For one binomial experiment, n 1 = 75 binomial trials produced r 1 = 45 successes. For a second independent binomial experiment, n 2 = 100 binomial trials produced r 2 = 65 successes. At the 5% level...


For one binomial experiment,


n1 = 75

 binomial trials produced


r1 = 45

 successes. For a second independent binomial experiment,


n2 = 100

 binomial trials produced


r2 = 65

 successes. At the 5% level of significance, test the claim that the probabilities of success for the two binomial experiments differ.



Compute the pooled probability of success for the two experiments. (Round your answer to three decimal places.)



Check Requirements: What distribution does the sample test statistic follow? Explain.



The standard normal. The number of trials is sufficiently large.


The Student'st. We assume the population distributions are approximately normal.


The Student'st. The number of trials is sufficiently large.


The standard normal. We assume the population distributions are approximately normal



(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 >p
2


H
0:p
1 p
2;H
1:p
1 =p
2









Compute p̂1 − p̂2.

p̂1 − p̂2 =




Compute the corresponding sample distribution value. (Test the differencep
1 −p
2. Do not use rounded values. Round your final answer to two decimal places.)



Find theP-value of the sample test statistic. (Round your answer to four decimal places.)




Conclude the test.


At the ? = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.


At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.


At the ? = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.


At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.







Interpret the results.



Fail to reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.


Reject the null hypothesis, there is sufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.


Fail to reject the null hypothesis, there is insufficient evidence that the probabilities of success for the two binomial experiments differ.


Reject the null hypothesis, there is insufficient evidence that the proportion of the probabilities of success for the two binomial experiments differ.









Jun 09, 2022
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