Each month the U.S. Bureau of Labor Statistics publishes a variety of unemployment statistics, including the number of individuals who are unemployed and the mean length of time the individuals have been unemployed. For November 2005, the Bureau of Labor Statistics reported that the national mean length of time of unemployment was 14.6 weeks.
The mayor of Philadelphia requested a study on the status of unemployment in the Philadelphia area. A sample of 50 unemployed residents of Philadelphia included data on their age and the number of weeks without a job. A portion of the data collected in November 2005 follows.
|
Age
|
Weeks
|
Age
|
Weeks
|
Age
|
Weeks
|
|
56
|
22
|
22
|
11
|
25
|
12
|
|
35
|
19
|
48
|
6
|
25
|
1
|
|
22
|
7
|
48
|
22
|
59
|
33
|
|
57
|
37
|
25
|
5
|
49
|
26
|
|
40
|
18
|
40
|
20
|
33
|
13
|
You are asked to write a managerial report that covers the following questions.(Answers are graded on the reasoning used to arrive at an answer, not simply on the answer. Thus, show the reasons and calculation process.)
1. Use descriptive statistics to summarize the data. (Including sample mean, standard deviation, median, mode, maximum, minimum, skewness.)
2. Use the graphical method and the numerical method to show whether there is a relationship between the age of an unemployed individual and the number of weeks of unemployment.
3. Develop 95% confidence interval estimate of the mean age of unemployed individuals in Philadelphia.
4. Conduct a hypothesis test to determine whether the mean duration of unemployment in Philadelphia is greater than the national mean duration of 14.6 weeks. Use a 0.01 level of significance. What is your conclusion?