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). $S S T R = 72$ .

b). $M S T R = 18$ .

c). $S S E = 32$ .

d). $M S E = 3.2$

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:

$S S T R = \sum T_{j}^{2} / n_{j} - (\sum x_{i}) 2 / n$

localid="1652191165558" $\sum T_{j}^{2} / n_{j} = (27 + 108 + 192 + 12 + 12 + 108)$

$= 447$

$(\sum x_{i}) 2 / n = 5625 / 15$

$S S T R = \sum T_{j}^{2} / n_{j} - (\sum x_{i}) 2 / n$

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

Part (b) Step 1: Given Information

Given data,

$k = 5$ ,

$n = 15$ .

Part (b) Step 2: Explanation

Formula used:

$M S T R = S S T R / k - 1$

Calculation:

$M S T R = 72 / 4$

$= 18$

Part (c) Step 1: Given Information

Given data:

$k = 5$ ,

$n = 15$ .

Part (c) Step 2: Explanation

Formula used:

$S S T = \sum x_{i}^{2} - (\sum x_{i}) 2 / n$

Calculation:

$SST = 479 - 375$

$= 104$

$SSE = SST-SSTR$

$=104-72$

$= 32$

Part (d) Step 1: Given Information

Given data:

$k = 5$ ,

$n = 15$ .

Part (d) Step 2: Explanation

To find the value of $M S E$ :

$M S E = S S E / n - k$

= 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:

$F = M S T R / M S E$

$= 18 / 3.2$

$= 5.625$

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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

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Explanation

Part (d) Step 1: Given Information

Part (d) Step 2: Explanation

Part (e) Step 1: Given Information

Part (e) Step 2: Explanation

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We have provided data from independent simple random samples from several populations. In each case, determine the following items.a. SSTRb. MSTRc. SSEd. MSEe. F

Short Answer

Step by step solution

Part (a) Step 1: Given Information

Part (a) Step 2: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Explanation

Part (d) Step 1: Given Information

Part (d) Step 2: Explanation

Part (e) Step 1: Given Information

Part (e) Step 2: Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Logic and Functions

Mechanics Maths

Statistics

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

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