Exercises. 1. The sample of 15 bus arrivals showed a sample variance at min.

1. The sample of 15 bus arrivals showed a sample variance at min.

a) Construct a 95 % confidence interval of the variance for the population of arrival times.

b) Suppose that the sample variance of had been obtained from a sample of 26 bus arrivals. Determine a 95 % confidence interval of the variance for the population of arrival times.

2. From production process a random sample of 25 a certain brand of light bulbs was taken. The variance of the lives of these bulbs was found to be 4710 hours. Assume that the lives of all such bulbs are approximately normally distributed.

a) Make a 99 % confidence interval for the variance and standard deviation of the lives of all such bulbs.

3. The time required to complete a certain operation by the sample of 25 employees of auditing company has a standard deviation of 3.1 min. Construct a 98 % confidence interval for .

4. From a data set of n=10 observation, one has calculated the 95 % confidence interval for and obtained the result (0.81; 2.15).

Calculate a 90 % confidence interval for .

5. Given the sample data

12, 18, 9, 15, 14

Construct a 95 % confidence interval for .

6. A sample of 7 observations taken from a population produced the following data

10, 8, 13, 15, 6, 8, 13

Make the 98 % confidence intervals for the population variance and standard deviation.

7. A random sample of 25 customers taken from the bank gave the variance of the waiting times equal to 7.9 min. Construct 99 % confidence intervals for the population variance.

8. Suppose that based on a random sample of size 10 from a normal distribution, one has found the 95 % confidence interval for the population mean to be (36.2; 45.8). Using this result determine a 95 % confidence interval for the population standard deviation.

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