Question

suppose a 90% confidence interval for the population mean resulted in an upper limit of $658 and a lower limit of $273. what is the correct interpretation of this confidence interval? question 5 options: 1) we are 90% confident the population mean is in this interval. 2) there is a .90 probability the population mean is in this interval. 3) we are 90% confident the population proportion is in this interval. 4) there is a .90 probability the sample mean is in this interval.

Answer 1

The correct interpretation of a 90% confidence interval with limits of $273 and $658 is that we are 90% confident that the true population mean is contained within this interval. This is a statement about our confidence in the sampling process, not the probability of the population mean being in the interval after it has been calculated.

Step-by-step explanation:

When interpreting a 90% confidence interval, such as the one with an upper limit of $658 and a lower limit of $273, the correct interpretation is that we are 90% confident that the true population mean falls within this interval. This means that if we were to take many samples and construct a confidence interval for each, we would expect 90% of those intervals to contain the actual population mean.

The most common mistake is to think it means there is a 90% probability that the population mean lies within the observed interval; however, probability statements about the population mean are not valid once the sample has been taken and the interval calculated. The population mean is a fixed value and either is or is not in the interval. What the confidence interval reflects is the reliability of the sampling method used when estimating the population mean.

Answer 2

The correct interpretation of this confidence interval is that "we are 90% confident the population mean is in this interval." This means that if we were to repeat the sampling process many times, we would expect that 90% of the resulting confidence intervals would contain the true population mean.