Is There a Relationship Between Shoe Size and Height? Purpose Data Collection Results Conclusion Sources We are evaluating to see if there is a significant linear correlation between the shoe size and height of students as SLCC, Redwood Campus. If a significant linear correlation exists, we can use this data to predict the height of a student based on their shoe size. The target population that our research group gathered data from were students at Salt Lake Community College, Redwood Campus. Our group sampled a total of 60 students; 30 were male and 30 were female. Each team member sampled 20 students by using a random number generator consisting of the numbers one, two, three, and four. The random number selected determined what student was included in our sample. To further randomize our sample, we collected data at the SI building, CT building, TB building, and the campus library. Critical Value for sample size of 30 is 0.361 R (correlation coefficient): Women= 0.6654 Men= 0.5582 The given data was analyzed and compared to the critical value for our sample size. The female’s R- value of 0.6654 is greater than the critical value of 0.361. This shows that a significant linear correlation exists between shoe size and height for the women in our sample. The male’s R-value of 0.5582 is greater than the critical value of 0.361. This shows that a significant linear correlation exists between shoe size and height for the men in our sample. One outlier was found in the data collected for women’s shoe size. The outlier influences the correlation coefficient of women’s shoe size compared to height. The outlier was removed and the correlation coefficient was recalculated to be 0.5588. The linear regression equation for women was found to be Height(in)(W) = 56.145763 + 1.1631961 Shoe Size(W). The linear regression equation for men was found to be Height(in)(M) = 58.90238 + 1.0785714 Shoe size(M). The linear regression equation for women with the outlier removed was found to be Height(in) (W) = 56.66579 + 1.0894737 Shoe Size(W) A hypothesis test was performed on the slopes of the different linear regression lines. A significance of 0.01 was used and the p-values for all three regression lines were found to be less than 0.01. The heights of both men and women in our sample were found to have more variability in height than shoe size. One outlier was found in the women's sample and the statistics were calculated with and without the outlier. Removing the outlier had a small effect on the regression equation, but not enough to put the correlation coefficient below the critical value for our sample size. Because the critical value is lower than our correlation coefficient there is a significant linear correlation. The results of the hypothesis tests confirm that there is a statistically significant relationship between shoe size and height with students at SLCC Redwood campus to a significance of .01. This means that using the linear regression equations we can give a prediction of a students height if we are given their shoe size. Hypothesis H o : The slope of the linear regression line = zero H 1 : The slope of the linear Sample Group Paramete r Estimat e Std. Err. Alternat ive DF T-Stat P- Value Women(outli er included) Slope 1.16319 61 0.246637 82 ≠ 0 28 4.71621 2 <0.000 1 Men Slope 1.07857 14 0.302990 65 ≠ 0 28 3.55975 17 <0.001 3 Women(outli er removed) Slope 1.08947 37 0.311278 3 ≠ 0 27 3.49999 86 <0.001 6 Shoe image: http://farm3.static.flickr.com/2239/2078976542_e53bef172a.jpg Height image: http://www.height-increase.net/wp-content/uploads/2012/04/height-increase- 2.jpg Eric Foulger, Caitlin Finn, John Robinson

Purpose Data Collection Results Conclusion Sources We are evaluating to see if there is a significant linear correlation between the shoe size and height

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Page 1: Purpose Data Collection Results Conclusion Sources We are evaluating to see if there is a significant linear correlation between the shoe size and height

Is There a Relationship Between Shoe Size and

Height?

Purpose

Data Collection

Results

Conclusion

Sources

We are evaluating to see if there is a significant linear correlation between the shoe size and height of students as SLCC, Redwood Campus. If a significant linear correlation exists, we can use this data to predict the height of a student based on their shoe size.

The target population that our research group gathered data from were students at Salt Lake Community College, Redwood Campus. Our group sampled a total of 60 students; 30 were male and 30 were female. Each team member sampled 20 students by using a random number generator consisting of the numbers one, two, three, and four. The random number selected determined what student was included in our sample. To further randomize our sample, we collected data at the SI building, CT building, TB building, and the campus library.

Critical Value for sample size of 30 is 0.361R (correlation coefficient):Women= 0.6654 Men= 0.5582 The given data was analyzed and compared to the critical value for our sample size. The female’s R-value of 0.6654 is greater than the critical value of 0.361. This shows that a significant linear correlation exists between shoe size and height for the women in our sample. The male’s R-value of 0.5582 is greater than the critical value of 0.361. This shows that a significant linear correlation exists between shoe size and height for the men in our sample.

One outlier was found in the data collected for women’s shoe size. The outlier influences the correlation coefficient of women’s shoe size compared to height. The outlier was removed and the correlation coefficient was recalculated to be 0.5588.

The linear regression equation for women was found to be Height(in)(W) = 56.145763 + 1.1631961 Shoe Size(W).

The linear regression equation for men was found to be Height(in)(M) = 58.90238 + 1.0785714 Shoe size(M).

The linear regression equation for women with the outlier removed was found to be Height(in)(W) = 56.66579 + 1.0894737 Shoe Size(W)

A hypothesis test was performed on the slopes of the different linear regression lines. A significance of 0.01 was used and the p-values for all three regression lines were found to be less than 0.01.

The heights of both men and women in our sample were found to have more variability in height than shoe size. One outlier was found in the women's sample and the statistics were calculated with and without the outlier. Removing the outlier had a small effect on the regression equation, but not enough to put the correlation coefficient below the critical value for our sample size. Because the critical value is lower than our correlation coefficient there is a significant linear correlation. The results of the hypothesis tests confirm that there is a statistically significant relationship between shoe size and height with students at SLCC Redwood campus to a significance of .01. This means that using the linear regression equations we can give a prediction of a students height if we are given their shoe size.

HypothesisHo: The slope of the linear regression line = zeroH1: The slope of the linear regression line ≠ zero

Sample GroupParameter Estimate Std. Err. Alternative DF T-Stat P-Value

Women(outlier included) Slope 1.1631961 0.24663782 ≠ 0 28 4.716212 <0.0001

MenSlope 1.0785714 0.30299065 ≠ 0 28 3.5597517 <0.0013

Women(outlier removed) Slope 1.0894737 0.3112783 ≠ 0 27 3.4999986 <0.0016

Shoe image: http://farm3.static.flickr.com/2239/2078976542_e53bef172a.jpgHeight image: http://www.height-increase.net/wp-content/uploads/2012/04/height-increase-2.jpgData was processed in Statcrunch: Http://www.Statcrunch.com

Eric Foulger, Caitlin Finn, John Robinson