Q 8.108. Why do you need to consider the ... [FREE SOLUTION]

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Chapter 8: Q 8.108. (page 342)

Why do you need to consider the student zed version of $\overset{炉}{x}$ to develop a confidence-interval procedure for a population means when the population standard deviation is unknown?

Short Answer

Expert verified

$t$ does not depend on population $s . d .$ , $蟽$ and follows $t$ distribution with $d f = n - 1$

Step by step solution

Concept

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

Explanation

The $Z -$ interval procedure of finding confidence interval of $渭$ is based on the standardized version of $\overset{炉}{x}, Z = \frac{\overset{炉}{x} - 渭}{\frac{蟽}{\sqrt{n}}}$ and hence the C.I of $渭$ depends on $蟽$ . But, if $蟽$ is unknown then we can not use the $Z -$ interval procedure based on $Z$ . In this situation we consider studentized version of $\overset{炉}{x}$ , $t = \frac{\overset{炉}{x} - 渭}{\frac{s}{\sqrt{n}}}$ and use one mean $t -$ interval procedure of finding confidence interval of $渭$ based on $t$ , since studentized variable $t$ does not depend on population s.d., $蟽$ and follows $t$ distribution with $d f = n - 1$

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91影视

Why do you need to consider the student zed version of $\overset{炉}{x}$ to develop a confidence-interval procedure for a population means when the population standard deviation is unknown?

Short Answer

Step by step solution

Concept

Explanation

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91影视

Why do you need to consider the student zed version of x炉 to develop a confidence-interval procedure for a population means when the population standard deviation is unknown?

Short Answer

Step by step solution

Concept

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Statistics

Geometry

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Why do you need to consider the student zed version of $\overset{炉}{x}$ to develop a confidence-interval procedure for a population means when the population standard deviation is unknown?