Question

How old are college students? The national age distribution for the youth is shown below.
       National Age Distribution for the college
Age Under 26 26–35 36–45 46–55 Over 55 Percentage 39% 25% 16% 12% 8%

The Mountain Colleges took a random sample of 212 students and obtained the following sample distribution.
       Sample Distribution, Mountain Colleges
Age Under 26 26–35 36–45 46–55 Over 55 Number of students 65 73 41 21 12        Is the sample age distribution for the   Mountain Colleges a good fit to the national distribution? Use  = 0.05.

i. A study to determine if management style affects the number of sick days taken by employees in a department was conducted. Three departments with the same number of employees were studied. The management style used in one department was top-down, with employees having little input into decisions. In another department, quality-control experts made recommendations. In the last department, the management gathered input informally from the employees. The total number of sick days taken per month by all the employees in the department was recorded. For a random sample of 3 months, the numbers follow:
Top-down management 19 34 28    Quality teams 16 21 15    Informal input 15 12 14                  Test if the mean number of sick days for departments managed in the various styles are      
                 different. Use  = 0.05.

Answer 1

Ho:   sample age distribution for the   Mountain Colleges is a good fit to the national distribution

H1: sample age distribution for the   Mountain Colleges is not a good fit to the national distribution

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
65	0.390	82.68	-17.68		3.781
73	0.250	53.00	20.00		7.547
41	0.160	33.92	7.08		1.478
21	0.120	25.44	-4.44		0.775
12	0.080	16.96	-4.96		1.451

chi square test statistic,X² = Σ(O-E)²/E =   15.031              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   5   -   1   =   4
                  
P value =   0.0046   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho  

              
There is enough evidence to conlcude that sample age distribution for the   Mountain Colleges is not a good fit to the national distribution

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