Question

For one binomial experiment, n1 = 75 binomial trials produced r1 = 30 successes. For a second independent binomial experiment, n2 = 100 binomial trials produced r2 = 50 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

a) =0.457 (answer to three decimal places)

b)

c)

Z= -1.31 (answer to three decimal places)

d) The p-value is p = 0.1888, and since p=0.1888≥0.05, it is concluded that the null hypothesis is not rejected

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population proportion p1 is different than p2 , at the 0.05 significance level.