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) Check Requirements: What distribution does the sample test statistic follow? Explain. The standard normal. We assume the population distributions are approximately normal.The standard normal. The number of trials is sufficiently large. The Student's t. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal. (c) State the hypotheses. H0: p1 = p2; H1: p1 ≠ p2H0: p1 = p2; H1: p1 > p2 H0: p1 < p2; H1: p1 = p2H0: p1 = p2; H1: p1 < p2 Compute p̂1 − p̂2. p̂1 − p̂2 = Compute the corresponding sample distribution value. (Test the difference p1 − p2. Do not use rounded values. Round your final answer to two decimal places.) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter9: Counting And Probability

Section9.3: Binomial Probability

Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...

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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)

Check Requirements: What distribution does the sample test statistic follow? Explain.

The standard normal. We assume the population distributions are approximately normal.The standard normal. The number of trials is sufficiently large. The Student's t. The number of trials is sufficiently large.The Student's t. We assume the population distributions are approximately normal.

(c)

State the hypotheses.

H₀: p₁ = p₂; H₁: p₁ ≠ p₂H₀: p₁ = p₂; H₁: p₁ > p₂ H₀: p₁ < p₂; H₁: p₁ = p₂H₀: p₁ = p₂; H₁: p₁ < p₂

Compute p̂₁ − p̂₂.

p̂₁ − p̂₂ =

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

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

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