Variance and Standard Deviation Confidence Intervals

Warm Up The weights of a sample of 20 students ended in a confidence interval of (120, 200). What was the point estimate of the mean?

Construct a Variance and St. Deviation Confidence Interval Objective Construct a Variance and St. Deviation Confidence Interval

Can Estimate Population Parameters from Sample Statistics Relevance Can Estimate Population Parameters from Sample Statistics

Objective Construct a Variance and Standard Deviation Confidence Interval

Relevance Be able to estimate a population parameter from sample statistics.

Why do we use them?...... Variance and St. Deviation can be as important as the mean. For example, in industry variations on pipe size diameters must be kept as small as possible; otherwise the pipes won’t fit together properly and they would have to be scrapped.

To find the confidence intervals for variances and st To find the confidence intervals for variances and st. deviations a new statistical distribution is needed. This distribution is called the CHI-SQUARE Distribution

Chi-Square ( ) Similar to a t-distribution in that it is based on degrees of freedom It cannot be negative It is NOT normal. It is positively skewed. (Tail goes to the right) At approximately 100 df, the distribution becomes somewhat symmetrical.

values can be found in table 8 of your textbook on p. 719 Because the distribution is not symmetrical until you get to 100 degrees of freedom, the values for will be different on the right and left side of the distribution.

Find the values in each tail for a 90% confidence interval and n=25…… df=24 Look in the table for the chi-square values on the right and left. Answer……

Example – You Try…… Find the chi-square values on the right and left for a sample size of 6 and a 95% confidence level. Answer:

Confidence Interval Formula…..

Example…… Find the 95% confidence interval for the variance and standard deviation of the nicotene content of cigarettes manufactured if a sample of 20 cigarettes has a st. deviation of 1.6 milligrams.

Answer…… Values:

Plug Values Into Equations……

Example… A manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval for the A. Population Variance B. Population Standard Deviation

A manufacturer measures 19 randomly selected dowels and finds the standard deviation of the sample to be s = 0.16. Find the 95% confidence interval for the A. Population Variance Values:

Variance Confidence Interval

Standard Deviation Confidence Interval Take the square root of the variance figures.

Example…. The football coach randomly selected 10 players and timed how long each player took to perform a certain drill. The drill times in minutes were: 9, 5, 7,12,14,14,5, 11,6, 9

Answer….

Assignments…… Worksheet