Question

Find the 98% confidence interval for the variance of annual earnings of coconut water vendors. A sample of 9 vendors has a standard deviation of $800.

• P – PARAMETER
  • Describe the parameter in context. This should be a complete sentence

• A – ASSUMPTIONS
  • Are we allowed to construct an interval and why?

• N – NAME THE INTERVAL
  • State what command you will be using the compute the interval along with the values you need.

• I – INTERVAL CALCULATION
  • Find the interval

• C – CONCLUSION
  • Write a sentence summarizing what you have found.

Answer 1

We need to construct the 98%confidence interval for the population variance.

P: The parameter here is VARIANCE.

A: Before constructing the interval, we must ensure that the data satisfies the following ASSUMPTIONS:

-The data is Normally distributed

- The data is random

- Population Variance is unknown, which is to be estimated.

N: The 98% CI for variance can be computed using the formula:

where s2 = Sample Variance, n = 9 and = 0.02

I - INTERVAL CALCULATION:

The chi-square values in the denominator can be obtained from Chi square table:

Substituting the given values:

= (254853.16, 3103030.30)

C - CONCLUSION:

If 100 such repeated samples of size 9 are drawn, and the CI computed for each of the 100 samples, 98 out of the 100 intervals would contain the true population variance.