Q 8.113. Explain why there is more variat... [FREE SOLUTION]

Chapter 8: Q 8.113. (page 342)

Explain why there is more variation in the possible values of the studentized version of $\overset{炉}{x}$ than in the possible values of the standardized version of $\overset{鈫�}{x}$

Short Answer

Expert verified

Variation in $\overset{炉}{x}$ is the single cause of variation in $Z$ values, but variation in $t$ values is produced by both $\overset{炉}{x}$ and $s$ The variety in $t$ values is obviously bigger than the variation in $Z$ values.

Step by step solution

Given information

The standardized version of $\overset{炉}{x}$ is given by, $Z = \frac{\overset{炉}{x} - 渭}{\frac{蟽}{\sqrt{n}}}$

Concept

The formula used: $Z = \frac{\overset{炉}{x} - 渭}{\frac{蟽}{\sqrt{n}}}$ , $t = \frac{\overset{炉}{x} - 渭}{\frac{s}{\sqrt{n}}}$

Calculation

Standardized version of $\overset{炉}{x}$ is given by,

$Z = \frac{\overset{炉}{x} - 渭}{\frac{蟽}{\sqrt{n}}}$ , Where $蟽$ is known. And studentized version of $\overset{炉}{x}$ is given by,

$t = \frac{\overset{炉}{x} - 渭}{\frac{s}{\sqrt{n}}}$ , Where $s$ is the sample S.D $s = \sqrt{\frac{1}{n - 1} {鈭�}_{i = 1}^{n} {(x_{i} - \overset{炉}{x})}^{2}}$

Explanation

We can see from the preceding two formulas that the standardized version of $\overset{炉}{x}, Z$ , is dependent on only one random variable, $\overset{炉}{x}$ The studentized form of $\overset{炉}{x}$ , on the other hand, is dependent on two random variables, $\overset{炉}{x}$ and $s$ Thus, variation in the values of $Z$ is caused solely by variation in $\overset{炉}{x}$ , but variation in the values of $t$ is caused by both $\overset{炉}{x}$ and $s$ . Obviously, the variation in $t$ is greater than the variation in $Z$ values.

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Explain why there is more variation in the possible values of the studentized version of $\overset{炉}{x}$ than in the possible values of the standardized version of $\overset{鈫�}{x}$

Short Answer

Step by step solution

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Concept

Calculation

Explanation

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91影视

Explain why there is more variation in the possible values of the studentized version of x炉 than in the possible values of the standardized version of x鈫�

Short Answer

Step by step solution

Given information

Concept

Calculation

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Mechanics Maths

Logic and Functions

Probability and Statistics

Decision Maths

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Explain why there is more variation in the possible values of the studentized version of $\overset{炉}{x}$ than in the possible values of the standardized version of $\overset{鈫�}{x}$