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Chapter 13: Q.13.27 (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=36.

b).MSTR=9.

c).SSE=52.

d). MSE=3.47.

e). F-statistic=2.60.

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=5

n1=4,

n2=3,

n3=5,

n4=5,

n5=3

n=4+3+5+5+3

n=20

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

x1¯=7+4+5+44

=5

x2¯=5+9+43

=6

x3¯=6+7+5+4+85

=6

x4¯=3+7+7+4+45

=5

x5¯=7+9+113

=9

03

Part (a) Step 3: Explanation

Calculate the mean:

x¯=12020

=6

SSTR (sum of squares treatment)

SSTR=n1x1¯-x¯2+n2x2¯-x¯2+n3x3¯-x¯2+n4x4¯-x¯2+n5x5¯-x¯2

=4(4-5)2+3(7-6)2+5(3-6)2+5(6-5)2+3(6-9)2

=36

04

Part (b) Step 1: Given Information

Given data:

05

Part (b) Step 2: Explanation

We know,

SSTR=36

MSTR=SSTRk-1

=365-1

=9

06

Part (c) Step 1: Given Information

Given data,

07

Part (c) Step 2: Explanation

Each sample's variance is

s12=2,

s22=7,

s32=2.5,

s42=3.5,

s52=4

SSE=n1-1s12+n2-1s22+n3-1s32

=(4-1)(2)+(3-1)(7)+(5-1)(2.5)+(5-1)3.5+(3-1)4

=52

08

Part (d) Step 1: Given Information

Given data,

09

Part (d) Step 2: Explanation

We know

n=20,

k=5

MSE=SSEn-k

=5220-5

=3.47
10

Part (e) Step 1: Given Information

Given data:

11

Part (e) Step 2: Explanation

F-statistic=MSTRMSE

=93.47

=2.60

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