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
Vaselesa [24]
3 years ago
11

Dual-energy X-ray absorptiometry (DXA) is a technique for measuring bone health. One of the most common measures is total body b

one mineral content (TBBMC). A highly skilled operator is required to take the measurements. Recently, a new DXA machine was purchased by a research lab and two operators were trained to take the measurements. TBBMC for eight subjects was measured by both operators. The units are grams (g). A comparison of the means for the two operators provides a check on the training they received and allows us to determine if one of the operators is producing measurements that are consistently higher than the other. Here are the data:
Subject
Operator 1 2 3 4 5 6 7 8
1 1.326 1.337 1.079 1.229 0.936 1.009 1.179 1.289
2 1.323 1.322 1.073 1.233 0.934 1.019 1.184 1.304






Take the difference between the TBBMC recorded for Operator 1 and the TBBMC for Operator 2. (Operator 1 minus Operator 2. Round your answers to four decimal places.)



X-bar=

S=

Mathematics
1 answer:
sesenic [268]3 years ago
8 0

Answer:

\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001

s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095

-The sample is too small to make judgments about skewness or symmetry.

H0:\mu_{1}=\mu_{2}

H1:\mu_{1} \neq \mu_{2}

t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013

p_v =2*P(t_{(14)}

So the p value is a very high value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

Step-by-step explanation:

First we need to find the difference defined as:

(Operator 1 minus Operator 2)

d1=1.326-1.323=0.003      d2=1.337-1.322=0.015

d3=1.079-1.073=0.006     d4=1.229-1.233=-0.004

d5=0.936-0.934=0.002   d6=1.009-1.019=-0.01

d7=1.179-1.184=-0.005      d8=1.289-1.304=-0.015

Now we can calculate the mean of differences given by:

\bar d=\frac{\sum_{i=1}^n d_i}{n}=-0.001

And for the sample deviation we can use the following formula:

s=\sqrt{\frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}}=0.0095

Describe the distribution of these differences using words. (which one is correct)

We can plot the distribution of the differences with the folowing code in R

differences<-c(0.003,0.015,0.006,-0.004,0.002,-0.01,-0.005,-0.015)

hist(differences)

And we got the image attached. And we can see that the distribution is right skewed but we don't have anough info to provide a conclusion with just 8 differnences.

-The sample is too small to make judgments about skewness or symmetry.

Use a significance test to examine the null hypothesis that the two operators have the same mean. Give the test statistic. (Round your answer to three decimal places.)

\bar X_{1}=1.173 represent the mean for the operator 1

\bar X_{2}=1.174 represent the mean for the operator 2

s_{1}=0.1506 represent the sample standard deviation for the operator 1

s_{2}=0.1495 represent the sample standard deviation for the operator 2

n_{1}=8 sample size for the operator 1

n_{2}=8 sample size for the operator 2

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means for the two groups are the same, the system of hypothesis would be:

H0:\mu_{1}=\mu_{2}

H1:\mu_{1} \neq \mu_{2}

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) like this:

t=\frac{1.173-1.174}{\sqrt{\frac{0.1506^2}{8}+\frac{0.1495^2}{8}}}=-0.013

Statistical decision

For this case we don't have a significance level provided \alpha, but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

df=n_{1}+n_{2}-2=8+8-2=14

Since is a bilateral test the p value would be:

p_v =2*P(t_{(14)}

So the p value is a very high value and using any significance level for example \alpha=0.05, 0,1,0.15 always p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and a we don't have a significant difference between the two means.

You might be interested in
Write a recursive rule for an= Зn — 6.
mart [117]

Answer:

Explicit formula: a(n)=3n-6

Recursive formula: a(n)=-3+(n-1)3 <--

Step-by-step explanation:

a(n)=3n-6 where a(1)=3(1)-6=-3 and d=3

<u>Plug values into recursive formula:</u>

a(n)=a1+(n-1)d

a(n)=-3+(n-1)3

8 0
2 years ago
Please help me with dis ion understand pwese help me :(
Morgarella [4.7K]

Answer:

The formula for calculating the circumference of a circle is 2*pi*r. Because pi does not have an end, we'll use 3.14, since that is the approximate value of pi.

2*6*3.14 = 37.68

The outer rim of the pool is about 37.68 meters long

Step-by-step explanation:

It’s probably 40 because it says about how long not exactly.

I hope this helped

6 0
2 years ago
Read 2 more answers
A chemist has a 100 gram sample of a radioactive
Nastasia [14]

Answer:

75

Step-by-step explanation:

did it 5 mins ago

3 0
2 years ago
If 12 cows produce 70 gallons of milk, how many gallons would 42 cows produce?
omeli [17]

Answer:

245

Step-by-step explanation:

-6 cows produce 35 gallons

6 x 7 =42

so 7 x 35 = 245

8 0
3 years ago
Conjecture about the properties that change and the
Makovka662 [10]

Answer:

A and C on Edge

Step-by-step explanation:

Just completed the assignment

7 0
3 years ago
Other questions:
  • What is the largest possible value x could take given that it must be an integer? x &lt; 5
    6·1 answer
  • Mrs. Baker paid $2.50 for 5 pounds of bananas. Write an equation realating the cost c to the number of pounds p of bananas. How
    10·2 answers
  • A container has 1 pink block and 3 green blocks. Juan wants to make the probability of randomly selecting a black block equal to
    9·1 answer
  • The coordinates of the vertices of quadrilateral DEFG are D(−2, 5) , E(2, 4) , F(0, 0) , and G(−4, 1) .
    7·2 answers
  • Jaimi went to have a manicure that cost $30. She wanted to tip the technician 20% and tax is 5.75%.
    7·1 answer
  • Two numbers have these properties
    9·1 answer
  • Please look at attached image to answer question!!! 15 points!!! Answer both to get BRAINLY!
    15·2 answers
  • Find each sum or difference. (x2-3x + 1) - (x3 + 7 – 12x) Oa. 2x3 - 15x + 8 Ob.-12x + 8 c. 9x - 6 d.-9x – 6​
    10·1 answer
  • Which set of measurements determines a unique triangle
    12·2 answers
  • Meeeeeeeeeeeeeeeeeeeeplsss help
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!