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
DENIUS [597]
3 years ago
14

A new screening test for Lyme disease is developed for use in the general population. The sensitivity and specificity of the new

test are 60% and 70%, respectively. Three hundred people are screened at a clinic during the first year the new test is implemented. Assume the true prevalence of Lyme disease among clinic attendees is 10%.
Calculate the following values:

The predictive value of a positive test

The predictive value of a negative test
Mathematics
1 answer:
Anit [1.1K]3 years ago
7 0

Answer:

predictive value of a positive test = 18.18%

predictive value of a negative test = 94.03%

Step-by-step explanation:

Sensitivity = 60% = 0.6

Specificity = 70% = 0.7

Let True Positive = TP

True Negative = TN

False Negative = FN

Sensitivity = \frac{TP}{TP + FN} \\0.6 = \frac{TP}{TP + FN} \\0.6TP + 0.6FN = TP\\0.4TP = 0.6FN\\TP = 1.5 FN

Specificity = \frac{TN}{TN + FP} \\0.7 = \frac{TN}{TN + FP} \\0.7TN + 0.7FP = TN\\0.7FP = 0.3 TN\\TN  = 7/3 FP

Prevalence = 10% = 0.1

Three hundred people are screened, T_{total} = 300

Total number of people having the disease, T_{disease} = ?

Prevalence = \frac{T_{disease} }{T_{total} } \\0.1 =  \frac{T_{disease} }{300 }\\T_{disease} = 30

T_{disease} = TP + FN\\30 = TP + FN

But TP = 1.5 FN

30 = 1.5 FN + FN

30 = 2.5 FN

FN = 30/2.5

FN = 12

TP = 1.5 FN = 1.5 * 12

TP = 18

FP + TN = T_{total} - T_{disease} \\FP + TN = 300 - 30\\FP + TN = 270\\FP + \frac{7}{3} FP = 270\\\frac{10}{3} FP = 270\\FP = 27 * 3\\FP = 81

81 + TN = 270

TN = 189

To calculate the Predictive value of positive test (PPT)

PPT = \frac{TP}{TP + FP} * 100\\PPT = \frac{18}{18+81} * 100\\PPT = \frac{18}{99} * 100\\PPT = 18.18 \%

To calculate the Predictive value of negative test (PNT)

PPT = \frac{TN}{FN + TN} * 100\\PPT = \frac{189}{189+12} * 100\\PPT = \frac{189}{201} * 100\\PPT = 94.03 \%

You might be interested in
Find the roots of this equation 7xsquare - 5x - 2 = 0
Sophie [7]

Answer:

x = 1, -2/7

Step-by-step explanation:

You could use the quadratic equation but this can be factored into

(7x + 2) (x - 1).  You can verify that by multiplying it out.

Since (7x + 2) (x - 1) = 0, if either factor is 0 then the equation would be equal to 0, thus we get x = 1, -2/7

7 0
2 years ago
If you do these 2 problems you get 100 points
frosja888 [35]

Answer:

BELOW

Step-by-step explanation:

DO I HEAR 100 POINTS? Yes.

For the first image, that answer is A.

For the second image, I'm a bit confused on which problems you want me to do, so I'll do number 10, 11, and 14.

10) Yeah, you're correct, it is J.

11) (1,-6), (-2,-5), (8,2) (4,0) and I can't see the last point so..

14)  Can't see the question :(

4 0
1 year ago
Read 2 more answers
Evaluate 4x-6y when x=-3 y=-1
pogonyaev

Answer:

First we substitute

4(-3) - 6(-1)

-7  -6

-13

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Express the integral as a limit of Riemann sums. Do not evaluate the limit. (Use the right endpoints of each subinterval as your
Veronika [31]

The expression of integral as a limit of Riemann sums of given integral \int\limits^5_b {1} \, x/(2+x^{3}) dxis 4 \lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3} from i=1 to i=n.

Given an integral \int\limits^5_b {1} \, x/(2+x^{3}) dx.

We are required to express the integral as a limit of Riemann sums.

An integral basically assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinite data.

A Riemann sum is basically a certain kind of approximation of an integral by a finite sum.

Using Riemann sums, we have :

\int\limits^b_a {f(x)} \, dx=\lim_{n \to \infty}∑f(a+iΔx)Δx ,here Δx=(b-a)/n

\int\limits^5_1 {x/(2+x^{3}) } \, dx=f(x)=x/2+x^{3}

⇒Δx=(5-1)/n=4/n

f(a+iΔx)=f(1+4i/n)

f(1+4i/n)=[n^{2}(n+4i)]/2n^{3}+(n+4i)^{3}

\lim_{n \to \infty}∑f(a+iΔx)Δx=

\lim_{n \to \infty}∑n^{2}(n+4i)/2n^{3}+(n+4i)^{3}4/n

=4\lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3}

Hence the expression of integral as a limit of Riemann sums of given integral \int\limits^5_b {1} \, x/(2+x^{3}) dxis 4 \lim_{n \to \infty}∑n(n+4i)/2n^{3}+(n+4i)^{3} from i=1 to i=n.

Learn more about integral at brainly.com/question/27419605

#SPJ4

5 0
1 year ago
How can 6.75 + (-10.25) be expressed as the sum of its integer and decimal part
attashe74 [19]
There you go please brainliest thanks!

4 0
3 years ago
Other questions:
  • Please i need help ASAP! Will give 15 points and name brainliest.
    15·2 answers
  • Factor the trinomial: 5x^2-2x-7
    7·1 answer
  • Range is a keyword for what operation in math
    15·1 answer
  • 2. To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. a. Would you
    11·1 answer
  • Hi I really need help can anyone help me out
    9·1 answer
  • What 2/3 multiplied by 1/3
    9·1 answer
  • Help me on this please
    15·1 answer
  • Y = a( x-h)^2 + k
    15·1 answer
  • Which of the following expressions are equivalent to 30 - 8x - 6 - 5x?
    5·1 answer
  • Find m\angle Am∠Am, angle, A.<br> Round to the nearest degree.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!