Question

Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume a normal distribution, with $n \geq 30$.

Name: Problem 23, Chapter 9: Introductory Business Statistics
Uploaded: 2020-09-21T02:38:15-08:00
Duration: 23 s
Channel: Bryan Meares
Description: Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume a normal distribution, with n ≥30.

   Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume a normal distribution, with $n \geq 30$.

Introductory Business Statistics

Alexander Holmes,… 1st Edition

Chapter 9, Problem 23

Instant Answer

Solved by Expert Bryan Meares

09/21/2020

Step 1

In this case, you are testing one population mean, the standard deviation of the population is not known, and the sample size is $n \geq 30$. Additionally, it is assumed that the population from which the sample is drawn follows a normal distribution. Show more…

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Which distribution do you use when the standard deviation is not known and you are testing one population mean? Assume a normal distribution, with $n \geq 30$.

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Key Concepts

Student's t-Distribution

The Student's t-distribution is used when the population standard deviation is unknown and the sample standard deviation is substituted as an estimate. This distribution is particularly important for hypothesis tests concerning a single population mean, as it adjusts for the extra variability due to estimating the standard deviation from the sample.

Degrees of Freedom

Degrees of freedom, generally calculated as the sample size minus one for a single mean test, determine the specific shape of the t-distribution. As the sample size increases, the t-distribution approaches the normal distribution, reducing the impact of the extra uncertainty from estimating the population standard deviation.

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