The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 94.8% of the people who have that disease. However, it erroneously gives a positive reaction in 3.3% of the people who do not have the disease. Consider the null hypothesis "the individual does not have the disease" to answer the following questions.

a. What is the probability of Type I error?
b. What is the probability of Type II error?

Answers

Answer 1

Answer:

Probability of Type 1 error = 0.033

Probability of type II error = 0.952

Step-by-step explanation:

H0: Individual does not have disease

H1: individual has disease

Type 1 error occurs when we fail to accept a correct null hypothesis and accept an alternate Instead

Type ii error occurs when we accept a false null hypothesis instead of the alternate hypothesis

Probability of people with disease = 98.4%

Probability of people without disease = 3.3%

1.probability of type 1 error = 3.3/100

= 0.033

2. Probability of type ii error = (1-98.4%) = 1-0.948

= 0.052


Related Questions

y x1 x2
10 1 16
11 5 11
15 5 14
15 9 11
20 7 1
23 11 8
27 16 7
32 21 3

a. Using technology, construct a multiple regression model with the given data.
b. Interpret the meaning of the values for b1 and b2.

Answers

Answer:

ŷ = 0.964X1 - 0.336X2 + 13.066

b1 = 0.964 which is the unit change in the value of y when x1 changes.

b2 = - 0.336 which is the unit change in the value of y when x2 changes

Step-by-step explanation:

Y

10

11

15

15

20

23

27

32

X1

1

5

5

9

7

11

16

21

X2

16

11

14

11

1

8

7

3

The general form of a multiple regression equation is in form:

ŷ = b1x1 + b2x2 + c

Where,

ŷ = predicted or dependent variable

b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.

c = intercept (constant)

Using the online multiple regression calculator, the model obtained by Inputting the values is written below:

ŷ = 0.964X1 - 0.336X2 + 13.066

Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.

Value b2 = - 0.336 which is the unit change in the value of y when x2 changes

Using minutes as the unit of measurement on the left-hand side of a constraint and using hours on the right-hand side is acceptable since both are a measure of time.

a. True
b. False

Answers

Answer:

True

Step-by-step explanation:

find the total area of the prism

Answers

Answer:

63.5

Step-by-step explanation:

Help me please thank you

Answers

Step-by-step explanation:

To solve for x, we set up our equation like this:

7x - 7 = 4x + 14

Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.

7x (-4x) - 7 = 4x (-4x) + 14

3x - 7 = 14

Then, we add 7 on both sides (to cancel the -7 out and place it on the right)

3x - 7 (+7) = 14 + 7

3x = 21

Finally, we divide both sides by 3 to isolate our variable, x.

3x ÷ 3 = x

21 ÷ 3 = 7

Our final answer: x = 7

prove triangle PQR to triangle TSR

Answers

Triangle PQR=TSR

PROVED

Answer:

Image provided is correct, thank you!

Convert the polar equation to an equivalent rectangular equation:

Answers

Answer:

The correct answer will be option b

Step-by-step explanation:

We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.

r = 4( x / r ) + 2( y / r ),

r = 4x / r + 2y / r,

r = 4x + 2y / r,

r / 1 = 4x + 2y / r ( Cross - Multiply )

4x + 2y = r²

We also know that r² = x² + y², so let's substitute.

x² + y² = 4x + 2y,

x² - 4x - 2y + y² = 0,

Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,

Solution : ( x - 2 )² + ( y - 1 )² = 5

How do you solve an expansion?

Answers

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]

Answer:

[tex]\large \boxed{560x^3}[/tex]

Step-by-step explanation:

[tex](x+2)^7[/tex]

Expand brackets.

[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]

[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]

[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]

[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]

The fifth term is 560x³.

Please help ! I’ll mark you as brainliest if correct.

Answers

Answer:

D = -87Dx = 174Dy = -435Dz = 0(x, y, z) = (-2, 5, 0)

Step-by-step explanation:

The determinant of the coefficient matrix is ...

  [tex]D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}[/tex]

The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.

Those determinants are ...

  [tex]D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174[/tex]

  [tex]D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435[/tex]

  [tex]D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0[/tex]

The solutions are ...

  x = 174/-87 = -2

  y = -435/-87 = 5

  z = 0

That is, (x, y, z) = (-2, 5, 0).

Put these numbers in order from greatest to least.
8
-2-
25
2.45
-0.84

Answers

Answer:

25, 2.45, 8, -0.84, -2

Step-by-step explanation:

negative is a least number

positive is a greater number

Positive number-8, 25, 2.45

Negative number-(-2), -0.84

ordering number from greatest to least:

25, 2.45, 8, -0.84, -2

-2 is smallest then -0.84 because 2 is bigger then 0.84. It is opposite with the positive number.

The bigger the positive number the biggest it is. While the bigger the negative number the smallest it is.

Answer:

Step-by-step explanation:

The numbers are:

● 8

● -2

● 25

● 2.45

● -0.84

To make it easy classify the positive numbers apart and the negatives ones alone

● 2.45<8< 25

● -2 < -0.84

25 is the greatest and -2 is the least

● 25 > 8 > 2.45 > -0.84 > -2

Solve the inequality -3 < 3/2(2-x)<5

Answers

Answer:

Step-by-step explanation:

Which property of equality was used to solve this equation? x − 5 = -14 x − 5 + 5 = -14 + 5 x = -9 A. addition property of equality B. subtraction property of equality C. multiplication property of equality D. division property of equality

Answers

Answer:

A

Step-by-step explanation:

In the second step, they added 5 to both sides to get rid of the -5 on the left side. Since the same thing was done to both sides (addition), the answer is the addition property of equality.

