Air traffic controllers perform the vital function of regulating the traffic of

Question

Air traffic controllers perform the vital function of regulating the traffic of passenger planes. Frequently, air traffic controllers work long hours with little sleep. Researchers wanted to test their ability to make basic decisions as they become increasingly sleep deprived. To test their abilities, a sample of 6 air traffic controllers is selected and given a decision-making skills test following 12-hour, 24-hour, and 48-hour sleep deprivation. Higher scores indicate better decision-making skills. The table lists the hypothetical results of this study. Sleep Deprivation 12 Hours 24 Hours 48 Hours 22 18 17 19 21 21 22 33 22 26 21 13 23 14 15 20 21 15 (a) Complete the F-table. (Round your answers to two decimal places.) Source of MS Variation Between 137.57 X 2 68.79 X .09 X groups Between 125.73 x 5 25.25 x Within 7561.4. x 10 756.14 x groups (error) 7699 x 17 Total

Explanation / Answer

Calculations:

b = 3 (# of columns), v = 6 (# of rows) , m = bv = 3*6 = 18

Grand Total = G = 363

CF = G2 / n = 3632 / 18 = 7320.5

SSBet/Group = (1 / v) * (1432 + 1172 + 1032 ) - CF

SSBet/Group = (1/6) * 44747 - 7320.5

SSBet/Group = 137.33

SSBet/Person = (1 / b) (572 + 612 + ........+ 562) - CF

SSBet/Person = ( 1 /3) * 22339 - 7320.5

SSBet/Person = 125.83

TSS = (222 + 182 + ......................... + 152) - CF

TSS = 7699 - 7320.5

TSS = 378.5

SSWith/group(error) = TSS - SSBet/Group - SSBet/Person

SSWith/group(error) = 378.5 - 137.33 - 125.83  

SSWith/group(error) = 115.33

DEGREES OF FREEDOM:

TSS = n - 1 = bv - 1 = 18-1 = 17

SSBet/Group = b - 1 = 3 - 1 = 2

SSBet/Person = v - 1 = 6 - 1 = 5

SSWith/group(error) = (b - 1) (v - 1) = 2 * 5 = 10

MEAN SUM OF SQUARES:

MSSBet/Group = SSBet/Group / b -1 = 137.33 / 3 - 1 = 68.67

MSSBET/Person = SSBet/Person / V- 1 = 125.83 / 6-1 = 25.17

MSSWith/group(error) = SSWith/group(error) / (b-1) (v-1) = 115.34 / 15 = 11.53

F-Ratio:

FBet/Group = MSSBet/Group /MSSWith/group(error) = 68.67 / 11.53 = 5.95

ANOVA TABLE:

Source of

Variation

Source of

Variation

SS    df    MS Fobt    Between group 137.33 2.00 68.67 5.95 Between persons 125.83 5.00 25.17 Within group (error) 115.33 10.00 11.53 Total 378.50 17.00

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