Question

A population mean is $13 .$ The sample mean is 12.8 , and the sample standard deviation is two. The sample size is $20 .$ What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

Name: Problem 24, Chapter 9: Introductory Business Statistics
Uploaded: 2020-09-21T02:39:00-08:00
Duration: 28 s
Channel: Bryan Meares
Description: A population mean is 13 . The sample mean is 12.8 , and the sample standard deviation is two. The sample size is 20 . What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

   A population mean is $13 .$ The sample mean is 12.8 , and the sample standard deviation is two. The sample size is $20 .$ What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

Introductory Business Statistics

Alexander Holmes,… 1st Edition

Chapter 9, Problem 24

Instant Answer

Solved by Expert Bryan Meares

09/21/2020

Step 1

We are given the population mean (µ = 13), sample mean (x̄ = 12.8), sample standard deviation (s = 2), and sample size (n = 20). Show more…

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A population mean is $13 .$ The sample mean is 12.8 , and the sample standard deviation is two. The sample size is $20 .$ What distribution should you use to perform a hypothesis test? Assume the underlying population is normal.

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Key Concepts

Student's t-Distribution

In hypothesis testing, when the population standard deviation is unknown and the sample size is small, the Student's t-distribution is used instead of the normal distribution. This distribution accounts for the additional uncertainty introduced by estimating the standard deviation from the sample and is applicable when the underlying population is normal.

Degrees of Freedom

Degrees of freedom, typically calculated as the sample size minus one (n - 1), are a crucial component of the t-distribution. They indicate the number of independent pieces of information available for estimating variability and influence the shape and spread of the t-distribution, which in turn affects the critical values used in hypothesis testing.

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