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Chapter 8: Q82E (page 501)

a.Consider testing \(H0\) : \(\mu \)=80. Under what conditions should you use the t-distribution to conduct the test?

Short Answer

Expert verified

a.Two conditions to conduct the test for t-distribution

Step by step solution

01

Given information

Testing hypothesis are as follows

\(H0\): \(\mu \)=80.

\(H\alpha :\mu \ne 80\)

02

Explaining the t-distribution

When the population standard deviation is unknown and the data are from a normally distributed population, the t-distribution defines the standardized distance between the sample and the population mean.

03

Conditions to use the t-distribution to conduct the test

Two requirements have got to be met before the t-distribution is employed. The first is the sampling distribution's normality. Such that the x-bar uses a traditional distribution. It may accomplish in one of two ways. It would be best to grasp that the individual observations follow a standard distribution, or like to own a large sample size (more than 30), so it can depend upon the central limit theorem. After calculating the population variance with the sample variance, we now have the t-distribution.

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Most popular questions from this chapter

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Question: Two independent random samples have been selected—100 observations from population 1 and 100 from population 2. Sample means x¯1=26.6,x¯2= 15.5 were obtained. From previous experience with these populations, it is known that the variances areσ12=9andσ22=16 .

a. Find σ(x¯1-x¯2).

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b. Does it appear that this value contradicts the null hypothesis H0:(μ1-μ2)=10?

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g. Which inference provides more information about the value of μ1-μ2— the test of hypothesis in part e or the confidence interval in part f?
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