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 6 6 11.4 11.4 9.2 9.2 11.3 11.3 5.5 5.5 10.2 10.2 14.9 14.9 8.9 8.9 15.6 15.6 12.3 12.3 7.1 7.1 6.2 6.2 6.4 6.4 9.3 9.3 4.5 4.5 6.6 6.6 Determine whether carpeted rooms have more bacteria than uncarpeted rooms at the alpha equals 0.05 α=0.05 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: <= 0

Alternative hypothesis: > 0

We carry out 2-sample independent T-test to determine if carpeted rooms have more bacteria than uncarpeted rooms.

T-statistic, T = [ ] / sqrt[(s1^2/n1) + (s2^2/n2)]

where, is the mean of sample i, si is the std deviation of sample i and ni is the size of sample i

Using the given samples, we get,

T = 1.0121

T-critical (right sided) at alpha= 0.05 and d.o.f = 16+16-2 = 30, is

T-crit = 1.697

Since T < T-crit, we cannot reject the null hypothesis at the 0.05 significance level.

Hence, the no. of bacteria for carpeted rooms is not statistically greater than that in uncarpeted rooms at the 0.05 significance level.