I tutor in business statistics. I used to teach college level business maths. Send your questions to ecommerceaid1@lycos.com
EXAMPLE1- ESTIMATING THE VARIANCE CONFIDENCE INTERVAL - NORMAL PUPULATION.
Want to estimate the variance of your customers' ages.
Select a random sample of 20 customers.
Compute a sample variance of 30 years.
This translates into a sample standard deviation of 5.5 years.
You can contruct your confidence interval as follows:
1. Choose a confidence level for your test, such as 95%.
2. Look up the appropriate values in the chi- square distribution table. Chi-square of 0.025 and Chi-square of 0.975.
For a chi-square distribution with 19 degrees of freedom(20-1), these values are 32.852 and 8.907.
3. Compute the confidence interval using the following formula:[(n-1)sigma squared]/[table chi-squared].
Your result is: [(20-1)30]/(32.852) to [(20-1)30]/(8.907)= 17 to 64.
Therefore can be 95% confident that the variance of your customers' ages is between 17 and 64 years.
This translates into a confidence interval of 4 to 8 years for the population standard deviation.
EXAMPLE2: TESTING A VARIANCE - NORMAL POPULATION.
Want: To compare the dispersion in ages of your competitor's customers with yours. Historically, the standard deviation in your customer's ages has been 6 years. The corresponding variance that you use in the test is 36 years.
A sample of 15 of your competitor's customers yields a sample standard deviation of 8 years and a variance of 64 years.
Perform the test as follows:
1. Form your null & alternate hypothesis.
For this test, your null hypothesis would be that the variance in ages is equal for your customers and those of your competitor. The alternate hypothesis is that the variance is greater for your competitor's customers.
2. Choose a confidence interval, such as 95% for your test.
3. Since your alternate hypothesis is that your competitor's variance is greater than yours your test is one-tailed. Look up in the chi-square distribution table the value that has 5% of the curve above it. This value for 14 degrees of freedom(15-1) is (chi-square of 0.05)= 23.685.
4. Use Formula 5.5 to compute the test-statistic:
Chi-square ={[(15 - 1)64]/36}= 24.89.
Since your test statistic is greater than the upper limit of a confience interval, you reject the null hypothesis + infer that the ages of your competitor's customers are more dispersed than the ages of your customers.
Posted by ecommerceaid1
at 11:45 AM EST
Updated: Saturday, 1 May 2004 10:28 AM EDT