A random sample of 12 measurements is obtained from a population. Let M be the median for the population. The research study requires an estimate of M. The sample median is determined to be 37 .8. The researchers want to assess a range of values for this point estimator.
a. Display a 95% confidence interval on M by obtaining the values of La/2 and Ua/2.
b. Obtain a 95% confidence interval on M using the large- sample approximations of La/2 and Ua/2. Compare the two confidence intervals.
c. Provide reasons for the difference in the two confidence intervals.