Question

you are given the sample mean and the population standard deviation. use this information to construct the 90% and 95% confidence intervals for the population mean. interpret the results and compare the widths of the confidence intervals.
from a random sample of 36 months from january 2005 through december 2020, the mean number of tornadoes per month in the united states was about 13. assume the population standard deviation is 111.
the 90% confidence interval
the 95% confidence interval
interpret the results. choose the correct answer below.
a. 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.
b. 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% confidence intervals.
c. 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.
d. you can be certain that the monthly number of tornadoes was within the 90% confidence interval for approximately 32 of the 36 days, and was within the 95% confidence interval for approximately 34 of the 36 days.

Explanation:

Confidence intervals give a range of values where the population parameter (here, the population mean number of tornadoes) is likely to be. A 90% confidence interval means we are 90% confident that the population mean lies within that interval, and a 95% confidence interval means we are 95% confident that the population mean lies within its respective interval.

• Option A: This is correct because the interpretation of confidence intervals is about the level of confidence that the population mean is within the interval. A 90% confidence interval implies 90% confidence and a 95% confidence interval implies 95% confidence for the population mean to be within their respective intervals.
• Option B: Confidence intervals are not about being "certain" and not about the mean being between lower bounds of one and upper bounds of another. The confidence level is about the probability that the population mean is within the specific interval.
• Option C: The confidence interval is for the population mean being within the interval, not outside.
• Option D: Confidence intervals are about the population mean, not about individual data points (number of tornadoes in a particular month).

Answer:

A. 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.