An experiment was designed to compare the lengths of time that four different dr

Question

An experiment was designed to compare the lengths of time that four different drugs provided pain relief after surgery. The results (in hours) follow. Is there enough evidence to reject the null hypothesis that there is no significant difference in the length of pain relief provided by the four drugs at = .05?

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(ii) Find the p-value. (Give your answer bounds exactly.)
__ < p < __

Explanation / Answer

H0: A = B = C= D
HA: At least one of the population means is different from at least one other population mean

Corrected Mean, CM = (Total of all observations)2/N = (6+6+4+7+4+5+4+5+12+11+11+11+10+4+3+3)2/16
= 702.25

SS(Total) = sum(square of all observations) - CM =
(62+62+42+72+42+52+42+52+122+112+112+112+102+42+32+32) - 702.25 = 157.75

Sum of square of treatment, SST = (sum of each drug)2/n - CM
= (6+6+4+7)2/4 + (4+5+4+5)2/4 + (12+11+11+11+10)2/5 + (4+3+3)2/3 - 702.25 = 149.33

Sum of square of error, SSE = SS(Total) - SST = 101/12

dfTreatment= 4-1 = 3, dferror = (N-1-dfTreatment) = 16-1-3 = 12
MST = SST/dfTreatment=49.77778, MSE = SSE/dferror = 0.7013889

F = MST/MSE = 70.97

p =0; 0 < p < 0.0001 (0<P<0.05)

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