For ane binamial experiment, n - 75 binomial trials produced r, - 60 successes. For a second independent binomial experiment, n - 100 binamial trials produced r - 85 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.) 0.829 (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 Student's t. The number of trials is sufficiently large. O The standard normal. We assume the population distributions are approximately normal. • The standard normal. The number of trials is sufficiently large. (c) State the hypotheses. O Họ: P < Pai Hy: P: " P2 O Họ: P " Pai H;: P; < P2 O Hg: P " Pzi Hi: P; > P2 O Ho: P " Pai Hy:P; * Pz (d) Compute p, - P2- P - P2 - 0.05 Compute the corresponding sample distribution value. (Test the difference p1 - Pz. Do not use rounded values. Round your final answer to two decimai places.) -0.87 (e) Find the P-value of the sample test statistic. (Round your answer to four decimal places.) 0.3844 () 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 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. O At the a- 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (9) Interpret the results.

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

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.