FINAL STAT PROJECT

WORKING OUT AND GYMS

Tori DeCesare and Abby Cummings

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

HISTORY OF GYMS “Gym” comes from Greek word

“gymnasion” ~ places where athletes trained for games Ex. Olympics

Interestingly enough Greek word “gymnos”~nakedUsed to perform in the nude…

Gyms disappeared during Renaissance and Medieval times

Made a comeback 19th centuryBuilt in schools and colleges

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 popularCelebrities encouraged memberships

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 activityBodies 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

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

TESTS WE USED

Chi-squared test of independenceGender vs. machine/weights used

T-TestAge range vs. Average time spent at gym

Chi-squared test of independence Age range vs. Machines used

Upperbody elliptical free bike swim treadmill lower body11 6 6 4 4 10 4

Upperbody24%

elliptical13%

free13%

bike9%

swim9%

treadmill22%

lower body9%

Machine/Weights

EXPLORATORY DATA

Percentages of people who used what machine/weights

HL

P

Time_Spent0 20 40 60 80 100 120 140 160

Collection 1 Box Plot

M58%

F42%

Gender

EXPLORATORY DATATime spent at each gym

10-2

020

-30

30-4

040

-50

50-6

0

Frequency of Age_RangeGym

1 2 3 4 5 6 7 8H

0 1 2 3 4 5 6 7 8L

0 1 2 3 4 5 6 7 8P

count

Collection 1 Bar Chart

EXPLORATORY DATA

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 anywayTest of Collection 1 Test for Independence

First attribute (categorical): Gender

Second attribute (categorical): Machines_Wts

First attribute: Gender Number of categories: 2Second attribute: Machines_Wts Number of categories: 7

Warning: 12 out of 14 cells have expected values less than 5.

Alternative hypothesis: There is an association betw een Gender and Machines_Wts

The test statistic, chi-square, is 23.95. There are 6 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Gender w ere independent of Machines_Wts (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.00053.

The numbers in parentheses in the table are expected counts.

RowSummary

Column Summary

Gender

M

Gender

F

bike

elliptical

free w eights

low er body

sw ims

treadmill

upper body

Machines_Wts

2 (1.7) 2 (2.3)

3 (2.5) 3 (3.5)

0 (2.5) 6 (3.5)

2 (1.7) 2 (2.3)

0 (1.7) 4 (2.3)

10 (4.2) 0 (5.8)

2 (4.6) 9 (6.4)

19 26

4

6

6

4

4

10

11

45

GENDER VS. MACHINES/WEIGHTS USED

CHI-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.

(2- 1.7)2 + (2–2.3)2 … = 23.95 1.7 2.3

CHI-SQUARED TEST OF INDEPENDENCE

Gen

der

0

2

4

6

8

10

12

F

2

4

6

8

10

12

M

Machines_Wtsbike elliptical free w eights low er body sw ims treadmill upper body

count

Collection 1 Bar Chart

P(x2 >23.95 I df = 6) = .00053Alpha=.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.

CHI-SQUARED TEST OF INDEPENDENCE

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

T-TEST AGE OF GYM MEMBERS VS. TIME SPENT AT GYM

Null Hypothesis (Ho): µ = 45 (minutes)

Alternative Hypothesis (Ha): µ > 45 (minutes)

Collection 1

Column Summary

Time_Spent

10-20

20-30

Age_Range

51089090

120120120

1187.2727

306090

120150

4578.6667

30606090

150S1 = countS2 = meanS3 = minS4 = Q1S5 = medianS6 = Q3S7 = max

T-TEST

P(t > 7.022 I df=44) = .0001

T = 7.022

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.

0

20

40

60

80

100

120

140

160

Age_Range10-20 20-30 30-40 40-50 50-60

Collection 1 Box Plot

T- INTERVAL*All conditions met*Use Student’s t-distribution*T-Interval

(69.0034, 88.329)

**95% confidence

* We are 95% confident that the true average time spent at the gym is

between 69.0034 and 88.329 minutes.

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

First attribute (categorical): Machines_Wts

Second attribute (categorical): Age_Range

First attribute: Machines_Wts Number of categories: 7Second attribute: Age_Range Number of categories: 5

Warning: 35 out of 35 cells have expected values less than 5.

Alternative hypothesis: There is an association betw een Machines_Wts and Age_Range

The test statistic, chi-square, is 23.72. There are 24 degrees of freedom (the number of row s minus one times the number of columns minus one).

If it w ere true that Machines_Wts w ere independent of Age_Range (the null hypothesis), and the sampling process w ere performed repeatedly, the probability of getting a value for chi-square this great or greater w ould be 0.48.

The numbers in parentheses in the table are expected counts.

Column Summary

Machines_WtsMachines_WtsMachines_WtsMachines_WtsMachines_WtsMachines_Wts

elliptical free w eights low er body sw ims treadmill upper body

Machines_Wts

bike

10-20

20-30

30-40

40-50

50-60

Age_Range

0 (0.4) 0 (0.7) 1 (0.7) 2 (0.4) 0 (0.4) 2 (1.1) 0 (1.2)

1 (1.0) 1 (1.5) 1 (1.5) 0 (1.0) 0 (1.0) 3 (2.4) 5 (2.7)

0 (0.7) 1 (1.1) 1 (1.1) 1 (0.7) 1 (0.7) 1 (1.8) 3 (2.0)

0 (0.7) 2 (1.1) 1 (1.1) 1 (0.7) 1 (0.7) 1 (1.8) 2 (2.0)

3 (1.2) 2 (1.7) 2 (1.7) 0 (1.2) 2 (1.2) 3 (2.9) 1 (3.2)

4 6 6 4 4 10 11

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.

(1-1)2 + (1-1.5)^2 … = 23.72

1 1.5P(x2 > 23.72I df=24) = 0.48Alpha = .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.

AGE VS. MACHINE

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

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