**Hypothesis Testing for Binomial Experiments**For one binomial experiment, \( n_1 = 75 \) binomial trials produced \( x_1 = 30 \) successes. For a second independent binomial experiment, \( n_2 = 100 \) binomial trials produced \( x_2 = 50 \) 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.)**\[ \hat{p} = \]**(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. We assume the population distributions are approximately normal.- The Student's t. The number of trials is sufficiently large.**(c) State the hypotheses.**- \( H_0: p_1 = p_2; \, H_1: p_1 < p_2 \)- \( H_0: p_1 = p_2; \, H_1: p_1 > p_2 \)- \( H_0: p_1 = p_2; \, H_1: p_1 \neq p_2 \)- \( H_0: p_1 < p_2; \, H_1: p_1 = p_2 \)**(d) Compute \(\hat{p}_1 - \hat{p}_2\):**\[ \hat{p}_1 - \hat{p}_2 = \]Compute the corresponding sample distribution value. (Test the difference \( p_1 - p_2 \). 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.)**\[ \text{P-value} = \]**(f) Conclude the test.**- At the \(\alpha = 0.05\) level, we reject the null hypothesis and conclude the data are statistically significant.- At the \(\alpha = 0.05\) level, we reject the null hypothesis and

Given, sample 1 : Binomial trials = n1 = 75 Number of successes = r1 = 30 Sample proportion = p^1 =…

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.