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Unformatted text preview: rred Strawberry overall, if the distributions for boys and girls are the same (H0 is true), then we would expect 23 of these children to be boys and the remaining 23 of these children to be girls. Note that our sample sizes were the same, 75 boys and 75 girls, 50% of each. If they were not 50‐50, we would have to adjust the expected counts accordingly. Let’s do the same for the Vanilla and Chocolate preferences. Chocolate: Since there were 53 children who preferred Chocolate overall, if the distributions for boys and girls are the same (H0 is true), then we would expect 26.5 of these children to be boys and the remaining 26.5 of these children to be girls. Vanilla: Since there were 51 children who preferred Vanilla overall, if the distributions for boys and girls are the same (H0 is true), then we would expect 25.5 of these children to be boys and the remaining 25.5 of these children to be girls. Enter these expected counts in the parentheses in the table below. Observed Counts (Expected Counts) Ice Cream Preference
Boys
Girls
Total Vanilla (V) 25( 25.5 )
26 ( 25.5 )
51 Chocolate (C) 30( 26.5 )
23 ( 26.5 ) 53 Strawberry (S) 20( 23 )
26 ( 23 )
46 Total 75
75
150 A Closer Look at the Expected Counts: Let's look at how we actually computed an expected count so we can develop a general rule: If H0 were true (i.e., no difference in preferences for boys versus girls), then our best estimate of the P(a child prefers vanilla) = 51/150. Since we had 75 boys, under no difference in preference, we would expect 75 x (51/150) to prefer vanilla. That is, the expected number of boys preferring vanilla = 150 . This quick recipe for computing the Total n
expected counts under the null hypothesis is called the Cross‐Product Rule. ( 75 )( 51) (row total)(column total) 212 The X 2 test statistic Next we need to compute our test statistic, our measure of how close the observed counts are to what we expect under the null hypothesis. 25 25.52 26 25.52 30 26.52 23 26.52 20 232 26 232
X2 25.5
25.5
26.5
26.5
23
23 1.73
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This document was uploaded on 02/25/2014 for the course STATS 250 at University of Michigan.
 Summer '10
 Gunderson
 Statistics

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