In: Statistics and Probability
You wish to test the following claim (HaHa) at a significance
level of α=0.002α=0.002.
Ho:p1=p2Ho:p1=p2
Ha:p1>p2Ha:p1>p2
You obtain 494 successes in a sample of size n1=565n1=565 from the
first population. You obtain 250 successes in a sample of size
n2=307n2=307 from the second population.
Which test would you use?
Here, we use 2-PropZTest
p1cap = X1/N1 = 494/565 = 0.8743
p1cap = X2/N2 = 250/307 = 0.8143
pcap = (X1 + X2)/(N1 + N2) = (494+250)/(565+307) = 0.8532
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Rejection Region
This is right tailed test, for α = 0.002
Critical value of z is 2.88.
Hence reject H0 if z > 2.88
Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.8743-0.8143)/sqrt(0.8532*(1-0.8532)*(1/565 + 1/307))
z = 2.39
P-value Approach
P-value = 0.0084
As P-value >= 0.002, fail to reject null hypothesis.