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\({n_1} = 5\)

\({n_2} = 6\)

\({n_3} = 7\)

\({n_4} = 6\)

\(\begin{aligned}{l}f = 3.68\\\alpha = 0.01\end{aligned}\)

The null hypothesis states that all population means are equal:

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3} = {\mu _4}\)

The alternative hypothesis states the opposite of the null hypothesis:

\({H_1}:\)not all of\({\mu _1},{\mu _2},{\mu _3},{\mu _4}\)are equal

The degree of freedom for the numerator is the number of groups decreased by 1:

\(\begin{aligned}{c}df = I - 1\\ = 4 - 1\\ = 3\end{aligned}\)

The degrees of freedom for the denominator is the total sample size decreased by the number of groups:

\(\begin{aligned}{c}df = N - I\\ = (5 + 6 + 7 + 6) - 4\\ = 24 - 4\\ = 20\end{aligned}\)

The P-value is the probability of obtaining the value of the test statistic, of a value more extreme. The P-value is the number (or interval) in the column title of the F-distribution table in the appendix containing the F-value in the row \(df = 3\)and\(dfd = 20\):

\(0.010 < P < 0.050\)

If the P-value is less than the significance level, then reject the null hypothesis

\(p > 0.01 \Rightarrow \)Fail to reject \({H_0}\)

There is not sufficient evidence to reject the claim that the true average flow rates are the same for the four different types of nozzle.

\({n_1} = 5\)

\({n_2} = 6\)

\({n_3} = 7\)

\({n_4} = 6\)

\(\begin{aligned}{l}f = 3.68\\\alpha = 0.01\\P = 0.029\end{aligned}\)

The null hypothesis states that all population means are equal:

\({H_0}:{\mu _1} = {\mu _2} = {\mu _3} = {\mu _4}\)

The alternative hypothesis states the opposite of the null hypothesis:

\({H_1}:\)not all of\({\mu _1},{\mu _2},{\mu _3},{\mu _4}\)are equal

If the P-value is less than the significance level, then reject the null hypothesis

\(P = 0.029 > 0.01 \Rightarrow \)Fail to reject \({H_0}\)

There is not sufficient evidence to reject the claim that the true average flow rates are the same for the four different types of nozzle.