## Related questions with answers

The following data represent a simple random sample of n=5 from three populations that are known to be normally distributed. Verify that the F-test statistic is 2.599.

Solution

VerifiedIf we suppose that $k$ samples come from the same normal population (whose mean is $\mu$ and variance is $\sigma^2$), the sample size of $i$th sample is $n_i$, the sample mean of $i$th sample is $\bar{x}_i$, and the sample standard deviation of $i$th sample is $s_i$, $i=1,2,\dots,k$, $\underline{\text{the }F\text{-test statistic}}$ can be computed using formula

$F_0= \dfrac{\text{MST}}{\text{MSE}}=\dfrac{\frac{\text{SST}}{k-1}}{\frac{\text{SSE}}{n-k}}=\dfrac{\frac{n_1(\bar{x}_1-\bar{x})^2+n_2(\bar{x}_2-\bar{x})^2+\dots+n_k(\bar{x}_k-\bar{x})^2}{k-1}}{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2+\dots+(n_k-1)s_k^2}{n-k}}$

where $\bar{x}$ is the mean of the entire set of data, and

$n=n_1+n_2+\dots+n_k$

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