sample consists of 2000 people with 1439 of them having the

sample consists of 2000 people with 1439 of them having the same common attribute. Compare the results from a hypothesis test of p P2 (with a 0.05 significance What is the conclusion based on the hypothesis test? ) More

Solution

Sample X N Sample proportion
1 11 20 0.550000
2 1439 2000 0.719500

Test:H0: p1 =p2 ag. H1 : p1 not equals p2...
Difference = p1- p2
Estimate for difference: p1-p2 = -0.1695..

pooled sample proportion =p = ( p1*20 + p2*2000 ) / (2000+20) = 0.7178

standard error = SE = sqrt{ p * ( 1 - p ) * [ (1/n₁) + (1/n₂) ] } = 0.101138323082992 ....

test statistic = -0.1695 /  0.101138323082992 = -1.675923...
p-value = 0.09375328...

critical values = + or - 1.96..

test statistic is outside of the critical region...i.e, | test stat | < | critical value |.....

so, we accept H0...there is no evidence to conclude otherwise..

95% CI for difference: (-0.388419, 0.0494194).....

since 0 is inside(belonging to) the interval we should accept H0...

THE results are same..since the hypothesis test concludes that p1 = p2 and confidence interval concludes that p1 = p2...