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For one binomial experiment, n, - 75 binomial trials produced r, - 30 successes. For a second independent binomial experiment, n - 100 binomial trials produced r, - 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. A 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 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. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. O Hg: P - Pai HiP> P2 O Hg: P - Pai HạiPz * P2 O Hạ: P < Pzi HP"P2 (d) Compute p, - P2 Compute the corresponding sample distribution value. (Test the difference p, -P,. 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.) () Conclude the test. O At the a- 0.0S level, we 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 a- 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 fail to reject the null hypothesis and conclude the data are not statistically significant. (9) Interpret the results. O 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. 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 Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.

For one binomial experiment, n, - 75 binomial trials produced r, - 30 successes. For a second independent binomial experiment, n - 100 binomial trials produced r, - 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. A 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 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. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. O Hg: P - Pai HiP> P2 O Hg: P - Pai HạiPz * P2 O Hạ: P < Pzi HP"P2 (d) Compute p, - P2 Compute the corresponding sample distribution value. (Test the difference p, -P,. 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.) () Conclude the test. O At the a- 0.0S level, we 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 a- 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 fail to reject the null hypothesis and conclude the data are not statistically significant. (9) Interpret the results. O 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. 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 Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.

College Algebra
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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For one binomial experiment, n, = 75 binomial trials produced r, = 30 successes. For a second independent binomial experiment, n, = 100 binomial trials produced r, = 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. A 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 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. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. O H: P = P2i HP1< P2 O Hạ: P = P2i H:P1 > P2 O Ho: P - P2i H,:P * P2 O Hạ: P, < Pzi H: P1 = P2 (а) Compute p, -р- P1 - P2 = Compute the corresponding sample distribution value. (Test the difference p, - P,: 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 a = 0.05 level, we 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 a = 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 fail to reject the null hypothesis and conclude the data are not statistically significant. (9) Interpret the results. O 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. 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 Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.
Transcribed Image Text:For one binomial experiment, n, = 75 binomial trials produced r, = 30 successes. For a second independent binomial experiment, n, = 100 binomial trials produced r, = 50 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ. A 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 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. We assume the population distributions are approximately normal. O The Student's t. The number of trials is sufficiently large. (c) State the hypotheses. O H: P = P2i HP1< P2 O Hạ: P = P2i H:P1 > P2 O Ho: P - P2i H,:P * P2 O Hạ: P, < Pzi H: P1 = P2 (а) Compute p, -р- P1 - P2 = Compute the corresponding sample distribution value. (Test the difference p, - P,: 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 a = 0.05 level, we 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 a = 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 fail to reject the null hypothesis and conclude the data are not statistically significant. (9) Interpret the results. O 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. 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 Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.
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