Question

An outcome in the cancer experiment is measured by a test for the presence of cells that trigger an immune response in the body and so may help fight cancer. Here are the data of 11 subjects: counts of active cells per 100,000 cells before and after infusion of thee modified cells. The difference ( after minus before) is the response variable.

Before	14	0	1	0	0	0	0	20	1	6	0
After	41	7	1	215	20	700	13	530	35	92	108
Difference	27	7	0	215	20	700	13	510	34	86	108

a). Do the data give an evidence that the count of active cells is higher after treatment ?

b). Construct a 95% confidence interval for the data ?

Answer 1

a). Do the data give an evidence that the count of active cells is higher after treatment ?

Since, all the differences taken ( After - before ) are either positive or zero

Hence the data suggest the count of active cells is higher after treatment

b). Construct a 95% confidence interval for the data ?

The sample size is n = 11 The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	27	729
	7	49
	0	0
	215	46225
	20	400
	700	490000
	13	169
	510	260100
	34	1156
	86	7396
	108	11664
Sum =	1720	817888

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The number of degrees of freedom are df = 11 - 1 = 10 , and the significance level is α=0.05.

Based on the provided information, the critical t-value for α=0.05 and df = 10 degrees of freedom is t_c = 2.228 .

The 95% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 95 % confidence for the population mean μ is

CI = (-1.038, 313.766)

which completes the calculation.