7. Sampling Distributions & Confidence Intervals: Mean

The procedure for constructing a confidence interval about a mean is ________, which means minor departures from normality do not affect the accuracy of the interval.

Critical Values Sir R. A. Fisher, a famous statistician, showed that the critical values of a chi-square distribution can be approximated by the standard normal distribution

χ²_k = [(z_k + √(2v – 1)) / 2]²

where v is the degrees of freedom and z_k is the z-score such that the area under the standard normal curve to the right of z_k is k. Use Fisher’s approximation to find χ²_0.975 and χ²_0.025 with 100 degrees of freedom. Compare the results with those found in Table VIII.

If we wish to obtain a 95% confidence interval of a parameter using the bootstrap percentile method, we determine the_______percentile and the_______ percentile of the resampled distribution.

The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = –1.56? Why?