A) One semester, I collected data from my students. It turned out that the corre

Question

A) One semester, I collected data from my students. It turned out that the correlation between their heights and handspans was about 50%. The average height was about 67 inches, with an SD of about 3 inches, while the average handspan was about 7 inches, with an SD of about 1 inch. The scatter plot turned out to be football-shaped. Predict the handspan of a student who is 73 inches tall.

7,8, or 9 inches?

B) The football shaped data indicate that the data in each vertical strip are normally distributed with the mean being given by the fitted value that we get using the regression method. Using the data from the previous problem, when you consider all the students who are 73 inches tall, the fraction that have a handspan of at least 8 inches is closest to:

10, 32, or 50%

Explanation / Answer

Z-factor = (value - mean)/standard deviation

a)

For 73 inches, Z-factor = (73-67)/3 = 6/3 = 2.

As correlation between height and handspan = 50% = 0.5, we can predict that the handspan will be 2*0.5 = 1 standard deviation away from the mean.

predicted handspan = mean + Z-factor * standard deviation = 7 + 1 * 1 = 8 inches.

Therefore, predicted handspan = 8 inches.

b)

As data in each vertical strip is normally distributed, we can assume a normal distribution with mean of 8 inches and SD of 1 inch for all students who are 73 inches tall.

So, for 8 inches, Z-factor = (8-8)/1 = 0/1 = 0. This corresponds to 50% of handspans above 8 inches.

Therefore, fraction of handspan above 8 inches = 50%.

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