Question

Interpret the meaning of: The 90% confidence interval is (82.66​, 88.02​). The​ 95% confidence interval is (82.14​, 88.54​). . A. You can be​ 90% confident that the population mean record high temperature is between the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval. B. You can be certain that the population mean record high temperature is either between the lower bounds of the​ 90% and​ 95% confidence intervals or the upper bounds of the​ 90% and​ 95% confidence intervals. C. You can be​ 90% confident that the population mean record high temperature is outside the bounds of the​ 90% confidence​ interval, and​ 95% confident for the​ 95% interval. D. You can be certain that the mean record high temperature was within the​ 90% confidence interval for approximately 72 of the 80 ​days, and was within the​ 95% confidence interval for approximately 76 of the 80 days.

Answer 1

Explanation:

The correct interpretation is:

A. You can be 90% confident that the population mean record high temperature is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

The confidence interval provides a range of values within which we can estimate the true population parameter (in this case, the mean record high temperature) with a certain level of confidence.

For the 90% confidence interval (82.66, 88.02), it means that if we were to repeat the sampling process many times and construct 90% confidence intervals, approximately 90% of those intervals would contain the true population mean record high temperature.

Similarly, for the 95% confidence interval (82.14, 88.54), approximately 95% of the constructed intervals would capture the true population mean record high temperature.

It's important to note that the interpretation does not imply certainty about the exact value of the population parameter. Instead, it provides a range of values within which we can estimate the population parameter with a specified level of confidence.