BrownMath.com → Statistics → Fa15 ME50 → Shoe-Size Lab
Updated 26 Aug 2015

Shoe-Size Lab (Due on 6 Oct)

Copyright © 2007–2015 by Stan Brown

Summary: It seems obvious that taller adults have bigger feet, but is it true? What “everybody knows” isn’t always true. Statistics uses numerical arguments, not intuition.

Data Collection

Pick 24 adults (18 or older) of the same sex as yourself. Ask them their height (to the nearest half inch) and their shoe size. (Show heights in the original feet and inches, then in inches.)

In the interests of time, you can take a convenience sample, and add yourself as the 25th data point. Record the data on the form at the end of this lab, or use separate paper laid out the same way.

Directions for This Lab

Data Analysis

Question 1 (4 points):  Make a scatterplot of your data with x=height, y=shoe size. Label axes with titles and show the scales. Plot points as boxes or circles, not small dots. Either way, start the x and y axes at sensible numbers (not 0) and scale the plot to take up most of a sheet. This will show the relationship (if any) better than bunching all the points close together.

Question 2 (3 points):  Compute the correlation coefficient, using Excel or your TI calculator. Write it down with its proper symbol.

Question 3 (3 points):  Compute the equation of the line of best fit, and write it down with its proper symbol. Round coefficients to four decimal places.

Question 4 (3 points):  Give the coefficient of determination with its proper symbol, and interpret the number in terms of heights and shoe sizes.

Question 5 (3 points):  Plot the line of best fit on your scatter diagram. If you’re plotting by hand (not using Excel or a similar computer program), show the three x,ŷ pairs that you used to plot the line.

Question 6 (3 points):  State the numerical value of the y intercept and interpret the number in terms of heights and shoe sizes.

Question 7 (3 points):  State the numerical value of the slope and interpret the number in terms of heights and shoe sizes.

Question 8 (3 points): Your sample is not random, but just for this problem let’s assume it is. From your sample, what can you say about a relation between height and shoe size for all men or all women? No hand-waving, please: use the numerical argument that you learned in class. Use plain English — no city-slicker words like “correlated” or “associated”. Just talk about heights and shoe sizes for all men or women.

Question 9 (3 points):  Use your regression line to predict the average shoe size for women of height 65″ or men of height 70″, and write a short English interpretation.

Question 10 (2 points): Find the residual(s) for x=65″ (women) or x=70″ (men). If you don’t have data with that x, pick the nearest x you do have.

Data Collected from 25      Men    Women   (circle one)
Height (x) in the form 5′6½″ = 66.5″   Shoe size (y)
(include half sizes)
Height (x) in the form 5′6½″ = 66.5″   Shoe size (y)
(include half sizes)
    
    
    
    
    
    
    
    
    
    
    
    
YOU  

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