Question

Common Misinterpretation: Suppose a 90% confidence interval is given as 22.5 < µ < 32.0 and aclassmate says this means that 90% of the data falls between the values 22.5 and 32.0. What is wrongwith this statement?

Answer 1

A 90% confidence interval does not mean that 90% of the data falls between the values given. The 90% confidence interval represents the range of values within which we are 90% confident that the true population mean lies.

Step-by-step explanation:

A confidence interval is a statistical range that estimates the true value of a parameter with a certain level of confidence. It provides a range of values rather than a single point estimate, helping to quantify the uncertainty associated with the estimation process.

A 90% confidence interval does not mean that 90% of the data falls between the values given. The 90% confidence interval represents the range of values within which we are 90% confident that the true population mean lies. For example, if the confidence interval is (22.5, 32.0), it means that based on the sample data and the statistical calculations, there is a 90% chance that the true population mean falls within this range.

Answer 2

The statement made by the student is false.

A confidence interval, in statistics, implies the probability that a population parameter will fall between a set of values for a certain proportion of times.

It measures the degree of uncertainty or certainty in a sampling method.

The statement is wrong because the classmate mistook 22.5 and 32.0 to be mean values.