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First year students: Mean 125, SD?, size 350 Third year students: Mean 112, SD?, size 150 Significance level = 0.02 Solution Let group 1 = first year group 2 = third year Formulating the hypotheses Ho: p1^ - p2^ >= 0 Ha: p1^ - p2^ < 0 Here, we see that pdo = 0 , the hypothesized population proportion difference. Getting p1^ and p2^, p1^ = x1/n1 = 0.357142857 p2 = x2/n2 = 0.746666667 Also, the standard error of the difference is sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.043783715 Thus, z = [p1 - p2 - pdo]/sd = -8.896545395 As significance level = 0.02 , then the critical z is zcrit = -2.053748911 Also, the p value is P = 2.8806E-19 Thus comparing z and zcrit (or p and significance level), then we REJECT THE NULL HYPOTHESIS. Thus, there is significant evidence that the proportion of third year students who buy used textbooks is greater than the proportion of first year student who buy used textbooks. [CONCLUSION].

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First year students: Mean 125, SD?, size 350 Third year students: Mean 112, SD?, size 150 Significance level = 0.02 Solution Let group 1 = first year group 2 = third year Formulating the hypotheses Ho: p1^ - p2^ >= 0 Ha: p1^ - p2^ < 0 Here, we see that pdo = 0 , the hypothesized population proportion difference. Getting p1^ and p2^, p1^ = x1/n1 = 0.357142857 p2 = x2/n2 = 0.746666667 Also, the standard error of the difference is sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.043783715 Thus, z = [p1 - p2 - pdo]/sd = -8.896545395 As significance level = 0.02 , then the critical z is zcrit = -2.053748911 Also, the p value is P = 2.8806E-19
Thus comparing z and zcrit (or p and significance level), then we REJECT THE NULL HYPOTHESIS. Thus, there is significant evidence that the proportion of third year students who buy used textbooks is greater than the proportion of first year student who buy used textbooks. [CONCLUSION]

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  • 1. First year students: Mean 125, SD?, size 350 Third year students: Mean 112, SD?, size 150 Significance level = 0.02 Solution Let group 1 = first year group 2 = third year Formulating the hypotheses Ho: p1^ - p2^ >= 0 Ha: p1^ - p2^ < 0 Here, we see that pdo = 0 , the hypothesized population proportion difference. Getting p1^ and p2^, p1^ = x1/n1 = 0.357142857 p2 = x2/n2 = 0.746666667 Also, the standard error of the difference is sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] = 0.043783715 Thus, z = [p1 - p2 - pdo]/sd = -8.896545395 As significance level = 0.02 , then the critical z is zcrit = -2.053748911 Also, the p value is P = 2.8806E-19
  • 2. Thus comparing z and zcrit (or p and significance level), then we REJECT THE NULL HYPOTHESIS. Thus, there is significant evidence that the proportion of third year students who buy used textbooks is greater than the proportion of first year student who buy used textbooks. [CONCLUSION]