Assume that we have selected two independent random samples from populations hav

Question

Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that picture 1 = 800/1000 = 0.8 and picture 2 = 950/1000 = 0.95. Test H0: p1 – p2 > –.12 versus Ha: p1 – p2 < –.12 by using a p-value and by setting equal to .10, .05, .01, and .001. How much evidence is there that p2 exceeds p1 by more than .12? (Round p-value to 4 decimal and z value to 2 decimal places. Negative amount should be indicated by a minus sign.) z = p - value= Reject H0 at = , but not at = ; rev: 04_07_2016_QC_CS-48200, 04_17_2017_QC_CS-86295, 02_26_2018_QC_CS-119770 Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that picture 1 = 800/1000 = 0.8 and picture 2 = 950/1000 = 0.95. Test H0: p1 – p2 > –.12 versus Ha: p1 – p2 < –.12 by using a p-value and by setting equal to .10, .05, .01, and .001. How much evidence is there that p2 exceeds p1 by more than .12? (Round p-value to 4 decimal and z value to 2 decimal places. Negative amount should be indicated by a minus sign.) z = p - value= Reject H0 at = , but not at = ; rev: 04_07_2016_QC_CS-48200, 04_17_2017_QC_CS-86295, 02_26_2018_QC_CS-119770 Assume that we have selected two independent random samples from populations having proportions p1 and p2 and that picture 1 = 800/1000 = 0.8 and picture 2 = 950/1000 = 0.95. Test H0: p1 – p2 > –.12 versus Ha: p1 – p2 < –.12 by using a p-value and by setting equal to .10, .05, .01, and .001. How much evidence is there that p2 exceeds p1 by more than .12? (Round p-value to 4 decimal and z value to 2 decimal places. Negative amount should be indicated by a minus sign.) z = p - value= Reject H0 at = , but not at = ; rev: 04_07_2016_QC_CS-48200, 04_17_2017_QC_CS-86295, 02_26_2018_QC_CS-119770

Explanation / Answer

Sol:

H0:p1-p2=0.12

H1:p1-p2<=0.12

Left tail test

Z=p1^-p2^-(p1-p2)/sqrt(p1^(1-p1^)/n1+p2^(1-p2^)/n2)

=((0.8-0.95)-0.12)/(sqrt(0.8*(1-0.8)/1000+0.95(1-0.95)/1000))

Z=-0.15-0.12/sqrt(0.8*0.2+0.95*0.05/1000)

Z=-18.74

P=0.0000

REJECT H0 AT ALPHA=0.05

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