Question

a. you can be 90% confident that the population mean number of tornadoes is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.
b. you can be certain that the monthly number of tornadoes was within the 90% confidence interval for approximately 33 of the 37 days, and was within the 95% confidence interval for approximately 35 of the 37 days.
c. you can be certain that the population mean number of tornadoes is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95%
d. you can be 90% confident that the population mean number of tornadoes is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

Explanation:

Step1: Understanding Confidence Intervals

A confidence interval is a range of values within which we expect the population parameter (in this case, the population mean number of tornadoes) to lie with a certain level of confidence. A 90% confidence interval means that if we were to take many samples and construct confidence intervals, about 90% of those intervals would contain the true population mean.

Step2: Analyzing Option A

Option A is incorrect. A confidence interval is not about being outside or inside in terms of a single - sample relationship with two different confidence intervals (90% and 95%) in the way it is described.

Step3: Analyzing Option B

Option B is incorrect. The confidence level is about the population mean, not about the number of days in a month.

Step4: Analyzing Option C

Option C is incorrect. A confidence interval is for a single confidence level. We cannot say that the population mean is between two different confidence intervals (90% and 95%) in the way described.

Step5: Analyzing Option D

Option D is correct. By the definition of a confidence interval, a 90% confidence interval implies that we can be 90% confident that the population mean lies within the bounds of that 90% confidence interval.

Answer:

D. You can be 90% confident that the population mean number of tornadoes is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.