Question

Consider the following competing hypotheses and accompanying sample data. H0: p1 − p2 ≥ 0 HA: p1 − p2 < 0 x1 = 248 x2 = 266 n1 = 444 n2 = 444

a. At the 1% significance level, find the critical value(s).

b. Calculate the value of the test statistic.

Answer 1

Test Statistic :-

is the pooled estimate of the proportion P
= ( x1 + x2) / ( n1 + n2)
= ( 248 + 266 ) / ( 444 + 444 )
= 0.5788

Z = -1.2221

Test Criteria :-
Reject null hypothesis if

Critical values

= -1.2221 > -2.33, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = P ( Z < -1.2221 )
P value = 0.1108
Reject null hypothesis if P value <
Since P value = 0.1108 > 0.01, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0