In Problems 3–10, use the Wilcoxon matched-pairs signedranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomly.
4. Hypotheses: H0: MD = 0 versus H1: MD 7 0 with n = 20 and T- = -65.
Step 1 of 5) Use the Wilcoxon matched-pairs signed-ranks test to test the given hypotheses at the a = 0.05 level of significance. The dependent samples were obtained randomly. 4. Hypotheses: H0: MD = 0 versus H1: MD 7 0 with n = 20 and T- = -65. The Effect of Sample Size on the Margin of Error We know that larger sample sizes produce more precise estimates (the Law of Large Numbers). Given that the margin of error is za 2 # B pn 11 - pn 2 n , we can see that increasing the sample size n decreases the standard error; so the margin of error decreases. This means that larger sample sizes will result in narrower confidence intervals. To illustrate this idea, suppose the survey conducted in Example 4 resulted in pn = 0.34 for the proportion of 16- to 17-year-old teenagers who text while driving, but the sample size is only 200.
