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Chapter 13: Q.13.25 (page 533)

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

Expert verified

The determined values are

a).SSTR=24.

b).MSTR=12.

c).SSE=16.

d).MSE=2.29.

e).F-statistic=5.25.

Step by step solution

01

Part (a) Step 1: Given Information

Given data:

02

Part (a) Step 2: Explanation

Based on the information provided,

k=3

n1=3,

n2=3,

n3=4

n=3+3+4

n=10

Samples one, two, and three have the following mean values:

x1¯=8+4+63

=6

x2¯=2+1+33

=2

x3¯=4+3+6+34

=4

03

Part (a) Step 3:Explanation

Calculate the mean.

x¯=8+4+6+2+!+3+4+3+6+310

=4

SSTR (sum of squares treatment)

localid="1652767430243" SSTR=n1x1¯-x¯2+n2x2¯-x¯2+n3x3¯-x¯2 =3(6-4)2+3(2-4)2+4(4-4)2

=24

04

Part (b) Step 1: Given Information

Given data,

05

Part (b) Step 2: Explanation

We know

SSTR=24

MSTR=SSTRk-1

=243-1

=12

06

Part (c) Step 1: Given Information

Given data:

07

Part (c) Step 2: Explanation

Each sample's variance is s12=4,

s22=1,

s32=2

SSE=n1-1s12+n2-1s22+n3-1s32 =(3-1)(4)+(3-1)(1)+(4-1)(2)

=16

08

Part (d) Step 1: Given Information

Given data,

09

Part (d) Step 2: Explanation

We know

n=10,

k=3

MSE=SSEn-k

=1610-3

=2.29

10

Part (e) Step 1: Given Information

Given data:

11

Part (e) Step 2: Explanation

We know

n=10,

k=3

F-statistic=MSTRMSE

=122.29

=5.25

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