Question

1. Eight operating rooms were tested to see if a bacterial soap has reduced the contamination rates. The data shows the contamination in each room the year before and the year after using the soap. What do you conclude at .05 significance level

Before: 6.6           6.5       9          10.3    11.2      8.1       6.3      11.6

After:    6.8          2.4      7.4       8.5      8.1      6.1       3.4      2         

1. Hypothesis being tested: M1=M2? Or should it be a one tail test?
2. Critical Value
   1. What is the appropriate calculated T or Z
   2. Statistical conclusion
   3. Practical conclusion. Does the contamination significantly change?

Answer 1

The table given below ,

Before(X)	Afetr(Y)	di=X-Y	di^2
6.6	6.8	-0.2	0.04
6.5	2.4	4.1	16.81
9	7.4	1.6	2.56
10.3	8.5	1.8	3.24
11.2	8.1	3.1	9.61
8.1	6.1	2	4
6.3	3.4	2.9	8.41
11.6	2	9.6	92.16
	Sum	24.9	136.83

Let ,

a) Hypothesis: Vs  

The test one-tailed test.

b) The critical value is ,

; From t-table

c) The test statistic is ,

d) Decision ; Here , the value of the test statistic lies in the rejection region.

Therefore , reject Ho.

e) Conclusion : There is sufficient evidence to support the claim that the contamination is significantly change.