Question

4. A private industry analyst claims that there is no difference in the salaries earned by workers in the wholesale trade and manufacturing industries. The table shows the salaries (in thousands of dollars) of a random sample of 10 wholesale trade workers and 10 manufacturing workers. At a-0.1, can you reject the analyst's claim? Wholesale trade 70 66 65 80 62 69 73 77 74 72 Manufacturing 71 67 56 74 54 65 7o 58 64 52

Answer 1

a)

Ho : there is no difference in salaries earned

Ha: there is difference in salaries

b)

we use Wilcoxon rank-sum test

Wilcoxon rank-sum test is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.

Wicoxon signed rak test is like paired t-test which is not true here

c)
A <- c(70, 66, 65, 80, 62, 69, 73, 77, 74, 72)

B <- c(71, 67, 56, 74, 54, 65, 76, 58, 64, 52)

wilcox.test(A, B, paired = FALSE, alternative = "two.sided", mu = 0.0, exact = TRUE, correct = TRUE, conf.int = TRUE, conf.level = 0.90)

d)

Test statistic W : 74

p-value : 0.075442

e)

we reject the null hypothesis

as p-value < alpha

f)

we conclude that there is evidence of difference in salaries