91Ó°ÊÓ

The data is given

Calculate the SST, SSTR and SSE using given relation

\(SST=\sum x^{2}-\frac{(\sum x)^{2}}{n}\)

\(SST=1561154-\frac{(4228)^{2}}{12}=7.15\times 10^{4}\)

\(SSTR=\frac{\sum (x_{i})^{2}}{n_{i}}-\frac{\sum (x)^{2}}{n}\)

\(SSTR=\frac{1828^{2}}{4}+\frac{1225^{2}}{4}+\frac{1175^{2}}{4}-\frac{(4228)^{2}}{12}=6.60\times 10^{4}\)

\(SSE=SST-SSTR=5.45\times 10^{3}\)

Then,

\(df_{T}=k-1=3-1=2\)

\(df_{E}=n-k=12-2=10\)

\(MSTR=\frac{SSTR}{df_{T}}=\frac{6.60\times10^{4}}{2}=3.30\times 10^{4}\)

\(MSE=\frac{SSE}{df_{E}}=\frac{5.45\times 10^{3}}{10}=0.545\times 10^{3}\)

\(F=\frac{MSTR}{MSE}=\frac{3.30\times 10^{4}}{0.545\times 10^{3}}\approx 60.55\times 10^{3}\)

Then make an ANOVA table.

At the \(1%\) significance level data provide the sufficient evidence because p-value reject null hypothesis.

\(P<0.01\Rightarrow \) Reject \(H_{0}\)

Program:

Query:

• First, we have defined the samples.
• Calculate the value of SST and SSTR.
• Then calculate the SSE.
• Then calculate MSTR and MSE and F.

• Make an ANOVA table.