In an experiment on relaxation techniques, subjects brain signals were measured before and after the relaxation exercises with the following results: Person 1 2 3 4 5
Before 31 38 62 52 28
After 27 36 58 49 24
Assuming the population is normally distributed, is there sufficient evidence to suggest that the relaxation exercise slowed the brain waves? (Use α=0.05)
a) Fail to reject the null hypothesis which states there is no change in brain waves.
b) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation.
c) There is not enough information to make a conclusion.

b) Reject the null hypothesis which states there is no change in brain waves in favor of the alternate which states the brain waves slowed after relaxation.

Step-by-step explanation:

Given the data:

Person 1 2 3 4 5

Before 31 38 62 52 28

After 27 36 58 49 24

H0 : μd = 0

H0 : μd ≠ 0

This is a dependent / paired sample t test:

The difference, d = (before - after) ;

d = 4, 2, 4, 3, 4

Sample size, n = 5

The test statistic : dbar ÷ (Sd/√n)

Mean of difference, dbar = Σd / n = (4+2+4+3+4) / 5 = 17 /5 = 3.4

Sd =standard deviation of difference = 0.894 (calculator)

Test statistic = 3.4 / (0.894/√5)

Test statistic = 3.4 / 0.3998089

Test statistic = 8.50

df = n - 1 = 5 - 1 = 4

α = 0.05

critical value (4, 0.05) = 2.776

Test statistic > Critical value ; Reject the Null

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.