Suppose that 2,000 scientists compute 90% confidence
intervals for parameters they are interested in. How many of
these intervals would we expect to successfully capture their
parameters
To answer this question, we need to understand the concept of a confidence interval and how it relates to the success of capturing the true parameter.
A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the scientists computed 90% confidence intervals, which means that if they repeated their experiments multiple times and calculated 90% confidence intervals each time, about 90% of these intervals would contain the true parameters.
Since we are given that there are 2,000 scientists and each of them computed a 90% confidence interval, we can estimate the number of intervals that would successfully capture their parameters.
To estimate this, we need to understand that a confidence level of 90% implies that 90% of the intervals calculated will contain the true parameter. Therefore, we can expect approximately 90% of the intervals to be successful in capturing their parameters.
Hence, the number of intervals that would successfully capture their parameters can be estimated as:
Number of intervals = 2,000 x 0.9 = 1,800
Therefore, we would expect approximately 1,800 of the 2,000 confidence intervals to successfully capture their parameters.