The data below consists of two samples (one from population X and one from popul

Question

The data below consists of two samples (one from population X and one from population Y). Assume that the two populations have equal standard deviations (but we don't know what they are). Please conduct a test for equality of the two population means (alpha is 10%).

Question 1 options:

The test rejects the null hypothesis that the two population means are equal

The test fails to reject the null hypothesis that the two population means are equal

Not enough information is provided

X Y 66 67 69 59 87 65 61 62 89 62 68 52 70 61 90 78 64 72 62 72 78 75 70 70 81 69 73 71 80 78 87 72 76

Explanation / Answer

here

pooled std deviation =((s12/n1+s22/n2)2/((s12/n1)2/(n1-1)+(s2/n2)2/(n2-1))1/2=8.3193

std error =sp(1/n1+1/n2)1/2=2.9302

hence tstat=(x1-x2)/std error =2.7314

for above t stat and(n1+n2-2 =31) degree of freedom ; p value=0.01

as p value is less then 0.1 level, hence we reject null hypothesis

The test rejects the null hypothesis that the two population means are equal

child adult 66 67 69 59 87 65 61 62 89 62 68 52 70 61 90 78 64 72 62 72 78 75 70 70 81 69 73 71 80 78 87 72 1 76 total 1421.000 935.000 mean 74.789 66.786 std deviation(S) 9.138 7.029

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