Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.
<h3>What is the critical probability?</h3>
Critical probability is the essentially cut-off value that defines the region where the test statistic is unlikely to lie.
As it is given that the confidence level is 58%. therefore, in order to calculate the critical probability, we need to calculate the margin of error within a set of data, and it is given by the formula
![\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}](https://tex.z-dn.net/?f=%5Crm%20Critical%5C%20Probability%2C%20%28P%2A%29%20%3D%201-%5Cdfrac%7B%5Calpha%20%7D%7B2%7D)
where the value of the α is expressed as,
![\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}](https://tex.z-dn.net/?f=%5Calpha%3D%201%20-%5Cdfrac%7B%5Crm%20Confidence%5C%20interval%7D%7B100%7D)
Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,
![\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42](https://tex.z-dn.net/?f=%5Calpha%3D%201%20-%5Cdfrac%7B%5Crm%2058%5C%25%7D%7B100%7D%20%3D%200.42)
Further, the critical probability, assuming a confidence level of 58% is,
![\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79](https://tex.z-dn.net/?f=%5Crm%20Critical%5C%20Probability%2C%20%28P%2A%29%20%3D%201-%5Cdfrac%7B%5Calpha%20%7D%7B2%7D%5C%5C%5C%5C%5Crm%20Critical%5C%20Probability%2C%20%28P%2A%29%20%3D%201-%5Cdfrac%7B0.42%7D%7B2%7D%20%3D%200.79)
Hence, the critical probability is 0.79.
Learn more about Critical Probability:
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