Final answer:
The critical value for α=0.01 and n=20 using a standard normal distribution is approximately 2.326. This value is used to identify the cutoff point on a normal curve. If using a t-distribution for this calculation, the degrees of freedom (df) would be 19, and the critical t-value would need to be looked up in a t-table or calculated using statistical software.
Step-by-step explanation:
To find the critical value when α=0.01, n=20, and s.d.=2, we first need to acknowledge that this scenario likely pertains to hypothesis testing or constructing a confidence interval. With the given information, the critical value can be found in the context of the t-distribution because we have a sample standard deviation rather than the population standard deviation, and the sample size is small (< 30).
However, there seems to be a slight confusion in the question provided. To clarify, the initial information suggests we should find the critical value '20.01', which does not correspond to any standard terminology. Instead, we typically look for the critical value 'z0.01' for the z-distribution or 't0.01' for the t-distribution at a specified significance level α. Assuming the t-distribution is to be used, the degrees of freedom (df) is calculated as n - 1 (not n - 2 as erroneously mentioned in the reference). This means for n=20, the degree of freedom would be df=19. Given this df, you would look up the value in a t-distribution table or use statistical software to obtain the critical t-value for a one-tailed test at α=0.01.