Question

Passing the ball between two players during a soccer game is a critical skill for the success of a team. A random sample of passes made by two teams in the 2010 World Cup was​ drawn, and the number of successful passes in each sample was counted. Construct a ​95% confidence interval to estimate the difference in accuracy between the two​ countries' passes. What conclusions can be​ made?

x1=74

n1=78

x2=73

n2=93

The 95% confidence interval is (___,___)

What conclusions can be​ made?

A.Because this confidence interval

does not

include​ zero, there

is no

evidence that the successful pass rates are different between these two countries.

B.Because this confidence interval

does

include​ zero, there

is

evidence that the successful pass rates are different between these two countries.

C.Because this confidence interval

does not

include​ zero, there

is

evidence that the successful pass rates are different between these two countries.

D.Because this confidence interval

does

include​ zero, there

is no

evidence that the successful pass rates are different between these two countries.

Answer 1

p̂1 = 74 / 78 = 0.9487
p̂2 = 73 / 93 = 0.7849

(p̂1 - p̂2) ± Z(α/2) * √( ((p̂1 * q̂1)/ n1) + ((p̂2 * q̂2)/ n2) )
Z(α/2) = Z(0.05 /2) = 1.96
Lower Limit = ( 0.9487 - 0.7849 )- Z(0.05/2) * √(((0.9487 * 0.0513 )/ 78 ) + ((0.7849 * 0.2151 )/ 93 ) = 0.067
upper Limit = ( 0.9487 - 0.7849 )+ Z(0.05/2) * √(((0.9487 * 0.0513 )/ 78 ) + ((0.7849 * 0.2151 )/ 93 )) = 0.2606
95% Confidence interval is ( 0.0670 , 0.2606 )
( 0.0670 < ( P1 - P2 ) < 0.2606 )

C.Because this confidence interval does not include​ zero, there is evidence that the successful pass rates are different between these two countries.