7-4 Confidence Intervals for Variances and Standard Deviations

  1. To calculate the confidence intervals of variances and standard deviations, we need to use the ______distribution.
  2. The symbol is ______, pronounced ______.
  3. A chi-squared variable cannot be ______, and the distributions are skewed to the ______.
  4. At about ______degrees of freedom, the chi-square distribution becomes somewhat symmetric.
  5. The area under each chi-square distribution is equal to ______.
  6. ______different values are used in the formula because the distribution is not ______. One value can be found on the ______side of the table. The other is found on the ______side of the table.

How to use the chart: Find the table values that correspond to 95% confidence interval.

To find :

1) Change 95% to a decimal: ______

2)Subtract it from 1 (to find the area of the two tails): ______

3)Divide the answer by 2 (to find the area of each tail): ______=

4)Use this value as the column on the right side of the table.

To find :

1) Subtract the value of from 1: ______

Find the degrees of freedom:

1)n – 1.

Example 7-13: Find the values for and for a 90% confidence interval when n = 25.

To find :

  1. Change to decimal:
  2. Subtract from 1:
  3. Find by dividing by 2:
  4. Degrees of freedom:
  5. Look up on chart:

To find :

  1. Subtract from 1:
  2. Look up on chart:

Formula for the Confidence Interval for a Variance:

Formula for the confidence interval for a standard deviation:

Recall: s2 is the symbol for ______and s is the symbol for ______.

Example: 7-14: Find the 95% confidence interval for the variance and standard deviation of the nicotine content of cigarettes manufactured if a sample of 20 cigarettes has a standard deviation of 1.6 milligrams.

Find

Find

Find the lower part of the interval:

Find the upper part of the of the interval

The interval is ______<< ______

Find the standard deviation by square rooting:

______< < ______

One can be ______% confident that the standard deviation for the price of all single day ski lift tickets of the population is between ______and ______based on a sample of 10 nationwide ski resorts.

Classwork:

#1-12. Skip 2.