A transportation company wants to estimate the variance of the length of time goods are in transit across the country. A random sample of 20 shipments gives days and day. Give a 95% confidence interval for the variance of the transit time for all goods.
Insufficient data.
To find the 95% confidence interval for the variance of the transit time for all goods, we can use the chi-square distribution.
1. Calculate the sample variance, denoted by s^2, from the given random sample of 20 shipments.
2. We need to determine the degrees of freedom (df) for the chi-square distribution. For estimating the variance, the degrees of freedom is equal to the sample size minus 1. In this case, the sample size is 20, so the degrees of freedom (df) is 20 - 1 = 19.
3. Determine the critical values for a chi-square distribution with 95% confidence and 19 degrees of freedom. The critical values mark the bounds of the confidence interval. You can find these critical values in a chi-square table or calculate them using statistical software. Let's denote the lower critical value as L and the upper critical value as U.
4. Calculate the lower and upper confidence limits for the variance using the formula:
Lower Confidence Limit = (n-1) * s^2 / U
Upper Confidence Limit = (n-1) * s^2 / L
where n is the sample size and s^2 is the sample variance.
5. Substitute the values from step 1, step 3, and step 4 into the formulas to calculate the lower and upper confidence limits for the variance.
6. The 95% confidence interval for the variance of the transit time for all goods is given by [Lower Confidence Limit, Upper Confidence Limit].
Note: In this explanation, the actual values of the sample sizes, sample variance, and critical values were not provided, so you will need to calculate them to obtain the specific 95% confidence interval.