Question

2. The following data refers to airborne bacteria count (number of colonies/ft3) both for m = 8
carpeted (1) hospital rooms and for n = 8 uncarpeted (2) rooms. Make any necessary
assumptions and answer the questions below.
Carpeted 11.8, 8.2, 7.1, 13.0, 10.8, 10.1, 14.6, 14.0
Uncarpeted 12.1, 8.3, 3.8, 7.2, 12.0, 11.1, 10.1, 13.7
a. Is the evidence sufficient to support the variance for carpeted rooms being greater than 8
(colonies/ft3)2 at level 0.1?
b. Give a 95% confidence interval for the standard deviation of carpeted rooms.
c. Is the evidence sufficient to support the variance for uncarpeted rooms being greater than
10 (colonies/ft3)2 at level 0.1?
d. What is the P-value for the test in part “c.”?
e. Is the evidence sufficient to support the variance for uncarpeted rooms being greater than
the variance for carpeted rooms at level 0.1?
f. What is the P-value for the test in part “a.”?
g. Give a 97% confidence interval for the variance of bacteria count in carpeted rooms over
the variance of bacteria count in uncarpeted rooms.

Answer 1

a)

Following table shows the calculations for variance of carpeted room :

	X	(X-mean)^2
	11.8	0.36
	8.2	9
	7.1	16.81
	13	3.24
	10.8	0.16
	10.1	1.21
	14.6	11.56
	14	7.84
Total	89.6	50.18

Conclusion : The evidence is not sufficient to support the variance for carpeted rooms being greater than 8
(colonies/ft3)2 at level 0.1.

(b)

(c)

Following table shows the calculations for variance of uncarpeted room:

	X	(X-mean)^2
	12.1	5.3361
	8.3	2.2201
	3.8	35.8801
	7.2	6.7081
	12	4.8841
	11.1	1.7161
	10.1	0.0961
	13.7	15.2881
Total	78.3	72.1288

Conclusion; The evidence is not sufficient to support the variance for uncarpeted rooms being greater than
10 (colonies/ft3)2 at level 0.1.

(d)

The p-value is 0.4073