What does this 95% confidence interval around the sample mean indicate?
Suppose we want to generate a 95% confidence interval estimate for an unknown population mean. This means that there is a 95% probability that the confidence interval will contain the true population mean. Thus, P( [sample mean] – margin of error < μ < [sample mean] + margin of error) = 0.95.
What is the mean in confidence interval?
A confidence interval for the mean is a way of estimating the true population mean. Instead of a single number for the mean, a confidence interval gives you a lower estimate and an upper estimate. For example, instead of “6” as the mean you might get {5,7}, where 5 is the lower estimate and 7 is the upper.
When to make a statement about the confidence interval?
Nevertheless, the intervals may vary among the samples, while the true population parameter is the same regardless of the sample. Therefore, the probability statement regarding the confidence interval can be made in the case when the confidence intervals are recalculated for the number of samples.
How is the level of confidence expressed in a sample?
In the long term, 95% of all samples give an interval that contains µ, the true (but unknown) population mean. Level of confidence is expressed as a percent. The compliment to the level of confidence is α (alpha), the level of significance. The level of confidence is described as (1- α) * 100%.
What is the confidence interval for high school basketball?
Assume the interval is between 72 inches and 76 inches. If the researchers take 100 random samples from the population of high school basketball players as a whole, the mean should fall between 72 and 76 inches in 95 of those samples.
What is the 95% confidence interval for the census?
We can increase the expression of confidence in our estimate by widening the confidence interval. For the same estimate of the number of poor people in 1996, the 95% confidence interval is wider — “35,363,606 to 37,485,612.” The Census Bureau routinely employs 90% confidence intervals.