Consider a situation in which there is a population with a mean of 25 and a seco

Question

Consider a situation in which there is a population with a mean of 25 and a second population with a mean that differs. The populations are homoscedastic and have a standard deviation of 3. If we took two samples of size 12 from each population, which of the values below is closest to the minimum magnitude of the difference between the means of the two populations that we would be able to detect with a two-tailed homoscedastic t test?

(A) 2.50 (B) 2.55 (C) 2.60 (D) 2.65 (E) 2.70

The answer is B, please show work as to how one would arrive at B.

Explanation / Answer

the mean of population 1 is 25 and let mean of population 2 is X

both have standerd deviation = 3 and two samples are derived from both population which is equal to 12

Here equal variance so degree of freedom (dF)= 12 + 12 - 2 = 22

so for dF = 22 , and for alpha = 0.05 significance level, t - stastictics or t value = 2.074

= >  x -25 = sp sqrt ( 1/n1 + 1/n2)

sp = sqrt [ (n1 -1) S12 + (n2 -1) S22/ (n1 + n2 -2) ] = sqrt ( 9) = 3

x -25 = 9 * sqrt( 1/6) = 1.225

difference (x -25)/x -25 = 2.074

x - 25 = 2.074 * 1.225 = 2.55

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