Using R for Introductory Statistics : John Verzani

Significance tests 223parameters. A plot of the data shows that a normal population assumption is not correct;rather, the population appears to be lognormal.Perform a significance test ofH 0 : median=.005, H A : median>.005.After taking logs, we can see that the data is symmetric, so the signed-rank test can applyto the log-transformed data. The significance test of this data isH 0 : median=log(.005), H A : median>log(.005).>wilcox.test(log(salmon.rate),mu=log(.005),alt="greater”)Wilcoxon signed rank test with continuitycorrectiondata: log(salmon.rate)V = 2077, p-value = 0.065alternative hypothesis: true mu is greater than −5.298A small p-value is found.To contrast, the p-value for the sign test is found with these commands:> T = sum(salmon.rate > .005); n = length(salmon.rate)> 1 − pbinom(T − 1, n, 1/2)[1] 0.13618.4.3 Problems8.17 The exec. pay (UsingR) data set contains data on the salaries of CEOs at 199 topcompanies in the United States. The amounts are in $ 10,000s. The data is not symmetric.Do a sign test to determine whether the median pay is more than $220,000.8.18 Repeat the previous exercise, using the signed-rank test on the log-transformeddata. Do you reach the same conclusion?8.19 The babies (UsingR) data set contains data covering many births. Informationincluded is the gestation period, and a factor indicating whether the mother was a smoker.Extracting the gestation times for mothers who smoked during pregnancy can be donewith these commands:> attach(babies)> smokers=gestation[smoke == 1 & gestation != 999]> detach(babies)Perform a significance test of the null hypothesis that the average gestation period is 40weeks against a two-sided alternative. Explain what test you used, and why you chosethat one.8.20 If the sign test has fewer assumptions on the population, why wouldn’t we alwaysuse that instead of a t-test? The answer lies in the power of the sign test to detect whenthe null hypothesis is false. The sign test will not reject a false null as often as the t-test.