Question

This is a written, statistical report, not simply a collection of different types of Excel output. It is not necessary to include the formulas you used or a copy of the dataset. When answering the questions, make sure to include any relevant statistics and/or the results of your calculations. Like any other written report, you will want to start with an introductory paragraph or problem statement and finish with a conclusion that summarizes the information presented.

1. Use descriptive statistics to summarize the data.

2. Develop a 95% confidence interval estimate of the mean age of unemployed individuals in Philadelphia.

3. 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 .01 level of significance. What is your conclusion?

4. Is there a relationship between the age of an unemployed individual and the number of weeks of unemployment? Explain.

Age	Weeks
56	22
35	19
22	7
57	37
40	18
22	11
48	6
48	22
25	5
40	20
25	12
25	1
59	33
49	26
33	13
56	15
20	17
31	11
27	17
23	3
45	17
29	14
31	4
59	39
39	7
35	12
44	38
27	14
24	6
27	7
45	25
42	33
45	16
44	12
21	13
31	16
42	4
23	14
51	31
27	7
30	10
33	23
32	8
22	7
51	12
50	16
21	9
38	5
26	8
55	35

Answer 1

a)

Age		Weeks
Mean	36.6	Mean	15.54
Standard Error	1.6893	Standard Error	1.4038
Median	34	Median	13.5
Mode	27	Mode	7
Standard Deviation	11.9455	Standard Deviation	9.9267
Sample Variance	142.6939	Sample Variance	98.5392
Kurtosis	-1.1451	Kurtosis	0.0537
Skewness	0.3573	Skewness	0.9108
Range	39	Range	38
Minimum	20	Minimum	1
Maximum	59	Maximum	39
Sum	1830	Sum	777
Count	50	Count	50

b)

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   49          
't value='   tα/2=   2.010   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   11.9455   / √   50   =   1.6893
margin of error , E=t*SE =   2.0096   *   1.6893   =   3.3949
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    36.60   -   3.394861   =   33.2051
Interval Upper Limit = x̅ + E =    36.60   -   3.394861   =   39.9949
95%   confidence interval is (   33.21   < µ <   39.99   )

c)

Ho :   µ =   14.6                  
Ha :   µ >   14.6       (Right tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   9.9267                  
Sample Size ,   n =    50                  
Sample Mean,    x̅ = ΣX/n =    15.5400                  
                          
degree of freedom=   DF=n-1=   49                  
                          
Standard Error , SE = s/√n =   9.9267   / √    50   =   1.4038      
t-test statistic= (x̅ - µ )/SE = (   15.540   -   14.6   ) /    1.4038   =   0.670
                          
critical t value, t* =        2.4049   [Excel formula =t.inv(α/no. of tails,df) ]              
                          
p-Value   =   0.2531   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis                       
Conclusion: There is not enough evidence to conclude that the mean duration of unemployment in Philadelphia is greater than the national mean duration of 14.6 weeks

d)

correlation coefficient between two variables=0.6591

so, there is moderate positive linear relationship between the age of an unemployed individual and the number of weeks of unemployment