(Round all intermediate calculations to at least 4 decimal places.) A random sam
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Question
(Round all intermediate calculations to at least 4 decimal places.) A random sample of five observations from three normally distributed populations produced the following data Use Table 4 30 21 26 24 30 16 20 25 26 23 18 16 si 163 280 16.0 a. Calculate the grand mean. (Round your answer to 2 decimal places.) Grand mean b. Calculate SSTR and MSTR. (Round your final answers to 2 decimal places.) SSTR MSTR c. Calculate SSE and MSE. (Round your final answers to 2 decimal places.) SSE d. Specify the competing hypotheses in order to determine whether some differences exist between the population means O Ho ?-As CMA Not all population means are equal @ Ho lA sue s ?c. HA Not all population means are equal O Type here to searchExplanation / Answer
(A) Calculate the grand mean
XGM = (25.6 + 23.0 + 21.0)/3 = 23.2
(B) SSTR = 3 * (25.6 - 23.2)2 + 3 * (23.0 - 23.2)2 + 3 * (21.0 - 23.2)2 = 53.2
MSTR = 53.2/ 2 = 26.6
(C) SSE = (5 -1) * 16.3 + (5 - 1) * 28.0 + (5 - 1) * 16.0= 241.2
dF = 5+ 5 + 5 - 3 = 12
MSE = 241.2/12 = 20.1
(D) Option A is correct.
(E) F (df1,df2) = (2,12)
F statistic = 26.6/20.1 = 1.32
F(Critical) = 6.92
(F) Donot reject H0 . since the test statistic does not exceed 6.93.
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