Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
Old design samples(n1) = 220
New design samples (n2) = 220
P1 = 81/220 = 0.368 ; P2 = 41/220 = 0.186
Null hypothesis : p1 - p2 ≥ 0.05
Alternative hypothesis : p1 - p2 < 0.05
Using the test statistic formula :
t = (P1 - P2) / √[P(1-P)(1/n1 + 1/n2)]
P = (81 + 41)/(220 + 220) = 122/440 = 0.277
1 - P = 0.723
t = (0.368 - 0.186) / (√(0.277(0.723)(1/220 + 1/220)))
t = 4.265
P value from z test at α = 0.05
P value = 0.00002
Test for significance at α = 0.01 ;
Test for significance at α = 0.1
Result is significant at both α levels, hence reject the Null.
