Respuesta :
The critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom are roughly 21.02 and 32.36.
The critical value for the 95% confidence interval using the 15 degrees of freedom chi-square distribution is the value that divides the distribution into two;
lower tail and upper tail. These values are calculated such that the area under the curve of the chi-square distribution between the critical values represents 95% of the total area under the curve.
To find critical values, you can use a chi-square table or a computer program that calculates critical values for a given confidence level and degree of freedom.
In this case, the critical value for the 95% confidence interval with 15 degrees of freedom can be determined as follows:
Lower critical value:
The lower critical value is the value corresponding to the area under the chi-square distribution curve to the left of the value, equal to 2.5% (half of 5% not included in the confidence interval). Using a chi-square table or computer program, we can find that the lower critical value for the 95% confidence interval with 15 degrees of freedom is approximately 21.02. Upper critical value:
The upper critical value is the value corresponding to the area under the chi-square distribution curve to the right of the value, equal to 2.5% (half of 5% is not included in the confidence interval).
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