Question

PVC pipe is manufactured with the following diameter (in cm)

5.7 5.3, 5.8, 5.5, 5.1, 5.9

(a) Construct a 99% two-sided confidence interval for σ2.

(b) Calculate a 99% lower confidence bound for σ.

Answer 1

n = 6

Let x be the diameter (in cm) of PVC pipe.

Sample mean :

x
5.7	0.0225
5.3	0.0625
5.8	0.0625
5.5	0.0025
5.1	0.2025
5.9	0.1225

Sample standard deviation :

.

s = 0.3082 (Round to 4 decimal)

a) Confidence level = c = 0.99

= 1 -c= 1 - 0.99 = 0.01

Degrees of freedom = n - 1 = 6 - 1 = 5

Critical values:

From excel using function:

=CHIINV(0.005,5)

= 16.750 (Round to 3 decimal)

From excel using function:

=CHIINV(0.995,5)

= 0.412 (Round to 3 decimal)

99% two-sided confidence interval for Population variance is

(Round to 3 decimal)

99% two-sided confidence interval for Population variance is (0.028,1.153)

b)

99% two-sided confidence interval for Population standard deviation is

   (Round to 3 decimal)

99% two-sided confidence interval for Population variance is (0.168,1.074)

99% lower confidence bound for = 0.168