(a) The 95th percentile of the chi-squared distribution with > = 8 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.

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(a) The 95th percentile of the chi-squared distribution with = 8
For the chi-squared critical value X, ², the area under the curve to the right of X, ² 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 a = 1 - p =
for the critical value.
Transcribed Image Text:(a) The 95th percentile of the chi-squared distribution with = 8 For the chi-squared critical value X, ², the area under the curve to the right of X, ² 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 a = 1 - p = for the critical value.
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