# Interpreting confidence intervals

The weight of an SRS of 35 pumpkins is measured. A 95% confidence interval for the mean weight, in pounds, for the pumpkins on this farm is (9,22). Which of the following statements gives a valid interpretation of this interval?

a. 95% of the sample of pumpkins have a weight, in pounds, between 9 and 22.
b. We can be 95% confident that the true mean weight of the pumpkins on the family farm is between 9 and 22 pounds.
c. If the procedure were repeated many times, 95% of the sample means would be between 9 and 22.


I understand that the correct interpretation would be that there is a 95% confindence that the interval (9,22) contains the population parameter; however, none of the choices seem to match this.

Also, is it correct to interpret a 90% confidence interval of, for example, $1\pm0.2$, as saying that any value between $(0.8,1.2)$ is believable as the true mean of the population?

• The answer is b. But what does this really mean? It means that if you were to draw samples and repeatedly construct 95% confidence intervals over and over again for each sample, 95% of those many confidence intervals would contain the population mean. In other words: if you drew 1,000,000 random samples and constructed a confidence interval based on the data in each sample, about 950,000, or 95%, of them would contain the true mean. – symplectomorphic Mar 18 '16 at 23:47

But both statements depend on what you mean by "95% confident that the true weight is between 9 and 22". The only reasonable definition of "confident" here is that $[9,22]$ is a 95% confidence interval for the true weight, so this is a tautology.