Question

For one binomial experiment, n₁ = 75 binomial trials produced r₁ = 45 successes. For a second independent binomial experiment, n₂ = 100 binomial trials produced r₂ = 65 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.

(a) Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)

(b) Compute p̂₁ - p̂₂.
p̂₁ - p̂₂ =

(c) Compute the corresponding sample distribution value. (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

(d) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

Answer 1

sample proportion of 1st binomial experiment is p1 = 45/75 = 0.6

and sample proportion of 2nd binomial experiment is p2 = 65/100 = 0.65

a) Poold probability of success for the two experiments is P-hat = (x1 + x2) / (n1 + n2) = (45+65)/(75+100) = 0.6286

b) p1 - p2 = 0.6 - 0.65 = -0.05

c) Test statistic :

d) P-value = 0.4981

since P-value > alpha 0.05 so we accept H0

Thus we conclude that the probabilities of success for the two binomial experiments are not different