Question

In a experiment on relaxation techniques, subject's brain signals were measured before and after the relaxation exercises with the following results:

Person	1	2	3	4	5
Before	42.2	42.4	38.8	41.6	38.6
After	44.2	40.9	40.8	35.3	33.5

Is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? Assume the population is normally distributed. Select the test statistic, p-value, Decision to Reject (RH₀) or Failure to Reject (FRH₀)].

Explain how to do using RStudio, please

Answer 1

Solution:

Here, we have to use paired t test. The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The relaxation exercise does not slow the brain waves.

Alternative hypothesis: H_a: The relaxation exercise slowed the brain waves.

H₀: µ_d = 0 versus H_a: µ_d < 0

(Lower tailed or left tailed (one tailed) test)

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

Required R commands and output are given as below:

> x = c(42.2, 42.4, 38.8, 41.6, 38.6)

> y = c(44.2, 40.9, 40.8, 35.3, 33.5)

> t.test(y,x,paired = TRUE, alternative = "less")

        Paired t-test

data: y and x

t = -1.0268, df = 4, p-value = 0.1813

alternative hypothesis: true difference in means is less than 0

95 percent confidence interval:

     -Inf 1.915789

sample estimates:

mean of the differences

                  -1.78

We get P-value = 0.1813

We assume α = 0.05

P-value > α = 0.05

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that the relaxation exercise slowed the brain waves.