Independent random samples of n1 140 andn2 140 observations were randomly selected

Chapter 9, Problem 42

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Independent random samples of n1 140 andn2 140 observations were randomly selected frombinomial populations 1 and 2, respectively. Sample 1had 74 successes, and sample 2 had 81 successes.a. Suppose you have no preconceived idea as to whichparameter, p1 or p2, is the larger, but you want onlyto detect a difference between the two parameters ifone exists. What should you choose as the alternativehypothesis for a statistical test? The nullhypothesis?b. Calculate the standard error of the difference inthe two sample proportions, ( p1 p2). Make sureto use the pooled estimate for the common valueof p.c. Calculate the test statistic that you would use forthe test in part a. Based on your knowledge of thestandard normal distribution, is this a likely orunlikely observation, assuming that H0 is true andthe two population proportions are the same?d. p-value approach: Find the p-value for the test.Test for a significant difference in the populationproportions at the 1% significance level.e. Critical value approach: Find the rejection regionwhen a .01. Do the data provide sufficient evidenceto indicate a difference in the populationproportions?