Question

Complete the following chi square test:

Show All Work.

Example Chi Sq.

40% of Americans say that their favorite pastime is sports, 40% say that it’s time with their family, and 20% name something else. A survey of your neighborhood finds that 10 people report a preference for sports, 15 for being with their families, and 5 something else. Do your neighbors differ from Americans overall?

Activity	Observed	Expected	EF	O-E	(O-E)2	(O-E)2/E
Sport	10	.4	12	-2	4	.33
Family	15	.4	12	3	9	.75
Other	5	.2	6	-1	1	.17
	30					2 = ∑ (O-E)2/E = 1.25

Is Paris, Chicago, or NY the most romantic city?

City	Observed	Expected	EF	O-E	(O-E)2	(O-E)2/E
Chicago	2	.33
New York	40	.33
Paris	58	.33
	100					2 = ∑ (O-E)2/E =

Please show all steps.

Answer 1

ANSWER::

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
sports	10	0.400	12.00			0.333
family	15	0.400	12.00			0.750
something else	5	0.200	6.00			0.167

chi square test statistic,X² = Σ(O-E)²/E

= 0.333+ 0.750+ 0.167

=   1.250             
                  
level of significance, α=   0.05              
Degree of freedom=k-1

=   3   -   1  

=   2
                  
P value =   0.5353   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value >α , Do not reject Ho          

so, neighbors do not differ from Americans overall

................

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
chicago	2	0.333	33.33			29.453
NY	40	0.333	33.33			1.333
PARIS	58	0.333	33.33			18.253

chi square test statistic,X² = Σ(O-E)²/E

=29.453+1.333+18.253

=   49.040             
                  
level of significance, α=   0.05              
Degree of freedom=k-1=  

3   -   1  

=   2
                  
P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho               

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