(a) The 95th percentile of the chi-squared distribution with v = 8 2 For the chi-squared critical value X, ², the area under the curve to the right of X² is a with v degrees of freedom. Recall that a percentile describes the area under the curve to the left of a critical value. However, the chi-squared distribution is not symmetric so chi-squared distribution tables provide the area under the curve to the right of a critical value. Therefore, the (100p)th percentile under the chi-squared distribution uses a critical value corresponding to the complement of p, the area under the curve to the right of the critical value, a = 1 - p. For the 95th percentile, we have p = 0.95, where 95% of the area under the curve falls to the left of the critical value. To find the 95th percentile under the chi-squared distribution, we will use the right-tailed area a = 1 p = for the critical value.
(a) The 95th percentile of the chi-squared distribution with v = 8 2 For the chi-squared critical value X, ², the area under the curve to the right of X² is a with v degrees of freedom. Recall that a percentile describes the area under the curve to the left of a critical value. However, the chi-squared distribution is not symmetric so chi-squared distribution tables provide the area under the curve to the right of a critical value. Therefore, the (100p)th percentile under the chi-squared distribution uses a critical value corresponding to the complement of p, the area under the curve to the right of the critical value, a = 1 - p. For the 95th percentile, we have p = 0.95, where 95% of the area under the curve falls to the left of the critical value. To find the 95th percentile under the chi-squared distribution, we will use the right-tailed area a = 1 p = for the critical value.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 7E
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Transcribed Image Text:(a) The 95th percentile of the chi-squared distribution with v = 8
For the chi-squared critical value X«, v²
2, the area under the curve to the right of Xa, v 2 is a with v degrees of freedom.
Recall that a percentile describes the area under the curve to the left of a critical value. However, the chi-squared
distribution is not symmetric so chi-squared distribution tables provide the area under the curve to the right of a critical
value. Therefore, the (100p)th percentile under the chi-squared distribution uses a critical value corresponding to the
complement of p, the area under the curve to the right of the critical value, a = 1 - p.
For the 95th percentile, we have p = 0.95, where 95% of the area under the curve falls to the left of the critical value.
To find the 95th percentile under the chi-squared distribution, we will use the right-tailed area x = 1 - p =
for the critical value.
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