What is the critical z-value for a one tailed lower test at the 1% level of risk?
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A. B. C. D. E.E
This is found by subtracting the 0.01 from 0.5 and then finding the z-value for 0.49.
To determine the critical z-value for a one-tailed lower test at the 1% level of risk, we need to find the z-value that corresponds to a 1% (0.01) significance level in the lower tail of the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. The area under the curve to the left of any given z-value represents the cumulative probability of observing a value less than or equal to that z-value.
To find the critical z-value, we can look up the corresponding value from a standard normal distribution table or use statistical software. However, I'll provide you with a brief explanation using the table.
First, identify the desired significance level, which is 1% or 0.01.
Since this is a one-tailed lower test, the critical region is in the left tail of the distribution.
Look up the value closest to 0.01 in the body of the standard normal distribution table. In this case, the closest value is 0.0099.
Locate the corresponding z-value in the leftmost column of the table. The closest value to 0.0099 is approximately -2.33.
Therefore, the correct answer is E. -2.33.
This value represents the point on the standard normal distribution below which lies 1% of the distribution's total area, indicating that there is a 1% chance of observing a value lower than this critical z-value in a one-tailed lower test at the 1% level of risk.