For one binomial experiment,n₁= 75binomial trials producedr₁=30 successes. For a second independent binomial experiment,n₂= 100binomial trials producedr₂=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'st. The number of trials is sufficiently large.
• The Student'st. We assume the population distributions are approximately normal.

(c)State the hypotheses.

• H₀:p₁=p₂;H₁:p₁<p₂
• H₀:p₁=p₂;H₁:p₁p₂
• H₀:p₁<p₂;H₁:p₁=p₂
• H₀:p₁=p₂;H₁:p₁>p₂

(d)Computep₁p₂.

p₁p₂=

Compute the corresponding sample distribution value. (Test the differencep₁p₂. Do not use rounded values. Round your final answer to two decimal places.)

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

(f)Conclude the test.

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

(g)Interpret the results.

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