Is Shoe Size Generally Proportional to Height? Katilyn Pangborn Hilary Christensen Jessica Howsden Jeffrey Ellsworth Tammy Kiholm

Purpose of Study This study was formulated to examine if there is a correlation, whether positive or negative, between our study samples. For this study the question was asked “In adult women, is height related to shoe size (US)?’ for centuries it has been a common belief that “shoe size is generally proportional to height”. Our purpose is to test that theory.

Study Design In order to obtain data for our research, each member of our 7-member group will take a stratified sample of 20 adult women from separate locations (i.e. school campus, mall, restaurant, gym) and then place all of the data together. We will then separate groups by classes of height, class width being one inch, and record the shoe sizes (US) that occur in each one-inch class. We will then use that information to conclude whether height has any correlation to shoe size.

Study Analysis 140 women were asked their shoe size (US) and height (in) 280 pieces of data were collected Mean Height: 65 inches Span: 16 inches Standard Deviation: Mean Shoe Size (US): 7.7 Standard Deviation: Span: 7 sizes Correlation Coefficient: Critical Value: 0.195

First Quantitative Variable – Height: Mean: Standard Deviation: Five Number Summary: 58, 63, 65, 67, 74 Range: 16 Mode: 64 Outliers: 58, 74

First Quantitative Variable – Height:

Second Quantitative Variable - Shoe Size: Mean: Standard Deviation: Five Number Summary: 4, 7, 7.5, 8, 11 Range: 7 Mode: 7.5 Outliers: 4, 4.5, 5, 10, 10.5, 11

Second Quantitative Variable - Shoe Size:

Correlation Coefficient

The linear correlation between the two lines is R= The regression line is y=mx+b, where shoe size is “y” and the equation is: (0.347)height + ( )

Conclusion There is a positive correlation between shoe size and height, as height increases shoe size tends to as well. There were few outliers found through our research. Next time we would use a larger, more random data collection procedure. Challenges: Accuracy Randomness Relatively small sample size - unable to verify if it is actually attributable to a population