A Pew Poll asked randomly selected young men, between 20 and 30 years of age, \"

Question

A Pew Poll asked randomly selected young men, between 20 and 30 years of age, "Do you consider being successful in a high-paying career or profession one of the most important goals in your life?" This question was part of a poll given in 1977 and in 2015. The answers are summarized below. a. Find and compare the sample proportions of those who had high-paying career goals in 2015 and those who had such goals in 1997. Write a complete sentence explaining your results. b. Assume that the conditions necessary for using a confidence interval are met, and find the 95% confidence interval for the difference in the proportions of interest. Interpret your results using complete sentences. Program used: ________ 95% Confidence Interval: ________ Interpretation of Meaning:

Explanation / Answer

a) Sample Proportion who had high paying carrer goals in 2015 = 415/(415+288) = 0.5903

Sample Proportion who had high paying carrer goals in 1977 = 113/(113+82) = 0.5795

So,  Sample Proportion who had high paying carrer goals in 2015 is greater than  Sample Proportion who had high paying carrer goals in 1977, but we need to check whether this difference is Statistically different

b) Pooled Proportion = (415+113)/(195+703) = 0.587973

Margin of error = 1.960*Sqrt(0.587973*(1-0.587973))*Sqrt((1/195)+(1/703)) = 0.07808

95% Interval

(0.5703-0.5795-0.07808, 0.5903-0.5795+0.07808)

= (-0.0672, 0.0889)

So, we are 95% Confident that Differences will lies in this interval

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