Question

Use the sample data below to test the hypotheses

H ₀:  p ₁ =  p ₂ =  p ₃

H _a: Not all population proportions are the same

	Populations
Response	1	2	3
Yes	150	150	92
No	100	150	108

where  p _i is the population proportion of yes responses for population  i. Using a .05 level of significance. Use Table 12.4.

a. Compute the sample proportion for each population. Round your answers to two decimal places.

p̄ ₁ =  

p̄ ₂ =  

p̄ ₃ =  

b. Use the multiple comparison procedure to determine which population proportions differ significantly. Use a .05 level of significance. Round  p _i,  p_j and difference to two decimal places. Round critical value to four decimal places.

Comparison	p i	p j	Difference	n i	n j	Critical Value	Significant Diff > CV
1 vs 2							- Select your answer -YesNoItem 10
1 vs 3							- Select your answer -YesNoItem 17
2 vs 3							- Select your answer -YesNoItem 24

- Select your answer -1 and 21 and 32 and 3none of themItem 25

Answer 1

a)

p̅1=150/250=	0.6
p̅2=150/300=	0.5
p̅3=92/200 =	0.46

b)

for 2 df and 0.05 level X2 =

5.9915

As Criitcal value =√X2*√(p̅1*(1-p̅1)/n1+p̅2*(1-p̅2)/n2)

						critical val
Comparison	pi	pj	|abs diff|	ni	nj	value	significant diff >CV
1 vs 2	0.60	0.50	0.10	250	300	0.1037	not significant difference
1 vs 3	0.60	0.46	0.14	250	200	0.1149	significant difference
2 vs 3	0.50	0.46	0.04	300	200	0.1115	not significant difference

1 vs 3 are different