Do you think your height and shoe size are related? Probably so.There is a known “quick” relationship that says your height (in inches) can be approximated by doubling your shoe size and adding 50 (y = 2x = 50) A random sample of 30 community college students’ heights and shoe sizes was taken to test this relationship.
Heights Shoe Sizes
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a. Construct a scatter diagram of the data with shoe size as the independent variable (x) and height as the dependent variable (y). Comment on the visual linear relationship.
b. Calculate the correlation coefficient, r. Is it significant at the 0.05 level of significance?
c. Calculate the line of best fit.
d. Compare the slope and intercept from part c to the slope and intercept of y = 2x = 50 List similarities and differences.
e. Estimate the height of a student with a size 10 shoe, first using the line of best fit found in part c and then using the relationship y = 2x + 50 Compare your results.
f. Construct the 95% confidence interval for the mean height of all community college students with a size 10 shoe, using the equation formed in part c. Is your estimate using y = 2x + 50 for a size 10 included in this interval?
g. Construct the 95% prediction interval for the individual heights of all community college students with a size 10 shoe, using the equation formed in part c.
h. Comment on the widths of the two intervals formed in parts f and g. Explain.