A 95 confidence interval for the average lifetime of a cellp

A 95% confidence interval for the average lifetime of a cellphone was (1.89, 2.78) years.

Which of the following are statistically valid statements?

______ 95% of all cellphones will last between 1.89 and 2.78 years

______ We are 95% confident the average lifetime for cell phones is between 1.89 and 2.78 years

______ 95% of the time the average cell phone lifetime is between 1.89 and 2.78 years

______ There is a 95% probability the average lifetime for cellphones is between 1.89 and 2.78 years

______ The average lifetime for cellphones is between 1.89 and 2.78 years 95% of the time

______ A new confidence interval has a 95% probability of being 1.89 to 2.78 years

______ 95% of all studies would have a confidence interval between 1.89 and 2.78

______ There is a 95% probability the next confidence interval will capture the true population average

______ There is a 95% probability that the next cellphone will last between 1.89 and 2.78 years

______ If we did 100 confidence intervals about 95 of them would capture the true average

______ 95% of confidence intervals done this way will correctly capture the true average

______ If we did many similar studies, 95% would have a sample mean between 1.89 and 2.78 years

______ 95% of the time the sample average will be within a margin of error of the true average

______ The true average lifetime of a cellphone is between 1.89 and 2.78 years with 95% confidence

______ The probability that the true average is between 1.89 and 2.78 years is either 0 or 1

______ It is completely impossible to ever actually understand what confidence really means

Solution

Following are correct interpretations:

We are 95% confident the average lifetime for cell phones is between 1.89 and 2.78 years

There is a 95% probability the next confidence interval will capture the true population average

If we did 100 confidence intervals about 95 of them would capture the true average

95% of confidence intervals done this way will correctly capture the true average

95% of the time the sample average will be within a margin of error of the true average

The true average lifetime of a cellphone is between 1.89 and 2.78 years with 95% confidence

The probability that the true average is between 1.89 and 2.78 years is either 0 or 1 (I am doubtful about this one, after calculating the CI limits, the true mean is either inside it or not, but this event is not random, thus we do not write this in terms of probability, but this line is logically correct.)