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Corporate raider A has been successful in 10 of 30 takeover attempts. Another corporate raider B...

Corporate raider A has been successful in 10 of 30 takeover attempts. Another corporate raider B has been successful in 20 of 50 takeover bids. Corporate raider B is bragging that they have had the greater success. At the .01 level of significance, you want to conduct a test of hypothesis to determine if there is evidence that corporate raider A has a lower proportion of success than corporate raider B. Select the appropriate null and alternative hypotheses from below.

Ho: πA ≤ πB
H1: πA > πB

Ho: πA ≥ πB
H1: πA < πB

Ho: µA ≥µB
H1: µA <µB

Ho: πA = πB
H1: πA ≠ πB

Ho: πA > πB
H1: πA ≤ πB
math   Statistics-And-Probability   
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Answer #1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 >= p2
Alternate Hypothesis, Ha: p1 < p2

Ho: πA ≥ πB
H1: πA < πB

Option B

p1cap = X1/N1 = 10/30 = 0.3333
p1cap = X2/N2 = 20/50 = 0.4
pcap = (X1 + X2)/(N1 + N2) = (10+20)/(30+50) = 0.375

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.3333-0.4)/sqrt(0.375*(1-0.375)*(1/30 + 1/50))
z = -0.6

P-value Approach
P-value = 0.2743
As P-value >= 0.01, fail to reject null hypothesis.

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