Question

data are collected in a clinical trial evaluating a new compound designed to improve wound healing in trauma patients. The new compound is compared against a placebo. After treatment for 5 days with the new compound or placebo, The extent of wound healing is measured and the data are shown in Table 7-6. Is there a difference in the extent of wound healing by Treatment? (Hint: are treatment and the percent wound healing independent? ) run the appropriate test at a 5% level of significance.

Percent wound healing Treatment

0-25% 26-50% 51-75% 76-100%

New Compound 15 37 32 41

Placebo       0-25% 26-50% 51-75% 76-100%

36 45 34 10

Answer 1

As we do not know population standard deviation (or variance) we have to perform two sample t-test to test equality of mean.

Suppose, the percent of wound healing using treatment is denoted random variable by X and that by placebo is denoted by random variable Y.

We know, class mark is average of lower and upper class limits.

Serial number (i)	Interval of percent of wound healing	Class mark (xi and yi)	Frequency for treatment (fx,i)	Frequency for placebo (fy,i)
1	0.5-25.5	13	15	36
2	25.5-50.5	38	37	45
3	50.5-75.5	63	32	34
4	75.5-100.5	88	41	10

We have to test for null hypothesis

against the alternative hypothesis

Our test statistic is given by

where

Level of significance

Degrees of freedom

In not equal type alternative hypothesis i.e. in two tailed test we reject null hypothesis if .

Here we see, .

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significant difference in percent of wound healing by treatment compared to the placebo used.