What is meant by the 95% confidence interval of the mean ?


That 95% of my sample is OK to do more tests.

That I am 95% confident that the confidence interval will contain the parameter being estimated.

That 5% of my sample is not OK.

That I am 95% sure that the population mean is 95

95% confident

The correct answer is: That I am 95% confident that the confidence interval will contain the parameter being estimated.

The 95% confidence interval of the mean refers to a range of values within which we estimate that the true population mean lies with 95% confidence. This means that if we were to repeat the sampling procedure multiple times and construct 95% confidence intervals, approximately 95% of these intervals would contain the true population mean. It does not mean that 95% of the sample is OK for further tests, nor does it mean that we are 95% sure that the population mean is 95.

The correct answer is: "That I am 95% confident that the confidence interval will contain the parameter being estimated."

A 95% confidence interval is a range of values within which we are 95% confident that the true population mean lies. It is a statistical measure that allows us to estimate the likely range of values for a population parameter based on a sample.

To calculate the 95% confidence interval of the mean, you would typically follow these steps:

1. Collect a representative sample from the population of interest.
2. Calculate the sample mean (x̄) and sample standard deviation (s) from the sample data.
3. Determine the desired level of confidence (e.g., 95% confidence).
4. Find the critical value associated with the desired level of confidence. This value depends on the sample size and the distribution being used (e.g., t-distribution for small sample sizes or z-distribution for large sample sizes).
5. Calculate the margin of error by multiplying the critical value by the standard error of the mean. The standard error of the mean is equal to the sample standard deviation divided by the square root of the sample size (s/√n).
6. Construct the confidence interval by subtracting the margin of error from the sample mean to get the lower bound and adding the margin of error to the sample mean to get the upper bound.

The resulting interval is the 95% confidence interval of the mean, which means that we can be 95% confident that the population mean falls within that range. It is important to note that this interval estimation does not guarantee that the true population mean falls within the calculated interval, but offers a measure of the uncertainty associated with our estimate.