Final Stat Project Working Out and Gyms

1. Final Stat ProjectWorking Out and Gyms Tori DeCesare and Abby Cummings

2. Summary of topic • We were interested to see what gender and age groups were most likely to go to the gym to workout • We also wished to discover what types of machines people use and the average length of the time people spent at the gym each time they go

3. History of Gyms • “Gym” comes from Greek word “gymnasion” ~ places where athletes trained for games • Ex. Olympics • Interestingly enough Greek word “gymnos”~naked • Used to perform in the nude… • Gyms disappeared during Renaissance and Medieval times • Made a comeback 19th century • Built in schools and colleges

4. History of gyms Cont. • Boxing gyms popular in 1930’s • Not for general exercise • Gold’s gym chain founded 1965 in CA • Now 600 Gold’s gyms in 27 different countries, 3 million members world wide • 1980’s LA Fitness created and 24 Hour Fitness • 1990’s gyms became massively popular • Celebrities encouraged memberships

5. History of exercise • “Exercise is physical activity that is planned, structured, and repetitive for the purpose of conditioning any part of the body. Exercise is utilized to improve health, maintain fitness and is important as a means of physical rehabilitation” (medical dictionary) • 1950’s lack of physical activity • Bodies developing heart disease & diabetes • By 1970’s strength, cardiovascular heath and stretching were popular exercise choices • Soon enough treadmills, elliptical, leg presses and bikes took exercise to new level

6. Procedure-data collection • Went to 3 different gyms (Planet Fitness, LA Fitness and PSC Highpoint) • At each gym we noted the first 50 people we saw and wrote down their gender and the primary exercise equipment they use • Asked person what age range they were in and the approximate time they spent working out in a visit • Used 10 year age increments (ex. 20-30) and rounded to the nearest 30 minute increment for time spent (ex. 30, 60, 90…) • We categorized the equipment the individuals used • Ex. elliptical, treadmill, swimming, bike, upper body weights, lower body weights and free weights • Used random integer program on calculator to choose 15 subjects from each gym to gather a total sample of 45 subjects

7. Tests we used • Chi-squared test of independence • Gender vs. machine/weights used • T-Test • Age range vs. Average time spent at gym • Chi-squared test of independence • Age range vs. Machines used

8. Exploratory data Percentages of people who used what machine/weights

9. Exploratory data Time spent at each gym

10. Exploratory data

11. Chi-squared Conditions • 1) Categorical Data • 2) Random • 3) All expected values greater than or equal to 5 • *All conditions met • *Chi-square distribution • *Chi-square independence test • 1) Gender and Machines/Weights used are categorical • 2) SRS – stated (used generator on calculator) • 3) **Only two values greater than 5, but will proceed anyway

12. Gender vs. Machines/Weights UsedChi-Square Independence Test • Null Hypothesis (Ho): There is no association between gender and the machines they used. • Alternative Hypothesis (Ha): There is an association between genders and the machines they used.

13. Chi-squared test of independence (2- 1.7)2 + (2–2.3)2 … = 23.95 1.7 2.3

14. Chi-squared test of independence P(x2 >23.95 I df = 6) = .00053 Alpha=.01 *We reject the Ho because our P-value is less than alpha (.00053 < .01). *We have sufficient evidence that there is an association between the genders and what machines that they use.

15. T-Test Conditions • 1) Random • 2) population≥10n • Population> (10)(45) • 3) n ≥ 30 or Normal probability plot • *All conditions met • *Student’s T-distribution • *T-Test • 1) SRS – stated (used generator on calculator) • 2) There are more than 450 gym members • 3) n = 45 which is greater than 30

16. T-test age of gym members vs. time spent at gym • Null Hypothesis (Ho):µ = 45 (minutes) • Alternative Hypothesis (Ha):µ > 45 (minutes)

17. T-Test T = 7.022 P(t > 7.022 I df=44) = .0001 Alpha=.01 *We reject the Ho because our P-value is less than alpha: (.0001 < .01) *We have sufficient evidence that the true average time spent at the gym is greater than 45 minutes.

18. T- interval **95% confidence *All conditions met *Use Student’s t-distribution *T-Interval (69.0034, 88.329) * We are 95% confident that the true average time spent at the gym is between 69.0034 and 88.329 minutes.

19. Chi-squared Conditions • 1) Categorical Data • 2) Random • 3) All expected values greater than or equal to 5 • *All conditions met • *Chi-squared distribution • *Chi-squared independence test • 1) Age range and Machines/Weights used are categorical • 2) SRS – stated (used generator on calculator) • 3) **All expected values less than 5, but will proceed anyway

20. Age vs. machineChi-squared test- Association • Null Hypothesis (Ho): There is no association between machines used and age ranges. • Alternative Hypothesis (Ha): There is an association between machine and age.

21. Age vs. machine (1-1)2+ (1-1.5)^2… = 23.72 1 1.5 P(x2 > 23.72I df=24) = 0.48 Alpha = .01 *We fail to reject the Ho because the P-value is greater than our alpha: (.048 > .01). *We have sufficient evidence that there is no association between age range and machines used.

22. Bias/Error • Collected data over holiday break • More people off of work/school • Time of day • During afternoon, so missed morning and evening gym-goers • For conditions not all expected values were ≥ 5, but proceeded anyway • Planet Fitness does not have a pool and didn’t have access to Highpoint’s pool • Went to 3 gyms in Bucks County, so can’t conclude population • Saw people working out in groups/pairs that met all the same criteria

23. Personal opinion/conclusion • We thought that expense of gyms would affect age of members • Thought that Highpoint would have generally older people, but had large teen population • Thought that a holiday break would mean a busier gym • Not very crowded over the week; took longer to gather 50 subject • Probably would have been better if we observed in the early morning and evening • Predicted that the treadmill would be the most common machine used • 2nd most popular in our sample, upper body machines being the first • Surprises • Many 50-60 year old gym-goers • Many people who work out longer than an hour