For one binomial experiment, ni = 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. O The Student's t. The number of trials is sufficiently large. O The standard normal. We assume the population distributions are approximately normal. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. The number of trials is sufficiently large. (c) State the hypotheses. O Ho: P1 = P2i H1: P1 * P2 O Ho: P1 = P2i Hị: P1 < P2 O Ho: P1 < Pzi Hị: P1 = P2 O Họ: P1 = P2i Hị: P1 > P2 (d) Compute p1 -p^2- 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 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 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. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
For one binomial experiment, ni = 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. O The Student's t. The number of trials is sufficiently large. O The standard normal. We assume the population distributions are approximately normal. O The Student's t. We assume the population distributions are approximately normal. O The standard normal. The number of trials is sufficiently large. (c) State the hypotheses. O Ho: P1 = P2i H1: P1 * P2 O Ho: P1 = P2i Hị: P1 < P2 O Ho: P1 < Pzi Hị: P1 = P2 O Họ: P1 = P2i Hị: P1 > P2 (d) Compute p1 -p^2- 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 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 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. O At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:For one binomial experiment, ni = 75 binomial trials produced ri = 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.
O The Student's t. The number of trials is sufficiently large.
O The standard normal. We assume the population distributions are approximately normal.
The Student's t. We assume the population distributions are approximately normal.
O The standard normal. The number of trials is sufficiently large.
(c) State the hypotheses.
O Ho: P1 = P2i H1: P1 * P2
%3D
O Ho: P1 = P2i Hi: P1 < P2
O Ho: P1 < P2i H1: P1 = P2
O Ho: P1 = P2i H1: P1 > P2
%3D
(d) Compute p1 - p^2-
p'1-P°2 =
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 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 reject the null hypothesis and conclude the data are statistically significant.
At the a = 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 fail to reject the null hypothesis and conclude the data are statistically significant.
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