196 CONTINGENCY TABLES Incorrect Correct 10 tot noulo nrelb Program Program elt 7 23 Conventional Class 27 Experimental Class Is there reason to believe the experimental method is superior? Or could the preceding differences be due to chance fluctuations? One hundred men and 100 women were asked to trya new toothpaste and to state whether they liked or did not like the new taste. Thirty-two men and 26 women said they did not like the new taste. Does this indicate a difference in preferences between men and women 3. in general? 4. Contingency tables may be used to present data representing scales of measurement higher than the nominal scale. For example, a random sample of size 20 was selected from the graduate students who are U.S. citizens, and their grade point averages were recorded 3.42 3.54 3.21 3.63 3.22 3.80 3.70 3.20 3.75 3.31 2.86 2.92 3.59 3.77 2.70 3.06 3.30 s bar 3.86 4.00 e] ug Also, a random sample of 20 students was selected from the non-U.S. citizen group of graduate students at the same university. Their grade point averages were as follows. alb 3.50 4.00 3.43 3.85 3.84 3.21 3.58 3.94 3.48 3.76 3.87 2.93 4.00 3.37 3.72 4.00 3.06 3.92 3.72 3.91 s Test the null hypothesis that the proportion of graduate students with averages of 3.50 or higher is the same for both the U.S. citizens and the non-U.S. citizens. Fisher's exact test can be used as a quick test for correlation between two variables X and Y, each of which has at least an ordinal scale of measurement. Divide the scatterplot of the N values of (X, Y) with a vertical line at the median of X, and a horizontal line at the median of Y, and count the number of observations in each of the four quadrants. Note that the row and column totals are N/2, and are not random. Suppose that 16 observations of X = age of marriage of a husband, and Y = age marriage of his father, resulted in 7 pairs where both ages were above the median. Are the two variables positively correlated? 5. of Use the Fisher exact test as a test for positive correlation, as exnlained in the data in Example 3.5.4. There the reaction of a mati of the sam 6.