For df = 25, determine the value of A that corresponds to each of the following probabilites:
a. P(t >- A)= 0.025
b. P(t <- A)= 0.10
c. P(-A <- t <- A)=0.99
To determine the value of A that corresponds to each probability, we can use the t-distribution table or a statistical calculator/software. Here's how you can do it:
a. P(t > -A) = 0.025:
To find the value of A, we need to find the critical value that corresponds to the given probability. Since the t-distribution is symmetric, we want to find the t-value such that the area under the curve to the right of it is 0.025 (or 2.5% in decimal form).
Using a t-distribution table, find the row that corresponds to degrees of freedom (df) = 25. In this row, locate the column that corresponds to the desired probability of 0.025. The intersection of this row and column will give you the value of A.
Alternatively, you can use a statistical calculator or software to calculate it. Inputting the degrees of freedom (df) as 25 and the probability as 0.025, the calculator will provide the corresponding value of A.
b. P(t < -A) = 0.10:
Similar to part a, we want to find the t-value such that the area under the curve to the left of it is 0.10 (or 10% in decimal form).
Using a t-distribution table, find the row that corresponds to degrees of freedom (df) = 25. In this row, locate the column that corresponds to the desired probability of 0.10. The intersection of this row and column will give you the value of A.
Alternatively, you can use a statistical calculator or software to calculate it. Inputting the degrees of freedom (df) as 25 and the probability as 0.10, the calculator will provide the corresponding value of A.
c. P(-A < t < A) = 0.99:
In this case, we want to find the t-values such that the area under the curve between them is 0.99 (or 99% in decimal form).
Using a t-distribution table, find the row that corresponds to degrees of freedom (df) = 25. In this row, locate the column that corresponds to the desired probability of 0.99. The numbers in this column will give you the values of A for the lower and upper limits.
Alternatively, you can use a statistical calculator or software to calculate these values. Inputting the degrees of freedom (df) as 25 and the probability as 0.99, the calculator will provide the corresponding values of A for the lower and upper limits.