Question

Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume sample size is large. Assume a normal distribution with $\mathrm{n} \geq 30 .$

Name: Problem 22, Chapter 9: Introductory Business Statistics
Uploaded: 2020-09-21T02:37:57-08:00
Duration: 16 s
Channel: Bryan Meares
Description: Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume sample size is large. Assume a normal distribution with n ≥30 .

   Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume sample size is large. Assume a normal distribution with $\mathrm{n} \geq 30 .$

Introductory Business Statistics

Alexander Holmes,… 1st Edition

Chapter 9, Problem 22

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Solved by Expert Bryan Meares

09/21/2020

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We are testing a population mean. Show more…

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Which distribution do you use when you are testing a population mean and the population standard deviation is known? Assume sample size is large. Assume a normal distribution with $\mathrm{n} \geq 30 .$

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Key Concepts

Z Distribution

The z distribution, or standard normal distribution, is used for hypothesis testing when the population standard deviation is known. It provides a basis for calculating probabilities and significance levels under the assumption that the sampling distribution of the sample mean is normal, often justified by the central limit theorem when the sample size is large.

Central Limit Theorem

The central limit theorem is a fundamental concept in statistics stating that, for a sufficiently large sample size, the sampling distribution of the sample mean will be approximately normally distributed regardless of the shape of the population distribution. This justifies the use of the z distribution when testing hypotheses about the population mean with large samples.

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