Reference no: EM13503081

The vocabulary size is measured for 11 4-year-old children.  The results are below.  We want to test, at a = .05, if the population median differs from 450.

149    279    339    388    418    421    441    460    474    487    492

a. Write the null and alternative hypotheses.

b. Perform a sign test, "by hand".  Calculate the test statistic, find the p-value (using the Binomial distribution), and interpret the result of the test.

c. Calculate the test statistic for the Wilcoxon signed rank test, "by hand".  You do not have to compare this to a rejection region, and you do not have to interpret the result (yet).

d. Run PROC UNIVARIATE to carry out both tests above, and turn in the printout.  Give the p-value of the Wilcoxon signed rank test, and now interpret the result.

data five;

    input words @@;

datalines;

149 279 339 388 418 421 441 460 474 487 492

;

run;

e. Demonstrate how the test statistics you calculated in parts (b) and (c) relate to the statistics M and S you get from SAS.