Belly Button Ratios __________ Height in inches. __________ Long Measure - The distance from your belly button to the bottom of your foot in inches. __________ Short Measure - The distance from the top of your head to your belly button in inches. __________ First Ratio = height/long measure __________ Second Ratio = long measure/short measure Put your ratios on the board separated by gender. Homework: run hypothesis tests to determine if there is a gender difference. Note in the small sample size n study below, the differences are not significant. Gender First Second Gender First Second Sylvia F 1.66 1.58 Ertin M 1.6 1.66 Meranda F 1.69 1.46 Lee Ling M 1.68 1.47 Anastasia F 1.67 1.49 Serafin M 1.65 1.23 Agnes F 1.61 1.8 Kevin M 1.63 1.58 Kesarina F 1.67 1.5 A-1 M 1.73 1.37 Carolyn F 1.67 1.44 Kiumy F 1.63 1.53 n 7 7 5 5 mean 1.6540 1.5431 1.6572 1.4624 stdev 0.03 0.12 0.05 0.17 mean difference -0.0032 0.0807 Ho: µ1-µ2=0 Ho: µ1-µ2<>0 Hyp pooled 1/√n 0.5855 0.5855 Test degrees freedom 10 10 pooled s 0.0382 0.1436 t-statistic t -0.1432 0.9605 t critical tc 2.2281 2.2281 p-value 0.8890 0.3595 max c 0.1110 0.6405 Conf Error E 0.0498 0.1873 Int mean diff – E -0.0530 -0.1066 mean diff -0.0032 0.0807 mean diff + E 0.0466 0.2681 Both include zero: Zero cannot be ruled out as a possible pop value Section 9.4: If n were equal, solve for n. Note that using tc will overestimate n, which is considered a "conservative" approach. Better to overestimate than underestimate. The desired Error E would be equal to or less than the mean difference. n 1412.27 31.39 In theory the first and second ratios approach the Fibonacci Ratio: =(1+SQRT(5))/2 1.6180