Question

In a recent year, according to the Bureau of Labor Statistics, the median number of years that wage and salary workers had been with their current employer (called employee tenure) was 3.5 years. Information on employee tenure has been gathered since the early 1950's using the Current Population Survey (CPS), a monthly survey of 50,000 households that provides information on employment, unemployment, earnings, demographics, and other characteristics of the U. S. population. With respect to employee tenure, the questions measure how long workers had been with their current employer, not how long they plan to stary with their employer.

Employee Tenure of 20 workers

4.1, 2.3, 3.5, 4.6, 3.1, 1.2, 3.9, 2.1, 1.0, 4.5, 3.2, 3.4, 4.1, 3.1, 2.8, 1.4, 3.4, 4.9, 5.7, 2.6

A) A congressional representative claims that the median tenure for workers from the representative's district is less than the national median tenure of 3.5 years. Thae claim is based on the representative's data shown above. Assume that the employees were randomly selected.

1) How would you test the representative's claim?

2) Can you use a parametric test, or do you need a nonparametric test? Why?

3) State the null and alternative hypothesis.

4) Test the claim using alpha = 0.05. What can you conclude? Show your work, the process that you used, and the result.

Employee tenure for a sample of male workers

3.3, 3.9, 4.1, 3.3, 4.4, 3.3, 3.1, 4.1, 2.7, 4.9, 0.9, 4.6

Employee tenure for a sample of female workers

3.7, 4.2, 2.7, 3.6, 3.3, 1.1, 4.4, 4.4, 2.6, 1.5, 4.5, 2.0

B) A congressional representative claims that the median tenure for male workers is greater that the median tenure for female workers. The claim is based on the data shown above.

5) How would you est the representative's claim?

6) Can you use a parametric test, or do you need to use a nonparametric test?

7) State the null hypothesis and the alternative hypothesis.

8) Test the claim using alpha = 0.05. What can you conclude. Show your work, the process that you used, and the result.

Answer 1

A)

1. The representative's claim can be tested by using the below assumptions;

Statistical procedures require very few assumptions about the underlying population. They are often used when data is not from a normal population. Use the one-sample sign confidence intervals and test procedures to make inferences about a population median based on data from a random sample.

representative's claim can be tested by the use of one sample sign test for given specified value median=3.5.

2. we cannot use a parametric test, we have to use a nonparametric alternative to one sample Z and one sample T procedures.

By the use of Minitab output is

Sign test for median = Employee tenure

sign test of median = 3.500 versus ≠ 3.500

N below equal above Pmedian

Employee tenure 20 12 1 7 0.3593 3.300

3. from the given sample if the median is 3.5 yrs

then the Hypothesis is H0: median=3.5 and H1: not 3.5

4. Minitab uses these values to determine the p-value of 0.3593.

this value indicating that 35.93% of the chance that we would have obtained the sample median if the population median were actually 3.5.

Because the p-value is greater than 0.05, you fail to reject H0. Not enough evidence exists to conclude that the population median=3.5.