BrownMath.com → Statistics → Sum15 ME58 → Shoe-Size Lab
Updated 16 Jun 2015

# Shoe-Size Lab (Due on 17 Jun)

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

• On separate paper, show your work and then your answer for the first question, your work and then your answer for the second question, and so on. You must show your work for full credit. I recommend you use your calculator for calculations, but you may use Excel instead if you wish.
• Check the numbers you enter in your calculator! It’s pretty bad if your answers don’t match your data. When you can, use TI calculator commands instead of formulas. Show calculator commands, not keystrokes.
• Do all the graphs on graph paper or in Excel. Need graph paper? Here’s a sheet you can download and print (9 KB PDF), adapted from Kevin MacLeod’s Plain Graph Paper PDF Generator.
• Use all or most of the page for the graph. Know when an axis must start at zero and when it should not.
• Do a professional job: Write neatly and legibly, remove any “decorative fringe” from the paper, and so forth. I recommend pencil and eraser because correcting mistakes in ink is a bear. Word processing is also acceptable.
• Hand in your data sheet. I can’t accept the lab without the full set of raw data.
• Don’t hand in the questions.
• Staple all pages neatly before you come to class, because loose sheets and insecure fasteners cost a 10% penalty. You don’t need a report cover.

## 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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