MATH SOLVE

3 months ago

Q:
# Researchers are studying the yield of a crop in two locations. The researchers are going to compute independent 90% confidence intervals for the mean yield at each location. What is the probability that at least one of the intervals will cover the true mean yields at their location?

Accepted Solution

A:

Answer:There is a 99% probability that at least one of the intervals will cover the true mean yields at their locationStep-by-step explanation:In a 90% confidence interval of the mean of a population, there is a 90% probability that it cover the true mean of the population.What is the probability that at least one of the intervals will cover the true mean yields at their location?This is 1 subtracted by the probability that none of them cover the true mean yields at their location.For each one, there is a 10% probability that it does not cover the mean. So the probability that both do not cover the mean is [tex]0.1*0.1 = 0.01[/tex]The probability that at least one of the intervals will cover the true mean yields at their location is 1-0.01 = 0.99 = 99%.