Examples Chi-Square Analysis

Question 1 (11.13) A computer science major claimed to have written a program that randomly generates intergers from 1 to 10.
The program generates the following data. Use a 5% level of significance to test the claim.
 

Integers	Frequency
1-10	6
11-20	6
21-30	13
31-40	9
41-50	13
51-60	11
61-70	8
71-80	12
81-90	10
91-100	12

Solution:
 

Chi Square Statistics - From table / Program  Enter alpha  0.05  Enter Degree of Freedom  9  1 - alpha = 0.95  Ch-Square Statistics is  16.9189776  ( 1- alpha) Enter chi-sq test statistics  6.4  P-value is 0.699312575

Decision: Do not reject H0 , since Chi-square Stat < Chi-Square Table H0: p=0.10 for each category (equally likely),  Ha: H0 is not true,  alpha = 0.05 Observed chi-square statistics = 6.40, df = 10-1 = 9, Critical chi-square Table = 16.919 The data do not dispute the claim

Question 2 (11.19) A group of employees in a large firm claimed that gender and yearly salary are dependent.
For the following data, test the claim using a 10% level of significance.
 

	Salary (thousands of dollars)
	Less than 30	At leaset 30 but less than 35	At least 35 but less than 40	At least 40
Females	12	30	20	13
Males	7	26	31	27

Solution:
 

Chi Square Statistics  Enter alpha 0.1  Enter Degree of Freedom 3  1 - alpha = 0.9  Ch-Square Statistics is 6.251388746 ( 1- alpha) Enter chi-sq test statistics 7.4  P-value is 0.060184327

Decision: Reject H0 , since Chi-square Stat > Chi-Square Table and P-value < 0.05 H0: Characteristics of sex and salaries are independent  Ha: Characteristics of sex and salaries are related  alpha = 0.05 Observed chi-square statistics = 7.40, df = (4-1)(2-1)= 3, Critical chi-square Table = 6.251 The data suggest that the charateristics of sex and salary are related.

Question 3 (11.26 - 11.22) Former patients from 3 treatment centers were sampled and asked whether
they were satisfied with the care they received in these centers. The results are as follows: Use significance level of 5%.
 

	Are you satisfied with treatment?
	Yes	No
Center A	54	21
Center B	58	32
Center C	42	38

 

Chi Square Statistics Enter alpha 0.05 Enter Degree of Freedom 2 1 - alpha = 0.95 Ch-Square Statistics is 5.991464547 ( 1- alpha) Enter chi-sq test statistics 6.4581 P-value is 0.039595096

Decision: Reject H0 , since Chi-square Stat > Chi-Square Table and P-value < 0.05 H0: Treatment Centers are homegenious with respect to patient statisfaction  Ha:  H0 is not true, alpha = 0.05 Observed chi-square statistics = 6.4581, df = (3-1)(2-1)= 2, Critical chi-square Table = 5.9915 The data suggest that the treatment centers are not the same with respect to patient statisfaction.