Critical probability is the essentially cut-off value. The critical probability when the confidence level of 58% is 0.79.
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
[tex]\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}[/tex]
where the value of the α is expressed as,
[tex]\alpha= 1 -\dfrac{\rm Confidence\ interval}{100}[/tex]
Now, as the confidence interval is given to us, therefore, the value of the alpha can be written as,
[tex]\alpha= 1 -\dfrac{\rm 58\%}{100} = 0.42[/tex]
Further, the critical probability, assuming a confidence level of 58% is,
[tex]\rm Critical\ Probability, (P*) = 1-\dfrac{\alpha }{2}\\\\\rm Critical\ Probability, (P*) = 1-\dfrac{0.42}{2} = 0.79[/tex]
Hence, the critical probability is 0.79.
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