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fodschoole. org bookmarks Classes SIS K-12 360 Launch For one binomial experiment, \( n_{1}=75 \) binomial trials produced \( r_{1}=30 \) successes. For a second independent binomial experiment, \( n_{2}=100 \) binomial trials produced \( r_{2}=50 \) 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.) \( \square \) (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. \( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1}<p_{2} \) \( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1} \neq p_{2} \) \( H_{0}: p_{1}<p_{2} ; H_{1}: p_{1}=p_{2} \) \( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1}>p_{2} \) (d) Compute \( \hat{p}_{1}-p_{2} \hat{p}_{2} \). \( \hat{p_{1}-\hat{p}_{2}}= \) \( \square \) Compute the corresponding sample distribution value. (Test the difference \( p_{1}-p_{2} \). Do not use rounded values. Round your final answer to two decim olaces.)

          fodschoole. org bookmarks
Classes
SIS K-12 360
Launch
For one binomial experiment, \( n_{1}=75 \) binomial trials produced \( r_{1}=30 \) successes. For a second independent binomial experiment, \( n_{2}=100 \) binomial trials produced \( r_{2}=50 \) 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.) \( \square \)
(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.
\( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1}<p_{2} \)
\( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1} \neq p_{2} \)
\( H_{0}: p_{1}<p_{2} ; H_{1}: p_{1}=p_{2} \)
\( H_{0}: p_{1}=p_{2} ; H_{1}: p_{1}>p_{2} \)
(d) Compute \( \hat{p}_{1}-p_{2} \hat{p}_{2} \).
\( \hat{p_{1}-\hat{p}_{2}}= \) \( \square \)
Compute the corresponding sample distribution value. (Test the difference \( p_{1}-p_{2} \). Do not use rounded values. Round your final answer to two decim olaces.)

fodschoole. org bookmarks
Classes
SIS K-12 360
Launch
For one binomial experiment, n1=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.
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.
H0: p1=p2 ; H1: p1<p2
H0: p1=p2 ; H1: p1≠ p2
H0: p1<p2 ; H1: p1=p2
H0: p1=p2 ; H1: p1>p2
(d) Compute p̂1-p2p̂2.
p̂1̂-̂p̂̂̂2̂= □
Compute the corresponding sample distribution value. (Test the difference p1-p2. Do not use rounded values. Round your final answer to two decim olaces.)

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