Question

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?

• T-Test (Matched Pairs)
• 2-SampTTest (not pooled)
• 2-PropZInterval
• 2-PropZTest
• 2-SampTTest (pooled)
• 2-SampTInterval

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Answer 1

Here, we use 2-PropZTest

p1cap = X1/N1 = 494/565 = 0.874
p1cap = X2/N2 = 250/307 = 0.814
pcap = (X1 + X2)/(N1 + N2) = (494+250)/(565+307) = 0.853

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 = (0.874-0.814)/sqrt(0.853*(1-0.853)*(1/565 + 1/307))
z = 2.39

P-value Approach
P-value = 0.0084
As P-value >= 0.002, fail to reject null hypothesis.