Question

1. Researchers wanted to determine if carpeted rooms contained more bacteria than uncarpeted rooms. To determine the amount of bacteria in a room, researchers pumped the air from the room over a Petri dish at the rate of 1 cubic foot per minute for eight carpeted rooms and eight uncarpeted rooms. Colonies of bacteria were allowed to form in the 16 Petri dishes. The results are given in the table below. Assume the distribution to be approximately normal. Do carpeted rooms have more bacteria than uncarpeted rooms?

Carpeted Rooms	Uncarpeted Rooms
11.7	12.0
8.2	8.3
7.1	3.8
13.1	7.3
10.6	12.0
10.1	11.1
14.8	10.3
14.0	13.7

If group 1 is the carpeted rooms and group 2 is the uncarpeted rooms.

A. What is the p-value for this hypothesis test

B. What is the critical value(s) for this hypothesis test

C. What is the test statistic for this hypothesis test?

D. What is the decision for this hypothesis test?

Answer 1

Excel: Data --> Data analysis --> t-Test: Two-Sample Assuming Unequal Variances

Output:

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	11.2	9.8125
Variance	7.434286	10.18982
Observations	8	8
Hypothesized Mean Difference	0
df	14
t Stat	0.934812
P(T<=t) one-tail	0.182865
t Critical one-tail	1.76131
P(T<=t) two-tail	0.36573
t Critical two-tail	2.144787

(A)  0.182865

(B)  1.76131

(C)  0.934812

(D) Fail to reject H0 (since P-value = 0.182865>0.05)