91Ó°ÊÓ

The difference of the two means was tested here using two-sample t test. The given output suggests that the two methods differ. The hypotheses tested here are \({H_0}:{\mu _1} - {\mu _2} = 0 {\rm{versus}} {H_0}:{\mu _1} - {\mu _2} \ne 0 ,{\rm{where}} {\mu _1},{\mu _2}\) are the true averages of method 1 and 2 , respectively.

The conclusion to reject null hypothesis comes from the fact that

\(P = 0.001 < 0.01 = \alpha \) or any other significance level.

The given confidence interval does not include zero, thus the difference to be zero is highly unlikely.

The methods differ; Confidence interval indicates that it is highly unlikely for difference to be zero.

TWO-SAMPLE T-TEST

Given in the output:

\(\begin{array}{c}{H_0}:{\mu _1} - {\mu _2} = 0\\{H_0}:{\mu _1} - {\mu _2} \ne 0\\ t = 12.16\\P = 0.001\\ df = 3\end{array}\)

Let us assume:\(\alpha = 0.05.\)

If the P-value is less than the significance level, reject the null hypothesis. \(P < 0.05 \Rightarrow Reject {H_0}\)

There is sufficient evidence to support the claim that the population means are not equal.

Two sample confidence interval:

Given in the output:\((6.498,11.102)\)

The confidence interval does not contain 0, which indicates that the difference of the population means is not zero and thus the population means appear to be not equal.

We can then conclude: There is sufficient evidence to support the claim that the population means are not equal.

We then note that both methods lead to the same conclusion.