Question

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

Short answer

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

Step-by-step solution

Given information

Testing hypothesis are as follows

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

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

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.

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.