Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. An article reported on an experiment involving 84 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.2 and the sample mean for the treatment group was 3.2; both sample standard deviations were 2.3.
a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this α, and a sample mean difference of 2.1 also suggests practical significance).
b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.

Answer:

a) We reject H₀     We find difference between the mean of the two groups

b) we accept H₀ : There is no statistical difference  ( in the scale of pain) when the difference in samples means is 1

Step-by-step explanation:

Group 1: Only with educational material

Sample size     n₁  =  42

Sample mean   x₁  =  3,2

Sample standard deviation  s₁  =  2,3

Group 2: With exercises with the treatment of individuals

Sample size    n₂   =  42

Sample mean    x₂  = 5,2  

Sample standard deviation   s₂  = 2,3

Test Hypothesis

Null Hypothesis                     H₀           x₂  -  x₁  = 0  or    x₁  =  x₂

Alternative Hypothesis         Hₐ           x₂  -  x ₁ > 0  or    x₂  >  x₁

Significance level  α  = 0,01

Sample sizes are n₁  =  n₂  >  30

We use z-test

for α  = 0,01     z(c)  ≈  2,32

To calculate z(s)

z(s)  =  (  x₂  -  x₁ ) / √ (2,3)²/42  + (2,3)²/42

z(s)  = ( 5,2  -  3,2 )/ √0,2519

z(s)  =  2 / 0,5

z(s) = 4

Comparing  z(s)  and z(c)

z(s) > z(c)

z(s) is in the rejection region. We reject H₀ the true average pain level for the control condition exceeds that for the treatment condition.

b) Does the true average pain level for the control condition exceed that for the treatment condition by more than 1.

In this case

z( s) =  x₂ - x₁ / 0,5

z(s) =  1 /0,5

z(s) = 2

Comparing z(s) and z(c)  now

z(s) < z(c)        2 < 2,32

And z(s) is in the acceptance region ( for the same significance level) and we should accept H₀  equivalent to say that the two groups statistical have the same mean

Evaluate each expression if x = 3.

a. 2^x
b. x^2
c. 1^x
d. x^1
e. (1/2)^x

Find the common difference of the arithmetic sequence.
4, 10, 16, 22,

The ratio of A's to B's on the last test was 3 to 4. If there was 12 A's . how maby B's were there?​

The veterinarian’s practice had dog and cats clients. The number of dog clients was 5/6 of the number of cat clients. If the total number of clients was 924, how many dog clients and how many cat clients did the veterinarian have?

Which list of numbers is ordered from from greatest to least?

Mark buys a wooden board that is 7 1/2 feet long. The cost of the wooden board is $0.50 per foot, including tax. Enter the total cost, in dollars, of the wooden board.

Can you hellllllllllllllpppppppppp

GEOMETRY
please Help

Determine the amplitude or period as requested. Amplitude of y=3 cos 1 2

write the computer program for;urgent​

LOOK AT IMAGES I MARK BRAINLIEST

Which of the following statements is not true?

A) -3 divided by -8 is a positive number

B) - 2/8 = 3/-8

C) -1/2(5+3/8)= (-1/2)(5) + (-1/2)(3/8)

D) (-4)(-2/5)(0.5) is a positive number

DE is a midsegment of ABC . Find the value of x.​

Help me with 6 and 7

What is the area, in square centimeters of the shaded part of the rectangle shown below

Four brothers each bought two hotdogs and a bag of chips at the football concession stand.

Can someone pleaseee help

Please help me 7th math

need you to check if answer is correct

Given the definitions of f(x) and g(x) below, find the value of g(f(-1)).
f(x) = -4x – 7
g(x) = x² + 7x – 2
​

Three students, Matthew, Thompson and Amos shared #15000 in the ratio of 5:2:x respectively. If Matthew's share is 7500, calculate the value of x. ​

a)How many similar figures can be drawn inside the following figures?
Find the limit of area and perimeter


​

WHO WAS IN PARIS ??????????????????????

5(2 + 2m). Simplify the expression

A block of wood has the shape of a triangular prism. The bases
are right triangles. Find its surface area.

I need help like NOW

Plz help this if you want points

Submit

IM.MP3.PC.2020-2021

Question: 1-2

Examine the polygons on the coordinate plane.

162

Select the triangle that represents a translation of

GHK.

B В

A

H

D

B

Ο Ο Ο Ο

C С

A

С

What is the area of KLM?

[tex]\boxed {\boxed {prove : \: 3 \: is \: greater \: than \: 5​ }} [/tex]
​