1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kipiarov [429]
3 years ago
12

A study was conducted to determine whether magnets were effective in treating pain. The values represent measurements of pain us

ing the visual analog scale. Assume that both samples are independent simple random samples from populations having normal distributions. Use a 0.05 significance level to test the claim that those given a sham treatment have pain reductions that vary more than the pain reductions for those treated with magnets.
n xbar s
Sham 20 0.41 1.26
Magnet 20 0.46 0.93
Mathematics
1 answer:
Zanzabum3 years ago
3 0

Answer:

Step-by-step explanation:

Hello!

The objective of the study is to determine whether the magnets are effective in treating pain. For these two independent groups of individuals with equal affections were randomly sampled, one was treated with magnets and the other group of individuals, call it control group, was treated with a placebo treatment.

The information for both samples is:

X₁: pain measurement using a visual analog scale after the individual received magnet treatments.

X₁~N(μ₁;σ₁²)

n₁= 20

X[bar]₁= 0.46

S₁= 0.93

X₂: pain measurement using a visual analog scale of an individual of the control groups.

X₂~N(μ₂;σ₂²)

n₂= 20

X[bar]₂= 0.41

S₂= 1.26

The claim is that the pain reductions of the control group have more variation than the pain reductions of the target group. If it's so then we could suspect that the population variance of the control group, σ₂², will be greater than the population variance of the magnet group, σ₁².

To test the relationship between these two population variances you have to conduct a variance ratio test using the Snedecors F statistic.

The hypotheses are:

H₀: σ₂² ≤ σ₁²

H₁: σ₂² > σ₁²

α: 0.05

F= (\frac{S_2^2}{S_1^2}) * (\frac{Sigma_2^2}{Sigma_1^2} )~~ F_{(n_2-1);(n_1-1)}

This hypothesis test is one-tailed to the right, there is only one critical value:

F_{(n_2-1);(n_1-1); 1 - \alpha } = F_{19;19; 0.95}= 2.17

The decision rule for the test is:

If F_{H_0} ≥ 2.17, then the decision is to reject the null hypothesis.

If F_{H_0} < 2.17, then the decision is to not reject the null hypothesis.

F_{H_0}= \frac{S_2^2}{S_1^2}*\frac{Sigma_2^2}{Sigma_1^2}  = \frac{(1.26)^2}{(0.93)^2} * 1

F_{H_0} = 1.835 = 1.84

Since the calculated value of F is less than the critical value, the decision is to reject the null hypothesis. So using a 5% significance level the decision is to not reject the null hypothesis, you can conclude that the population variance of the pain reduction of the control group is less or equal than the population variance of the pain reduction on individuals treated with magnets.

I hope it helps!

You might be interested in
How to convert improper fractions to a mixed numeral
Deffense [45]
Say for example, you have the improper fraction 18/7
The first step is to find out how many times 7 fits into 18
This looks like flipping the fraction, 7/18 = 2 whole times  with 4 parts left over
The 4 left over gets put in front of the original number (7) to give 2 4/7

To check if you have done it correctly, multiply the whole number (2) by the denominator ( 7 ) and then add the numerator.
2 x 7 = 14 + 4 = 18

Hope this helps
4 0
2 years ago
Read 2 more answers
If k(x) = 5x – 6, which expression is equivalent to (k + k)(4)?. . 5(4 + 4) – 6. 5(5(4) – 6) – 6. 54 – 6 + 54 – 6. 5(4) – 6 + 5(
Dmitrij [34]
K(x) = 5x-6
(k+k)(x) = k(x) + k(x) = 5x-6 +5x-6
just plug in x = 4,
(k+k)(4) = 5(4) -6 + 5(4) -6
thats your answer, the last option.
6 0
3 years ago
Read 2 more answers
2(7x-9)=5(x+3)<br> Solve for x
Nadya [2.5K]

Answer:

x = 3.67

Step-by-step explanation:

Simplify both expressions

14x - 18 = 5x + 15

Subtract the bigger (n)x by the smaller

14x - 5x = 9x

Plus the smallest by itself, giving you:

9x - 18 = 15

     +18   +18

9x = 33

Simplify ( divided by 3 )

3x = 11

x = 3.67

7 0
2 years ago
A convex polyhedron has faces that consist of 30 squares, 20 triangles, and 12 pentagons. The polyhedron has 120 edges. How many
VLD [36.1K]
D)))))) which is 180
5 0
3 years ago
Read 2 more answers
If 8% of all cell phones are defective, and you have a random sample group of 100 Samsung Galaxy Vills,
Sati [7]

Answer:

Mean = 8

Variance = 7.36

Standard Deviation = 2.7129

Step-by-step explanation:

This is a binomial distribution with parameters, n and p.

Where

n is sample size (given as 100)

p is the probability of success, or probability of defective (given as 8% or 0.08)

The mean, variance, standard deviation formula for binomial distribution is shown below:

Mean = np

Variance = npq

Standard Deviation = \sqrt{npq}

Where q would be probability of failure, or "1 - p"

Thus,

n = 100

p = 0.08

q = 1 - 0.08 = 0.92

SO, we have:

Mean = np=100*0.08=8

Variance = npq=100*0.08*0.92 = 7.36

Standard Deviation = \sqrt{npq}=\sqrt{7.36}=2.7129

5 0
3 years ago
Other questions:
  • What is a rule that represents the function, (0,1), (1,3), (2,9), (3,27), (4, 81)?
    13·2 answers
  • Can you please check my answer for me ?(:
    14·2 answers
  • Answer the following question about the function whose derivative is given below
    6·1 answer
  • Which of the following is a monomial? A. 20x^11-3x B.9/x C. 20x^11 D. 11x-9
    10·2 answers
  • Which is bigger 500 ft or 40 ft?
    11·2 answers
  • What is the equation for f(x) ?
    6·2 answers
  • First I broke the numbers apart first I broke 3.54 + 3.00 + 0.50 + 0.04 + 12.09+ into 12. 00+ 0.09
    12·1 answer
  • Order Numbers least to greatest -4.3, 5/4 ,8.2, -6/2, 4, -2.5, 5.33
    11·1 answer
  • You want to buy 3 pounds of cherries that cost $2.99 per pound. You have a coupon for $1.50 off your total order.
    15·1 answer
  • What’s the unit rate for three dollars for 2 1/2 hours of work
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!