For one binomial experiment, n₁ = 75 binomial trials produced ₁ = 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.USE SALT(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.O The Student's t. We assume the population distributions are approximately normal.O The standard normal. We assume the population distributions are approximately normal.O The standard normal. The number of trials is sufficiently large.O The Student's t. The number of trials is sufficiently large.(c) State the hypotheses.O Hot P1 = P₂ H₁: P1 * P2O Ho: P₁ = P₂i H₁: P₁ < P2O Ho: P₁ = P₂² H₂i Pq > P2Ho¹ P1 P₂ H₁¹ P₁ = P2(d) Compute P₁-P2.P₁ P₂ = |Compute the corresponding sample distribution value. (Test the difference P₁ P₂. Do not use rounded values. Round your final answer to two decimal places.)(e) Find the P-value of the sample test statistic. (Round your answer to four decimal places.)(f) Conclude the test.O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.O At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.O At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.O At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.(g) Interpret the results.ⒸFail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.O Reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.O Fail to reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.O Reject the null hypothesis, there is insufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.

It is given that, r1 = 30, n1 = 75. Also, r2 = 50, n2 = 100. The pooled sample proportion can be…

(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 Student's t. We assume the population distributions are approximately normal. The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. Ho! PqPgl H₂¹ P1 P₂ Ho! P₂ P₂ H₂¹ P1 P₂ Ho! PyP₂² H₂¹ Pg > P₂ ܕO Ho! Pa < Pgs HE P: * P

(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 Student's t. We assume the population distributions are approximately normal. The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. Ho! PqPgl H₂¹ P1 P₂ Ho! P₂ P₂ H₂¹ P1 P₂ Ho! PyP₂² H₂¹ Pg > P₂ ܕO Ho! Pa < Pgs HE P: * P

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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