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Chapter 13: Q.13.26 (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

Determined values are

a).SSTR=46.

b). MSTR=15.33.

c).SSE=28.

d).MSE=2.33.

e).F-statistic=6.58.

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=4

n1=3

n2=5,

n3=5,

n4=3

n=3+5+5+3

n=16

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

x1¯=6+3+33

=4

x2¯=9+5+7+8+65

=7

x3¯=4+4+2+2+35

=3

x2¯=8+4+63

=6

03

Part (a) Step 3: Explanation

Calculate the mean:

x¯=6+3+3+9+5+7+8+6+4+4+2+2+3+8+4+616

=5

SSTR (sum of squares treatment):

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

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

=46

04

Part (b) Step 1: Given Information

Given data:

05

Part (b) Step 2: Explanation

We know,

SSTR=46

MSTR=SSTRk-1

=464-1

=15.33

06

Part (c) Step 1: Given Information

Given data:

07

Part (c) Step 2: Explanation

Each sample's variance is s12=3,

s22=2.5,

s32=1,

s42=4

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

=(3-1)(3)+(5-1)(2.5)+(5-1)(1)+(3-1)4

=28

08

Part (d) Step 1: Given Information

Given data:

09

Part (d) Step 2: Explanation

We know

n=16,

k=4

MSE=SSEn-k

=2816-4

=2.33

10

Part (e) Step 1: Given Information

Given data:

11

Part (e) Step 2: Explanation

F-statistic=MSTRMSE

=15.332.33

=6.58

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