Test whether the claim that the two sample groups come from populations with the

cistG 2021-10-17 Answered
Test whether the claim that the two sample groups come from populations with the same mean or not.
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Expert Answer

irwchh
Answered 2021-10-18 Author has 102 answers
State the test hypotheses.
Let first population denote the treatment and the second population denote the placebo.
Null hypothesis:
H0:μ1=μ2
Alternative hypothesis:
H1:μ1μ2
Test statistic:
The test statistic formula is,
t=(x1x2)(μ1μ2)sp2n1+sp2n2
Where sp2=(n11)s12+(n21)s22(n11)+(n21)
With degrees of freedom df=n1+n22
Let x1 denotes the first sample mean, s1 denotes the first sample standard deviation, n1 denotes the first sample size, x2 denotes the second sample mean, s2 denotes the second sample standard deviation, n2 denotes the second sample size, μ1 denotes the first sample population mean, and μ2 denotes the second sample population mean.
The pooled sample variance is,
sp2=(n11)s12+(n21)s22(n11)+(n21)
=(221)(0.015)2+(221)(0.000)2(221)+(221)
=0.004725+042
=0.0001125
Substitute n1=22x1=0.049,sp2=0.0001125,n2=22 and x2=0.000 in the test statistic formula
t=(0.0490.000)0.000112522+0.000112522
=0.0490.0032
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