The Z critical value for constructing a 99% confidence interval for a proportion is 2.58.
A z-score measures exactly how many standard deviations a data point is above or below the mean. It allows us to calculate the probability of a score occurring within our normal distribution and enables us to compare two scores that are from different normal distributions.
For the given situation,
The confidence interval for a proportion = 99% = 0.99
Area to the left of a positive Z score in this standard normal distribution table is
⇒ [tex]\frac{1+confidence level}{2}[/tex]
⇒ [tex]\frac{1+0.99}{2}[/tex]
⇒ [tex]\frac{1.99}{2}[/tex]
⇒ [tex]0.995[/tex]
The corresponding Z score in the table for 0.995 is
⇒ [tex]2.5+0.08[/tex]
⇒ [tex]2.58[/tex]
Hence we can conclude that the Z critical value for constructing a 99% confidence interval for a proportion is 2.58.
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