Temperature Monitoring LogsheetDate: 10-20-2010 to 10-26-2010Time: 1:00 pm

TemperatureLocation D - 1 D - 2 D - 3 D - 4 D - 5

1 Entrance 1 24.2 24.9 24.5 27.7 27.22 Entrance 2 24.9 24.8 23.8 26.2 24.63 Entrance 3 24.7 25.7 25.1 25.5 24.74 Activity Area 24.6 26.2 25.8 25.3 24.45 Supermarket Hallway 23.3 26.5 24.6 24.3 25.16 Supermarket Selling Area 22.5 25.4 24.1 24.9 24.17 2nd Floor Mall Area 24.8 25 25.4 24.2 24.98 Foodcove 23.9 24.3 25.7 24.3 24.39 3rd Floor Mall Area 24.1 23.8 22.8 25.4 23.310 Timezone 25.2 25.9 24.2 26.1 24.811 Department Store Selling Area 23.4 23.4 23.3 23.3 23.312 B3 Counter 25.4 24.9 24.1 24.3 24.413 Cinema 1 22.4 25.5 23.8 22.2 22.414 Cinema 2 22.6 21.8 22.8 22.6 22.915 Cinema 3 23.2 23.5 22.8 23.3 23.116 Cinema 4 23.1 23.7 22.6 22.8 23.2

Use a 0.05 level of significance to test the hypothesis that(a) same coldness can be felt despite what day of the week;(b) air-condition equally defused inside the mall;

HypothesesH

o': air-condition equally defused inside the mall

HA': air-condition not equally defused inside the mall

Ho'': same level of coldness can be felt each day

HA'': different level of coldness can be felt each day

Level of Significance: α = 0.05

TemperatureD - 6 D - 7

29.4 23.527.5 23.728.5 24.823.6 24.824.4 23.524.2 23.325.2 23.723.2 23.823.5 22.424.1 23.423.1 22.725.1 24.120.8 20.422.4 21.222.4 22.221.8 22.1

Use a 0.05 level of significance to test the hypothesis that(a) same coldness can be felt despite what day of the week;(b) air-condition equally defused inside the mall;

TABLE 1Analysis of Variance for the Two-Way Classification with single observation per cell

Source of VariationSum of Squares Mean Square Computed f

Row Means SSR r - 1SSR

r - 1

Column Means SSC c - 1SSC

c - 1

Error SSE (r - 1)(c - 1)SSE

(r - 1)(c - 1)

Total SST rc - 1

The sums of squares are usua'ly obtained by means of the following computational formulas:

Sum-of-Squares Computational Formulas

The computation in an analysis-of-variance problem, for a two-way classification with single observations per cell, are usually summarized as in Table 1

Degrees of Freedom

s1

2 = f1 =

s2

2 = f2 =

s3

2 =

SST =

1

r

i 1

c

j

Xij

2

==

T ..2

rc

SSR = 1

r

i

Ti .

2

=

c

T..

2

rc

SSC = 1

c

j

T. j2

=

r

T..

2

rc

SSE = SST - SSR - SSC

TABLE 1Analysis of Variance for the Two-Way Classification with single observation per cell

Computed f

The sums of squares are usua'ly obtained by means of the following computational formulas:

The computation in an analysis-of-variance problem, for a two-way classification with single observations per

s1

2

s3

2

s2

2

s3

2

TemperatureLoc. Label D - 1 D - 2 D - 3 D - 4 D - 5

1 Entrance 1 24.2 24.9 24.5 27.7 27.22 Entrance 2 24.9 24.8 23.8 26.2 24.63 Entrance 3 24.7 25.7 25.1 25.5 24.74 Activity Area 24.6 26.2 25.8 25.3 24.45 Supermarket Hallway 23.3 26.5 24.6 24.3 25.16 Supermarket 22.5 25.4 24.1 24.9 24.17 2nd Floor Mall Area 24.8 25 25.4 24.2 24.98 Foodcove 23.9 24.3 25.7 24.3 24.39 3rd Floor Mall Area 24.1 23.8 22.8 25.4 23.310 Timezone 25.2 25.9 24.2 26.1 24.811 Department Store 23.4 23.4 23.3 23.3 23.312 B3 Counter 25.4 24.9 24.1 24.3 24.413 Cinema 1 22.4 25.5 23.8 22.2 22.414 Cinema 2 22.6 21.8 22.8 22.6 22.915 Cinema 3 23.2 23.5 22.8 23.3 23.116 Cinema 4 23.1 23.7 22.6 22.8 23.2

