Five years ago,the average starting salary of a new college graduate with a major in marketing was $34,000.A random sample of 10 graduates from this year's graduating class of a local university yielded the following starting salaries in thousands of dollars: 28,36,25,37,35,24,38,45,39,36.The local university wants to determine if the median starting salary for marketing graduates has increased in the last five years.
Assume that the population of starting salaries in marketing is not normally distributed.Using α = .05,can we conclude that the starting salaries increased in the last five years?
A)Reject the null hypothesis.
B)Fail to reject the null hypothesis.

Question

Quizplus · Accepted Answer

To determine if the median starting salary has increased in the last five years, we need to conduct a non-parametric test. The most appropriate test for this scenario is the Wilcoxon signed-rank test. We need to set up the null and alternative hypotheses as follows:
H0: The median starting salary of marketing graduates has not increased in the last five years.
Ha: The median starting salary of marketing graduates has increased in the last five years.

We then rank the differences between the observed salaries and the median of $34,000 in absolute value and calculate the test statistic. The test statistic is the sum of the ranks of the positive differences. In this case, the test statistic is 42.

We then look up the critical value for a two-tailed test with alpha = .05 and 10 observations. The critical value is 22.

Since 42 is greater than 22, we fail to reject the null hypothesis. Therefore, we cannot conclude that the median starting salary for marketing graduates has increased in the last five years with 95% confidence.

Five Years Ago,the Average Starting Salary of a New College