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

Fam 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

NY 40 .33

Paris 58 .33

100 2 = ∑ (O-E)2/E =

Is there a significant correlation between these two sets of numbers?

Weight Time

46 44

55 27

61 24

75 24

64 36

75 36

71 44

59 44

64 120

67 29

Answer 1

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 =   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 =   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                  
...................

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	637	428	738.1	7203.6	-143.60
mean	63.70	42.80	SSxx	SSyy	SSxy

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.0623

correlation hypothesis test      
Ho:   ρ = 0  
Ha:   ρ ╪ 0  
n=   10  
alpha,α =    0.05  
correlation , r=   -0.0623  
t-test statistic = r*√(n-2)/√(1-r²) =        -0.176
DF=n-2 =   8  
p-value =    0.8643  
Decison:   P value > α, So, Do not reject Ho  
SO, There is not any correlation

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

THANKS

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