Question

You challenge a friend to a bottle flipping contest. Your friend flips 64 out of 226 bottles that land upright. You flip 72 out of 238 bottles that land upright. Is there evidence, at a 5% level of significance, that there is a difference in proportion of bottles that land upright between you and your friend?

Calculate the following:

Standard Error :

Standardized Test Statistic :

p-value:

Should the null hypothesis be rejected (yes or no)?

Answer 1

To Test ;-

H0 :- P1 = P2

H1 :- P1 P2

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 64 + 72 ) / ( 226 + 238 )
= 0.2931


Z = -0.4573

Test Criteria :-
Reject null hypothesis if

= -0.4573 > -1.96, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( Z < -0.4573 )
P value = 0.6474
Reject null hypothesis if P value <
Since P value = 0.6474 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Yes,  null hypothesis be rejected

Standard Error =