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
		11.411.4	14.914.9	9.19.1		7.97.9	6.26.2	1313
		14.114.1	12.212.2	6.66.6		6.56.5	9.19.1	12.912.9
		7.97.9	10.910.9			11.511.5	7.97.9

Answer 1

here our hypothesis be:-

where, is the true population mean of number of bacteria per cubic foot for carpeted room.

where, is the true population mean of number of bacteria per cubic foot for uncarpeted room

necessary calculation:-

11.4	7.9	0.262656	2.175625
14.9	6.2	16.10016	10.08063
9.1	13	3.195156	13.14063
14.1	6.5	10.32016	8.265625
12.2	9.1	1.722656	0.075625
6.6	12.9	18.38266	12.42563
7.9	11.5	8.925156	4.515625
10.9	7.9	0.000156	2.175625
sum=87.10	sum=75	sum=58.9088	sum=52.855

so,we have:-

so, our test statistic be:-

degrees of freedom:-

so, df = 13

p value = 0.152 ( using p value calculator for df=13,t score=1.0763, one sided test)

decision:-

i am considering level of significance = 0.01

p value = 0.152>0.01, so we do not have enough evidence to reject our null hypothesis.

hence,

reject null hypothesis. there is not sufficient evidence at 0.01 los to conclude that carpeted rooms have more bacteria than the uncarpeted rooms.

***if you have any doubt regarding the problem please write it in the comment section.if you are satisfied please give me a LIKE vote if possible...