In a 95% confidence interval approximately how many intervals would you expect to contain the population proportion and how many should not contain this value?
95% contain, 5% not
To determine approximately how many intervals would contain the population proportion and how many would not contain this value in a 95% confidence interval, we need to understand the concept of confidence intervals and the significance level associated with it.
A confidence interval is a range of values within which the true population parameter is likely to fall. It provides us with an estimate of the population parameter along with a measure of its precision. In this case, we are interested in the population proportion.
The confidence level of a confidence interval refers to the probability that the interval contains the true population parameter. A 95% confidence level means that if we were to repeatedly sample from the population and construct a confidence interval each time, approximately 95% of those intervals would contain the true population proportion, while the remaining 5% would not.
Therefore, in a 95% confidence interval, we would expect approximately 95% of the intervals to contain the population proportion, and about 5% of the intervals to not contain this value.
It is important to note that a confidence interval is an inference based on a sample, and it does not guarantee that a particular interval will contain the true population parameter.