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