Chapter 8: Q 8.108. (page 342)

Why do you need to consider the student zed version of $\bar{x}$ 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 $s . d .$ , $σ$ and follows $t$ distribution with $d f = n - 1$

Step by step solution

Concept

The formula used: $Z = \frac{\bar{x} - μ}{\frac{σ}{\sqrt{n}}}$

Explanation

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

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

Short Answer

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Explanation

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

Short Answer

Step by step solution

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Explanation

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Most popular questions from this chapter

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