Question

# Use the sample data below to test the hypotheses H 0:  p 1 =  p 2 =  p 3...

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.

1 =

2 =

3 =

b. Use the multiple comparison procedure to determine which population proportions differ significantly. Use a .05 level of significance. Round  p i,  pj 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

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