Question

A researcher wanted to determine if carpeted rooms contain more bacteria than uncarpeted rooms. The table shows the results for the number of bacteria per cubic foot for both types of rooms.		Full data set
		Carpeted				Uncarpeted
		13.1	6.5	11.8		7.7	12.2	7.7
		15.3	6.2	14.9		11	9.4	12.8
		12.1	8.1			5.9	5

Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the

α=0.01

level of significance. Normal probability plots indicate that the data are approximately normal and boxplots indicate that there are no outliers.

State the null and alternative hypotheses. Let population 1 be carpeted rooms and population 2 be uncarpeted rooms.

Answer 1

Null Hypothesis H0: Carpeted rooms have same average bacteria as uncarpeted rooms

Alternative Hypothesis H1: Carpeted rooms have more average bacteria than uncarpeted rooms.

Mean bacteria of carpeted, m1 = 11

Mean bacteria of uncarpeted, m2 = 8.9625

Standard deviation of bacteria of carpeted, s1 = 3.618603

Standard deviation of bacteria of carpeted, s2 = 2.873991

Assuming population variances of both groups to be equal,

Degree of freedom = n1 + n2 - 2 = 8 + 8 - 2 = 14

Pooled variance, Sp² = [(n1 - 1) s1² + (n2 - 1) s2² ]/ (n1 + n2 - 2)

= [(8 - 1) * 3.618603² + (8 - 1) * 2.873991² ] / (8 + 8 - 2)

= 149.4788 / 14

= 10.67706

Standard error of mean difference, SE =

= 1.633789

Test Statistic, t = (m1 - m2) / SE = (11 - 8.9625) / 1.633789

= 1.247

P-value = P(t > 1.247, df = 14) = 0.1164

Since, p-value is greater than 0.01 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that Carpeted rooms have more average bacteria than uncarpeted rooms.