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Chapter 13: Q.13.28 (page 535)

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=72.

b).MSTR=18.

c).SSE=32.

d). MSE=3.2

e).F-statistics=5.625.

Step by step solution

01

Part (a) Step 1: Given Information

Given data:

k=5,

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

02

Part (a) Step 2: Explanation

Formula used:

SSTR=鈭�Tj2/nj-鈭�xi2/n

localid="1652191165558" 鈭�Tj2/nj=(27+108+192+12+12+108)

=447

鈭�xi2/n=5625/15

SSTR=鈭�Tj2/nj-鈭�xi2/n

localid="1652191267352" 447-375=72

03

Part (b) Step 1: Given Information

Given data,

k=5,

n=15.

04

Part (b) Step 2: Explanation

Formula used:

MSTR=SSTR/k-1

Calculation:

MSTR=72/4

=18

05

Part (c) Step 1: Given Information

Given data:

k=5,

n=15.

06

Part (c) Step 2: Explanation

Formula used:

SST=鈭�xi2-鈭�xi2/n

Calculation:

SST=479-375

=104

SSE=SST-SSTR

=104-72

=32

07

Part (d) Step 1: Given Information

Given data:

k=5,

n=15.

08

Part (d) Step 2: Explanation

To find the value of MSE:

MSE=SSE/n-k

=32/15-5

=32/10

=3.2

09

Part (e) Step 1: Given Information

Given data:

k=5,

n=15.

10

Part (e) Step 2: Explanation

To find the value of F-statistics:

F=MSTR/MSE

=18/3.2

=5.625

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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
See all solutions

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