Temperature

Loc. D - 1 D - 2 D - 3 D - 4 D - 5 D - 6 D - 71 24.2 24.9 24.5 27.7 27.2 29.4 23.52 24.9 24.8 23.8 26.2 24.6 27.5 23.73 24.7 25.7 25.1 25.5 24.7 28.5 24.84 24.6 26.2 25.8 25.3 24.4 23.6 24.85 23.3 26.5 24.6 24.3 25.1 24.4 23.56 22.5 25.4 24.1 24.9 24.1 24.2 23.37 24.8 25 25.4 24.2 24.9 25.2 23.78 23.9 24.3 25.7 24.3 24.3 23.2 23.89 24.1 23.8 22.8 25.4 23.3 23.5 22.410 25.2 25.9 24.2 26.1 24.8 24.1 23.411 23.4 23.4 23.3 23.3 23.3 23.1 22.712 25.4 24.9 24.1 24.3 24.4 25.1 24.113 22.4 25.5 23.8 22.2 22.4 20.8 20.414 22.6 21.8 22.8 22.6 22.9 22.4 21.215 23.2 23.5 22.8 23.3 23.1 22.4 22.216 23.1 23.7 22.6 22.8 23.2 21.8 22.1

Total 382.3 395.3 385.4 392.4 386.7 389.2 369.6

146153.29 156262.09 148533.16 153977.76 149536.89 151476.64 136604.16Total2

TemperatureLoc. D - 1 D - 2 D - 3 D - 4 D - 5 D - 6 D - 7

1 585.64 620.01 600.25 767.29 739.84 864.36 552.252 620.01 615.04 566.44 686.44 605.16 756.25 561.693 610.09 660.49 630.01 650.25 610.09 812.25 615.044 605.16 686.44 665.64 640.09 595.36 556.96 615.045 542.89 702.25 605.16 590.49 630.01 595.36 552.256 506.25 645.16 580.81 620.01 580.81 585.64 542.897 615.04 625 645.16 585.64 620.01 635.04 561.698 571.21 590.49 660.49 590.49 590.49 538.24 566.449 580.81 566.44 519.84 645.16 542.89 552.25 501.7610 635.04 670.81 585.64 681.21 615.04 580.81 547.5611 547.56 547.56 542.89 542.89 542.89 533.61 515.2912 645.16 620.01 580.81 590.49 595.36 630.01 580.8113 501.76 650.25 566.44 492.84 501.76 432.64 416.1614 510.76 475.24 519.84 510.76 524.41 501.76 449.4415 538.24 552.25 519.84 542.89 533.61 501.76 492.8416 533.61 561.69 510.76 519.84 538.24 475.24 488.41

Grand Total

SST = 65372.87 -7294860.8

112

SST = 240.184196

SSR =456830.93

-7294860.8

7 112

SST =

1

r

i 1

c

j

Xij

2

==

T ..2

rc

SSR = 1

r

i

Ti .

2

=

c

T..

2

rc

SSR = 128.875625

SSC =1042543.99

-7294860.8

16 112

SSC = 26.3135714

SSE = 240.184196 - 128.87562 - 26.313571

SSE = 84.995

SSC = 1

c

j

T. j2

=

r

T..

2

rc

SSE = SST - SSR - SSC

TemperatureD - 6 D - 729.4 23.527.5 23.728.5 24.823.6 24.824.4 23.524.2 23.325.2 23.723.2 23.823.5 22.424.1 23.423.1 22.725.1 24.120.8 20.422.4 21.222.4 22.221.8 22.1

Total181.4 32905.96175.5 30800.25

179 32041174.7 30520.09171.7 29480.89168.5 28392.25173.2 29998.24169.5 28730.25165.3 27324.09173.7 30171.69162.5 26406.25172.3 29687.29157.5 24806.25156.3 24429.69160.5 25760.25159.3 25376.49

2700.9 456830.93

1042544 7294860.8

Total2

Total4729.644411.034588.224364.694218.414061.574287.584107.853909.154316.113772.694242.653561.853492.213681.433627.79

65372.87

Analysis of Variance for the Two-Way Classification with single observation per cell

Source of VariationSum of Squares Mean Square Computed f

Row Means 128.876 15 8.592

Column Means 26.314 6 4.386

Error 84.995 90 0.944

Total 240.184 111

Decisions:

Degrees of Freedom

s1

2 = f1 =

s2

2 = f2 =

s3

2 =

Note: Critical F is from the tabulation of F Distribution at 0.05 level of significance

(a) Since Computed f (9.10) > Critical F (1.79); Reject Ho' and conclude that air-condition not

equally defused inside the mall

(b) Since Computed f (4.64) > Critical F (2.21); Reject Ho'' and conclude that different level of

coldness can be felt each day

Interpolation

For Critical value F1;

60 = 1.836490 = F1120 = 1.7505

90 - 60=

F1 - 1.8364120 - 60 1.7505 - 1.8364

F1 = 1.7935

For Critical value F2;

60 = 2.254190 = F2120 = 2.175

90 - 60=

F2 - 2.2541

120 - 60=

2.175 - 2.2541

F2 = 2.2146

Computed f Critical F

9.10 1.79

4.64 2.21

' and conclude that air-condition not

'' and conclude that different level of