Chapter 13: Q.13.29 (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). $S S T R = 138$ .

B). $M S T R = 46$ .

C). $S S E = 72$ .

D). $M S E = 9$ .

E). $F - statistic = 5.11$ .

Step by step solution

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

Based on the information provided,

$k = 4$

$n_{1} = n_{2} = n_{3} = n_{4} = 3$

$n = 12$

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

$\bar{x_{1}} = 8,$

$\bar{x_{2}} = 5,$

$\bar{x_{3}} = 12,$

$\bar{x_{4}} = 3$

Part (a) Step 3: Explanation

Calculate the mean:

$\bar{x} = \frac{84}{12}$

$= 7$

SSTR (sum of squares treatment)

$S S T R = n_{1} {(\bar{x_{1}} - \bar{x})}^{2} + n_{2} {(\bar{x_{2}} - \bar{x})}^{2} + n_{3} {(\bar{x_{3}} - \bar{x})}^{2} + n_{4} {(\bar{x_{4}} - \bar{x})}^{2} + n_{5} {(\bar{x_{5}} - \bar{x})}^{2}$ $= 3 (8 - 7)^{2} + 3 (5 - 7)^{2} + 3 (12 - 7)^{2} + 3 (3 - 7)^{2}$

$= 138$

Part (b) Step 1: Given Information

Given data;

Part (b) Step 2: Explanation

We know $S S T R = 138$

$M S T R = \frac{S S T R}{k - 1}$

$= \frac{138}{4 - 1}$

$= 46$

Part (c) Step 1: Given Information

Given data:

Part (c) Step 2: Given Information

Each sample's variance is $s_{1}^{2} = 7,$

$s_{2}^{2} = 13,$

$s_{3}^{2} = 12,$

$s_{4}^{2} = 4$

$SSE = (n_{1} - 1) s_{1} {}^{2}+ (n_{2} - 1) s_{2} {}^{2}+ (n_{3} - 1) s_{3} {}^{2}$ $= (4 - 1) (7) + (4 - 1) (13) + (4 - 1) (12) + (4 - 1) 4$

$= 72$

Part (d) Step 1: Given Information

Given data:

Part (d) Step 2: Explanation

We know

$n = 12,$

$k = 4$

$M S E = \frac{S S E}{n - k}$

$= \frac{72}{12 - 4}$

$= 9$

Part (e) Step 1: Given Information

Given data:

Part (e) Step 2: Explanation

To find the value of

$F - statistic= \frac{MSTR}{M S E}$

$= \frac{46}{9}$

$= 5.11$

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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 (a) Step 3: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Given Information

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 (a) Step 3: Explanation

Part (b) Step 1: Given Information

Part (b) Step 2: Explanation

Part (c) Step 1: Given Information

Part (c) Step 2: Given Information

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

Geometry

Pure Maths

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

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