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Group D Math 1040 SlCC

Group D Math 1040 SlCC. Final Project Presentation “ Is shoe length related to height?”. Ariel Lee Jason Merrill Jacob Guss Ryan Huntington. Purpose of Study. Our research question is “Is shoe length related to height?”

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Group D Math 1040 SlCC

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  1. Group DMath 1040 SlCC Final Project Presentation “Is shoe length related to height?” Ariel Lee Jason Merrill Jacob Guss Ryan Huntington

  2. Purpose of Study • Our research question is “Is shoe length related to height?” • What can the shoe length of a person tell us about the height of that person? • Explanatory variable is Shoe length • Response variable is Height.

  3. Study Design • There were 4 people in our group and individually we set out to collect our data from fellow coworkers. • Each of us selected 6 males and 6 females. We ended up with 24 males and 24 females as our sample size. • Both of these are Quantitative variables, all of our measurements were done in centimeters. • The data is of the Interval level of measurement because differences in the value of the measurement make sense.

  4. Study Design • Our group decided to use the Stratified sample technique to gather the data. • We decided to obtain a Simple Random sample from our coworkers. Coworkers are the non-overlapping group, the strata. • This is an Observational study because we measured the value of the variable without attempting to influence the value.

  5. Data, Stats, and Graphs • Table of our data

  6. Stats for 1st Quantitative VariableShoe Size • Mean, Standard deviation, Five-number summary, Range, Mode, Outliers. • Mean = 26.137 Stn.Dev = 2.552 • Minimum = 17.80 • Q1 = 24.675 • Median = 26.00 • Q3 = 27.90 • Maximum = 31.00 • Range = 13.20 • IQR = 3.225 • Mode = 27.9

  7. Histogram for 1st Quantitative Variable

  8. Boxplot for 1st Quantitative Variable

  9. Graphic Summary for 1st Q.V.

  10. Stats for 2nd Quantitative VariableHeight • Mean, Standard deviation, Five-number summary, Range, Mode, Outliers. • Mean = 174.99 StnDev = 9.35 • Minimum = 160.00 • Q1 = 165.95 • Median = 175.30 • Q3 = 192.90 • Maximum = 193.00 • Range = 33.00 • IQR = 16.95 • Mode = 162.6

  11. Histogram for 2ndQuantitative Variable

  12. Boxplot for 2nd Quantitative Variable

  13. Graphic Summary for 2nd Q.V.

  14. Correlation Coefficient - Regression • Statistics for testing the correlation between the two variables: linear correlation coefficient and equation for line of regression. • Mean = 26.14 • Standard Deviation = 2.552 • Y = ax + b y = 2.559x + 108.087x • A = 2.559 • B = 108.087 R value is .6985

  15. Scatterplot that includes line of regression

  16. Difficulties / Surprises • Although we didn’t know it at the time of collection, adding the classification of male/female introduced a “third variable.” • We corrected this by classifying both Male/Female as Human Beings. • The second difficulty we had was trying to figure out if the data is normal? • By looking at the scatterplot above it certainly doesn’t pass the “fat finger test” but then we realized that the above chart is not testing for normality.

  17. Difficulties / Surprises • So we ran this chart and with a P-Value of .448 it shows that we have normal data. If the P-Value was less than .05 then the data would not be normal. Height Shoe Size

  18. Analysis • The data shows a clearly defined positive direction. • The form is clearly straight and not curved. • Data points are close together but could be tighter. • There are a few points that might be outliers but we don’t think that they are true outliers because they still support the positive direction of the data.

  19. R-Value • Our R Value is .6985 and the equation is Y=2.559x +108.087x • R values range from -1 to 1 A R-value of .6985 is strong

  20. Interpretation on Conclusion • To make our conclusion we needed to decide a couple of things. We needed to establish an “alpha level” This level is how willing we were to be wrong. • We choose an alpha level of .05, this is another way of saying that we wanted to be correct 95 out of 100 times. • The second thing we needed to establish was the degrees of freedom. The degrees of freedom are equal to 1 less than the number of subjects. We had 48 subjects so the degrees of freedom would be 47

  21. Interpretation on Conclusion • When we looked up .6985 in the Critical Values table using 47 and .05 we got the number .288 • .288 is the minimum correlation coefficient (R-value) that you would need to confidently state 95 times out of a hundred that the relationship you found with your 48 subjects exists in the population from which they were drawn. • In our case we have .6985 this is substantially over .288 so our conclusion is that there is a definite relationship between Shoe Size and Height!

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