 pounds, estimate the mean weight gain of the 18 respondents at a 95% confidence level.
14 13 20 22 12 12 17 10 12 9 11 17 15 24 29 13 13 19​
 
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  • #2
Okay, that's a pretty straightforward problem. Do you know how to find the average of 18 numbers?
 

FAQ: Point Estimate, Margin of Error and Confidence Level

What is a point estimate?

A point estimate is a single value that is used to estimate an unknown population parameter, such as a mean or proportion. It is calculated from a sample of data and is used to make inferences about the population.

What is margin of error?

The margin of error is a measure of the uncertainty in a point estimate. It represents the range of values that the true population parameter is likely to fall within, given a certain level of confidence.

How is margin of error calculated?

The margin of error is calculated by taking the critical value (based on the desired confidence level) and multiplying it by the standard error of the sample. The standard error is a measure of the variability in the sample data.

What is confidence level?

The confidence level is the probability that the true population parameter falls within the calculated margin of error. It is typically expressed as a percentage, such as 95% or 99%.

Why is it important to report the confidence level?

The confidence level is important because it provides a measure of the reliability of the point estimate. A higher confidence level means that there is a lower chance of the true population parameter falling outside of the calculated margin of error.

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