  Nicontio1 2021-12-11 Answered
a. In this ANOVA analysis, what are we trying to determine about the three populations they’re taken from?
b. State the null and alternate hypotheses for a three-sample ANOVA analysis.
c. What sample statistics must be known to conduct an ANOVA analysis?
d. In an ANOVA test, what does an F test statistic lower than its critical value tell us about the three populations we’re examining?

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Step 1
It is given that there are three samples involve in the ANOVA. Therefore,
a).
The ANOVA is a technique which is used to determine whether the population of more than two groups are significantly different or not.
Here, there are 3 sample groups available in the ANOVA, it means that the population means would be 3 as well.
Thus, for the given case, we are trying to determine whether these three population groups' means are significantly different or not.
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Step 1
b).
As per the above,
Consider that $$\displaystyle\mu_{{{1}}},\mu_{{{2}}}\ {\quad\text{and}\quad}\ \mu_{{{3}}},$$ are the population means for these 3 samples.
Thus, the null and alternate hypotheses are:
$$\displaystyle{H}_{{{0}}}:\mu_{{{1}}}=\mu_{{{2}}}=\mu_{{{3}}},$$
$$\displaystyle{H}_{{{1}}}:$$(At least one mean is different)