Question

We have provided data from independent simple random samples from several populations. In each case, determine the following items.

a. SSTR

b. MSTR

c. SSE

d. MSE

e. F

Short answer

The determined values are,

a).$SSTR=72$.

b).$MSTR=18$.

c).$SSE=32$.

d). $MSE=3.2$

e).$F-$statistics$=5.625$.

Step-by-step solution

Part (a) Step 1: Given Information

Given data:

$k=5$,

role="math" localid="1652191107356" $n=15$.

Part (a) Step 2: Explanation

Formula used:

$SSTR=\sum T_j^2/n_j-\left(\sum x_i\right)2/n$

localid="1652191165558" $\sum T_j^2/n_j=(27+108+192+12+12+108)$

$=447$

$\left(\sum x_i\right)2/n=5625/15$

$SSTR=\sum T_j^2/n_j-\left(\sum x_i\right)2/n$

localid="1652191267352" $447-375=72$

Part (b) Step 1: Given Information

Given data,

$k=5$,

$n=15$.

Part (b) Step 2: Explanation

Formula used:

$MSTR=SSTR/k-1$

Calculation:

$MSTR=72/4$

$=18$

Part (c) Step 1: Given Information

Given data:

$k=5$,

$n=15$.

Part (c) Step 2: Explanation

Formula used:

$SST=\sum x_i^2-\left(\sum x_i\right)2/n$

Calculation:

$\mathrm{SST}=479-375$

$=104$

$\text{SSE}=\text{SST-SSTR}$

$\text{=104-72}$

$=32$

Part (d) Step 1: Given Information

Given data:

$k=5$,

$n=15$.

Part (d) Step 2: Explanation

To find the value of $MSE$:

$MSE=SSE/n-k$

$=32/15-5$

$=32/10$

$=3.2$

Part (e) Step 1: Given Information

Given data:

$k=5$,

$n=15$.

Part (e) Step 2: Explanation

To find the value of $F-$statistics:

$F=MSTR/MSE$

$=18/3.2$

$=5.625$