If a sample of size 30 is selected, the value of A for the probability
P(t greater or less A) = 0.01 is?
Probablity of t greater than or less than A? You have to be kidding, it is near 1.0, not .01. t is either greater than, equal or less than A. If the Prob greater than or less than is .01, the the probability of it being equal to A is .99
Something is wrong with the problem.
To find the value of A for the given probability, we need to refer to the t-distribution table. The t-distribution table is a reference table used to determine critical values for the t-distribution, which is commonly used in hypothesis testing and confidence interval calculations when the sample size is small.
To use the t-distribution table, you need the degrees of freedom (df), which is calculated as n - 1, where n is the sample size. In this case, the sample size is 30, so the degrees of freedom is 30 - 1 = 29.
Since the probability is given as P(t greater or less A) = 0.01, we want to find the t-value that corresponds to a cumulative probability of 0.01 in either the upper (greater) or lower (less) tail of the t-distribution.
Because the t-distribution is symmetrical, we can find the t-value in the upper tail and then take its negative for the lower tail.
Now, let's find the t-value using the t-distribution table:
1. Look for the row corresponding to the degrees of freedom (df = 29).
2. Find the column that contains the desired cumulative probability (0.01).
3. Locate the intersection of the row and column to find the t-value.
For a cumulative probability of 0.01 with 29 degrees of freedom, the t-value is approximately -2.763.
Therefore, A would be -2.763 assuming we are referring to the upper end of the tail. If we are referring to the lower end, A would be 2.763 (negative value is not needed).