For df = 5 and the constant A, identify the value of A such that a. P(x² > A) = 0.90 b. P(x² > A) = 0.10 c. P(x² > A) = 0.95 d. P(x² > A) = 0.05 e. P(x² < A) = 0.975 f. P(x² < A) = 0.025
To find the value of A in each of the given scenarios, we need to use the chi-squared distribution with the degrees of freedom df = 5. The chi-squared distribution is commonly used in statistical inference for hypothesis testing and confidence interval construction.
a. P(x² > A) = 0.90:
To find the value of A for which P(x² > A) = 0.90, we need to determine the chi-squared value that corresponds to a cumulative probability of 0.90 in the right tail of the distribution. We can use a chi-squared table or a statistical software to look up this value.
b. P(x² > A) = 0.10:
To find the value of A for which P(x² > A) = 0.10, we need to determine the chi-squared value that corresponds to a cumulative probability of 0.10 in the right tail of the distribution.
c. P(x² > A) = 0.95:
Similar to the previous scenarios, we need to find the chi-squared value that corresponds to a cumulative probability of 0.95 in the right tail of the distribution.
d. P(x² > A) = 0.05:
Again, we need to find the chi-squared value that corresponds to a cumulative probability of 0.05 in the right tail of the distribution.
e. P(x² < A) = 0.975:
In this case, we want to find the chi-squared value that corresponds to a cumulative probability of 0.975 in the left tail of the distribution. This time we're interested in the left tail (less than), so we need to adjust our lookup accordingly.
f. P(x² < A) = 0.025:
Similarly, we want to find the chi-squared value that corresponds to a cumulative probability of 0.025 in the left tail of the distribution.
By looking up the appropriate chi-squared values based on the desired probabilities and degrees of freedom, we can identify the values of A for each scenario.