Temperature and Humidity

By: Nicole Adams, and Amy Schaefer

Tired of feeling hot and cold?•Hot in one classroom•Cold in another•Wanted to test if the temperatures throughout the school are different•Applies to all of us because we don’t know what we need to wear

•If we should bring sweatshirts, or if we are going to be sweating all day•We are the ones sitting in school all day•Can affect learning abilities

•If a student is not comfortable

Procedure

• Numbered Classrooms• Took a SRS of the whole school (35)• Split left and right

– Took 2 individual SRS (30% of classrooms)• 20/68- left , 17/55-right

• Recorded temperature and humidity of rooms– Wednesday 6/4/08 first block

Data from whole SchoolRoom #

Temperature (˚F) Humidity (%)

C101 70 70

C102 70 69

C104 70 69

C106 70 67

C118 70 53

Soph. House 70 54

C134 72 64

C135 72 64

C128 73 66

C126 72 66

C216 70 71

C233 72 70

C228 72 70

C229 72 69

Forum 70 67

School Store 70 68

A208 70 68

Library 70 71

Room # Temperature (˚F) Humidity (%)

B207 70 68

B216 72 70

B234F 72 68

B228 72 69

A.D. Office 70 70

Aux. Gym 70 67

D204 70 74

Women's Locker 70 76

Men's Locker 70 77

Fitness 70 72

C305 70 75

C306 70 73

C311 70 72

C317 70 70

C321 70 71

C332 70 73

C330 70 70

Whole Temperature Graph

Mean = 70.6

N = 35

Median = 70

Standard deviation = .9762

Number of rooms

Temperature (ºF)

25

9

1

70 72 73

Question

Does the temperature match what the average school

temperature is?

Assumptions

• SRS• normal populations n > 30

Check• SRS taken using calculator• n = 35 > 30

T-TestTemperature

Ho: µ=72°Ha: µ≠72°

P(t<-8.485|df=34) = 6.566 X 10-10

We reject Ho in favor of Ha because the p-value of 6.566 X 10-10 < α = .05. We have sufficient evidence that the mean temperature in the school does not equal 72°.

nsx

t = -8.485

Confidence Interval

• Test at 95% level

• (70.265, 70.935)• We are 95% confident that the mean of the

temperature of the whole school is between 70.265° and 70.935°

nstx *

Outlier Test

1.5 (71-67) = 6• 67 – 6 = 61%• 71 + 6 = 77%

Anything below 61% and above 77% are outliers• 2 outliers: 53% and 54%

Humidity of whole school

53 64 67 70 71 77

% Humidity

Question

Is the outside humidity higher than the average humidity of the

inside of the school of classrooms in everyday use?

Assumptions

• SRS• normal populations n > 30

Check• SRS taken using calculator• n = 35 > 30

T-testHumidity

Ho:µ = 77% Ha:µ < 77%

P (t < -9.85| df = 34) = 8.57 x 10-12

We reject Ho in favor of Ha because the p-value of 8.57 x 10-12 is < α = .05. We have sufficient evidence that the average humidity inside of the school is less than that outside of the school.

nsx

t

= -9.85

Confidence Interval

95 % test

(67.212, 70.56)We are 95% confident that the average humidity

inside of the school is between 67.212 and 70.56 degrees.

nstx *

Question

Is the temperature on the left side of the school warmer than on the

right side of the school?

Assumptions

• 2 independent SRS• 2 normal populations or n1 and n2 > 30

Check• 2 SRS taken using calculator• Small population so took 30%-part of our

error

Data from Left sampleRoom # Temperature (˚F) Humidity (%)

C102 70 69

C103 70 68

C112 70 68

C114 72 67

Soph. House 70 54

Sen. House 70 68

C218 70 71

C216 70 71

C206 70 71

C202 70 69

C211 70 72

C212 70 72

Library 70 71

B207 70 68

B214 72 73

B224 72 68

C317 70 70

C307 70 75

C301 70 72

C312 70 72

Data From Right sampleRoom # Temperature (˚F) Humidity (%)

C120 72 65

C121 72 67

C128 73 66

C127 72 66

C126 72 66

C124 72 64

C233 72 70

C232 72 69

Gym 70 67

Men's Locker 70 77

Fitness 70 72

C320 70 70

C321 70 71

C333 70 73

C332 70 73

C327 70 70

C324 70 70

Left and Right Temperature Graphs

Number of rooms

Left Side

Mean= 70.3

N = 20

Median = 70

Standard deviation = .714

Temperature (ºF)

17

3

70 72 Temperature (ºF)

9

7

1

70 72 73

Right Side

Mean = 71

N = 17

Median = 70

Standard deviation = 1.08

Number of rooms

Two sample T-test Temperature

Ho: µright = µleft

Ha: µright < µleft

P(t < 2.209 |df=26.81) = .9821We fail to reject Ho in favor of Ha because the p-value

of .9821 is > than α = .05. We have sufficient evidence that the mean of right side of temperature is not less than the mean of the left side temperature.

2

22

1

21

21

n

s

n

s

xxt

=2.209

Confidence Interval

• Test at 95% level

• (.04973, 1.3505)• We are 95% confident that the difference

between the mean of the temperature on the right side and the left side is between .04973° and 1.3505°.

2

22

1

21

21 *n

s

n

stxx

Question

Is the humidity on the right side of the school less than the humidity

on the left side of the school?

Assumptions

• 2 independent SRS• 2 normal populations or n1 and n2 > 30

Check• 2 SRS taken using calculator• Small population so took 30%-part of our

error

Outlier Test 1.5 (72-68) = 6

• 68 – 6 = 62• 72 + 6 = 78

Anything below 62% and above 78% on the left are outliers• One outlier: 54%

1.5 (71.5-66) = 8.25• 66 – 8.25 = 57.75• 71.5 + 8.25 = 79.75

Anything below 57.75% and above 79.75% on the right are outliers

54 64 66 70 72 75 77

Left Side

Right Side

Left vs Right Humidity Graphs

%

Two sample t-testHumidity

Ho: µright = µleft

Ha: µright < µleft

P (t < -.217| df=34.96) = .4143We fail to reject Ho in favor of Ha because the p-value

of .4143 is > α = .05. We have sufficient evidence that the humidity on the right side of the school is not less than that on the left side of the school.

2

22

1

21

21

n

s

n

s

xxt

= -.217

Confidence Interval

95% level

(-2.821, 2.2738)We are 95 % confident that the difference

between the mean of humidity on the right side and the left side is between -2.821% and 2.2738 % humidity

2

22

1

21

21 *n

s

n

stxx

Personal Opinions

• Thought right was cooler because sun hit the left in the morning

• First thought temperature changed but humidity’s were changing

• Mr. Lafferty’s classroom compared to Boy’s Locker room

• Found it interesting that temperatures did not fit what the school claims to be, a bit cooler

• Rooms being cold and hot are in our heads but the humidity is what is changing.

Errors/Bias

• Population is very small- 123 rooms (everyday use)• Time of day/position of the sun (could change throughout the

day)• Different set temperatures around the school• Thermometer only adjusted in room for 30 seconds• If students were in the room or not• Could change day to day since humidity was changing

– Wednesday was humid and wet out.