Kritieke Waarden Bepalen voor Chi-Kwadraat

Consider sample data on the fuel economy of some car brands. To obtain a 95% confidence interval for the population standard deviation, one must calculate the critical values that separate the likely results from the unlikely ones.

A 95% confidence level covers 95% of the area under the curve, while the remaining 5% area distributed equally on either side.

As the chi-square distribution is asymmetrical, the right and left critical values separating an area of  2.5% or 0.025 on both sides are individually determined.

To determine the right-tailed critical value, locate nine on the left column for degrees of freedom in the chi-square table and find 0.025 across the top row, yielding a value of 19.023.

Since the table provides cumulative areas to the right of the critical value, subtract the remaining 0.025 area from the total area under the curve to obtain 0.975. Now, using the chi-square table, the left-tailed critical value is calculated.