Question

In the North American population, the average IQ is 100. A team of scientists wants to test a new medication to see if it has either a positive or negative effect on intelligence or no effect at all. A sample of 39 participants who have taken the medication has been investigated and their IQ after treatment is noted as following:

95           90           100         110         108         105         98           105         120         115         99           100         90    118         112         110         120         120         95           100         90           110         100         105         100         90    105         103         108         112        

114         100         88           95           105         103         105         107         98

                1-Does the medication influence the North American population IQ? Explain and justify your answer.

The same medication is used on Scandinavian population. 20 participants have been treated and their IQs are noted.

112         114         100         88           95           105         108         105         98           105         120         115         99

100         90           112         110         120         120         90

2-Does the medication have the same effect on both samples (North American and Scandinavian) IQ? Explain and justify your answer.

Answer 1

Here, under normality assumption with equal variances for two independent samples, we have performed the folloeing tests:

1. Does the medication influence the North American population IQ? Perform one sample t-test.
2. Does the medication influence the Scandanavian population IQ?In the same direction?Perform one sample t-test.
3. Does the medication influence the North American as well as the Scandanavian population IQ to the same extent?Perform two independent sample Fisher's t-test.

For the first case R shows p-value=0.0105<0.05. hence we reject the null and can say that there is enough evidence to support the claim that the medication affects the North Americal population IQ, more specifically it increases its level(evident from 95% CI)

For the second case R shows p-value=0.03076<0.05. hence here also we reject the null and can say that there is enough evidence to support the claim that the medication affects the scandanavian population IQ, more specifically it increases its level(evident from 95% CI) in this case also.

For the third case we want to know whether this medication results in increment of the average IQ upto the same level for both the North American and the Scandanavian population IQ. Here p-value=0.5575>>0.05, so do not reject the null. Hence we can conclude that after this medication, both population end with same IQ level(after increment), on an average.

R CODE and OUTPUT:

> x=c(95,90,100,110,108,105,98,105,120,115,99,100,90,118,112,110,
+ 120,120,95,100,90,110,100,105,100,90,105,103,108,112,
+ 114,100,88,95,105,103,105,107,98)
> t.test(x,mu=100,alternative="two.sided",conf.level=0.95)

One Sample t-test

data: x
t = 2.6923, df = 38, p-value = 0.0105
alternative hypothesis: true mean is not equal to 100
95 percent confidence interval:
100.9414 106.6483
sample estimates:
mean of x
103.7949

> y=c(112,114,100,88,95,105,108,105,98,105,120,115,99,
+ 100,90,112,110,120,120,90)
> t.test(y,mu=100,alternative="two.sided",conf.level=0.95)

One Sample t-test

data: y
t = 2.3336, df = 19, p-value = 0.03076
alternative hypothesis: true mean is not equal to 100
95 percent confidence interval:
100.5463 110.0537
sample estimates:
mean of x
105.3

>
> t.test(x,y,mu=0,alternative="two.sided",var.equal=TRUE,paired=FALSE,conf.level=0.95)

Two Sample t-test

data: x and y
t = -0.58997, df = 57, p-value = 0.5575
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-6.613780 3.603523
sample estimates:
mean of x mean of y
103.7949 105.3000