Question

A drug company is developing a product which is intended to shorten the duration of colds. To determine if the product is effective, a study is done with two groups of physiologically similar people. The placebo group is given a sugar pill, the treatment group is given the cold remedy, and the results are given below.

Cold duration (days)	Placebo group (relative frequency)	Treatment group (frequency)
0-5 days	40%	102
6-9 days	35%	70
10-12 days	15%	14
13+ days	10%	14

We want to determine whether or not there is a significant difference in the distribution of the cold durations between the placebo group and the treatment group. Use α = .01 to make your conclusion.

The value of the chi-square statistic is:  


The p-value of the test is:

Answer 1

applying chi square test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.400	102	80.00	2.46	6.050
2	0.350	70	70.00	0.00	0.000
3	0.150	14	30.00	-2.92	8.533
4	0.100	14	20.00	-1.34	1.800
total	1.000	200	200		16.383

value of the chi-square statistic =16.3833

p-value of the test is =0.0009