Two samples each of size \"25\" are taken fronm independent populations assumed

Question

Two samples each of size "25" are taken fronm independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. 1. The pooled ( i.e. combined ) variance IS 2. The computed "t" statistic is 3. There are degrees of freedom for this test. The critical values for a two-tailed test of the null hypothesis of no difference in the population means at the ? .05 level of significance are 4. 5. A two-tailed test of the null hypothesis of no difference would (be rejected / not be rejected) at the a 0.05 level of significance.

Explanation / Answer

Solution:

S2p = (n1-1)S21 + (n2-1)S22 / (n1-1) + (n2-1)

S2p = (25-1)*3*3 +(25-1)*4*4 / (25-1)+(25-1)

S2p =24*9 + 24*16 /48

S2p =600/48 =12.5

Tstat can be calculated as

Tstat = (X1bar-X2bar) -(mean1-mean2) /Sqrt(S2p(1/n1)+(1/n2)

Tstat =35.3-33 /sqrt(12.5*(1/25)+(1/25))

Tstat =2.3/sqrt(12.5*0.08)

Tstat =2.3/1

Tstat =1

Degree of freedom for this test =25+25-2 =48

As this is two tailed test, at alpha =0.05

So tcrit value is +/-2.01063

As we can tstat is greater than tcrit value I.e. 2.3>2.01

So we will reject the null hypothesis.

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