Question

Which of the following would be a correct interpretation of a​ 99% confidence interval such as 4.1 less than mean less than​ 5.6?

Answer 1

Answer

it is given that the 99% confidence interval is between 4.1 and 5.6

so, we know that when the 99% confidence interval is between x and y, then we interpret it as

We are 99% confident that the true mean is between x and y value or we are 99% confident that the interval between x and y actually does contain the true mean

so, we can write it as

we are 99% confident that the interval between 4.1 and 5.6 actually does contain the true mean

Answer 2

A 99% confidence interval such as "4.1 less than mean less than 5.6" can be interpreted as follows:

We are 99% confident that the true population mean falls within the range of 4.1 to 5.6. This means that if we were to repeat the sampling process multiple times and construct 99% confidence intervals from each sample, approximately 99 out of 100 of these intervals would contain the true population mean.

In simpler terms, we have a high level of confidence that the true mean value of the population lies between 4.1 and 5.6 based on the sample data and the chosen level of confidence (99%).