Question

4. The duration, in hours, of the effect of the standard dose of a certain drug on a healthy adult female is thought to be exponentially distributed. The table below shows the results for a random sample of 200 healthy females all given standard dose.

Duration	0-	3-	6-	9-	12-	18-	24-36
Females	40	31	31	22	23	22	31

Test the hypothesis that the duration of the effect is exponentially distributed.

Answer 1

Solution:

The p.d.f. of an exponential distribution is given by

Where is the mean

Hence sample mean can be used as estimate of

Using the class mid points (x) of 1.5, 4.5, 7.5, 10.5, 15, 21, 30 gives

Hence

The following probabilities and expected frequencies can be now be calculated.

	Class Probability
		44.24
		34.45
		26.83
		20.90
		28.95
		17.56
		17.11
		9.96
Total	1.000	200.00

The calculation of the value of is completed as follows.

x
0-	40	44.24	-4.24	17.98	0.406
3-	31	34.45	-3.45	11.93	0.346
6-	31	26.83	4.17	17.37	0.647
9-	22	20.90	1.10	1.22	0.058
12-	23	28.95	-5.95	35.40	1.223
18-	22	17.56	4.44	19.72	1.123
24-	31	27.07	3.93	15.47	0.571
					4.375

Ho: Duration of effect is Exponential distribution

H1: Duration of effect is not Exponential distribution

Signigicance level,

Degree of freedom,

(6 classes; 2 constraints)

Critical region is >9.488

Test Statistic is

=4.375

This value does not lie in the critical region. There is no evidence, at the 5% significance level, to suggest that an exponential distribution is not appropiate.

Hence, Duration of effect is not Exponential distribution