# Confidence Interval Calculation for Sample Mean: 95% Confidence Level

• JOhnJDC
In summary, the individual needs to determine a value v in order to have 95% confidence that the average is v or less. They can calculate a 90% confidence interval using the given data, with the upper bound of this interval being the value v they are looking for. The formula for the confidence interval is B% CI = [x-(1.645*s)/sqrt(n), x+(1.645*s)/sqrt(n)] and the logic used to determine v is valid.
JOhnJDC

## Homework Statement

I know the sample size n, the observed sample mean x, and the observed sample standard deviation s. I need to determine a value v such that I'm 95% confident that the average is v or less.

## The Attempt at a Solution

If I calculate the 95% confidence interval, then I know that 95% of the resulting intervals will contain the true mean. Does the upper bound of the 95% confidence interval also tell me that this mean will be less than or equal to the upper bound with 95% confidence? Am I thinking about this the wrong way? Thanks

Last edited:
I think the answer is to construct the 90% confidence interval using the data given. Because this interval will be centered on the observed sample mean x, only 5% of averages will be above the upper bound of this interval. Therefore, I can be 95% confident that the upper bound is the value v that I'm looking for.

B% CI = [x-(1.645*s)/sqrt(n), x+(1.645*s)/sqrt(n)]

So, v = x+(1.645*s)/sqrt(n).

Does that logic work?

## 1. What is a confidence interval?

A confidence interval is a range of values that is likely to contain the true population parameter with a certain degree of confidence. It is calculated from a sample and is used to estimate the true population parameter.

## 2. How is a 95% confidence level determined?

A 95% confidence level means that if we were to take multiple samples from the same population and calculate a confidence interval for each sample, then 95% of those intervals would contain the true population parameter. It is a commonly used confidence level in statistical analysis.

## 3. What is the formula for calculating a confidence interval for sample mean?

The formula for calculating a confidence interval for sample mean is: sample mean ± (critical value * standard error of the mean), where the critical value is determined based on the desired confidence level and the standard error of the mean is calculated from the sample data.

## 4. How do I interpret a confidence interval?

A confidence interval can be interpreted as a range of values that is likely to contain the true population parameter with a certain degree of confidence. For example, if a 95% confidence interval for the population mean is 50 to 60, we can say with 95% confidence that the true population mean falls within this range.

## 5. Why is it important to calculate a confidence interval?

Calculating a confidence interval allows us to estimate the true population parameter with a certain level of confidence. This is important because we can never know the exact value of the population parameter, and using a confidence interval gives us a range of values that is likely to contain the true parameter. It also helps us to assess the precision and reliability of our sample data.

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