Answer:

Addition property of equality

Step-by-step explanation:

The equation is like:

=> x - 5 = -14

=> x - 5 + 5 = -14 + 5

=> x = -9

Since, we add 5 to both sides to solve for "x", the answer is "Addition Property of Equality".

Hope this helps.

Answer gets BRAINLIEST If q varies inversely as r, and g = 10 when r = 2.5, find the equation that connects a
and r.

Answers

Answer:

D.

Step-by-step explanation:

In direct variations, we would have:

[tex]q=kr[/tex]

Where k is some constant.

Since this is indirect variation, instead of that, we would have:

[tex]q=\frac{k}{r}[/tex]

To determine the equation, find k by putting in the values for q and r:

[tex]10=\frac{k}{2.5}\\k=2.5(10)=25[/tex]

Now plug this back into the variation:

[tex]q=\frac{25}{r}[/tex]

The answer is D.

the sum of the prime divisors of 2001 is a) 55, b) 56, c) 670, d) 671, e) 2001

Answers

Answer:

Option  A

Step-by-step explanation:

2001 can be divided by 3, 23, and 29 without remainders. This means that the three numbers are prime divisors of 2001.

2001/3 = 667

2001/23 = 87

2001/29 = 69

The sum of the prime divisors is 55.

3 + 23 + 29 = 55

Option A should be the correct answer.

Hope this helps.

Factor quadratic plz 15x^2-4x-4=

Answers

Answer:

x = 2/3 or x = -2/5

Step-by-step explanation:

15x^2 - 4x - 4 = ?

factor the left side of the expression and set factors equal to zero:

(3x-2)(5x+2)=0

3x - 2 =0 or 5x + 2 =0

3x =2 or 5x = -2

x = 2/3 or x = -2/5

if z and (z+50) are supplement of each other find the value of z​

Answers

Answer:

z=65

Step-by-step explanation:

supplementary angles means sum of those angles is 180 degrees

so,

z+z+50=180

2z=130

z=65

I did the best I could, I'm 12 don't judge me.

Heng tried to define a reflection across line r.

• Any point N on line r maps to itself.

• Any point M not on the line of reflection maps to a point M' such that the midpoint L of MM' is

on liner.

Which counterexample shows that Heng's definition does not fully define a reflection?

Choose 1 answer:

Answers

Answer:

Any point N on line r maps to itself.

Step-by-step explanation:

Reflection is one of the examples of solid transformation in which a given point, segment, or figure is flipped over a reference point or line to produce its image. The distance of the object to the reference point or line is the same as the distance of its image to the point or line. And both have the same size, but different orientation.

The option that does not fully define a reflection is; any point N on line r maps to itself, because no image of point N is produced after the operation.

Answer:

C. This matches Heng's definition, but is not a reflection, because MM'MM

M, M, prime is not perpendicular to line rrr.

Step-by-step explanation:

what are the like terms of the expression.
3x+8x+y+x+8

Answers

Answer:

the like terms are:

3x+8x+x+y+8

12x+y+8

Answer:

The like terms are

3x, 8x, x

Step-by-step explanation:

3x+8x+y+x+8

The like terms are

3x, 8x, x

They are the terms that are in terms of the first power of x

Given a sample of 35, what is the sample standard deviation of a pair of jeans if the 90% confidence interval is [37.14, 42.86]

Answers

Answer:

10.295

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

there are 12 eggs in one box and 12 boxes in one crate. how many eggs are in a shipment of 24 crates

Answers

Answer:

Step-by-step explanation:

12 eggs in one box

12 boxes = 1 crate

12 x 12 = 144 eggs

144 x 24 crates = 3456 eggs

Answer:

3,456 eggs

Step-by-step explanation:

There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12

12*12=144

144 eggs in one crate.

We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.

144*24=3,456

There are 3,456 eggs in 24 crates.

The entire graph of the function h is shown below write the domain and range of h using interval notation.

Answers

you can only see values of [tex] x[/tex] Ranging from $-3$ to $3$ and they're included, so domain is $[-3,3]$

and $y$ values ranging from $-2$ to $4$ but $-2$ is not included so range is $(-2,4]$

The function y=-2(x-3)2 + 4 shows the daily profit (in hundreds of dollars)

of a hot dog stand, where xis the price of a hot dog (in dollars). Find and

interpret the zeros of this function.

Select two answers: one for the zeros and one for the interpretation.

O A. Zeros at x = 3 1/2

B. The zeros are the hot dog prices at which they sell o hot dogs.

C. Zeros at x = 2 and x = 3

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Answers

Answer:

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Step-by-step explanation:

Given the function  y=-2(x-3)² + 4

The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.

Therefore:  y=2(x-3)² + 4

0 = 2(x-3)² + 4

-2(x² - 6x + 9) + 4 = 0

-2x² + 12x - 18 + 4 = 0

2x² - 12x + 18 - 4 = 0

2x² - 12x + 14 = 0

2(x² - 6x + 7) = 0

x² - 6x + 7 = 0

Solving the quadratic equation gives:

x = 3 + √2 and x = 3 - √2

This means that the graph crosses x at 3 + √2 and 3 - √2.

The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).

What is the nearest 100 of 1730

Answers

Answer:

1700

Step-by-step explanation:

pls thnx and mark me brainliest

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be

Answers

Answer:

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

Step-by-step explanation:

Here in this question, we want to state what will happen if the null hypothesis is true in a chi-square test.

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

This is because at a higher level of discrepancies, there will be a strong evidence against the null. This means that it will be rare to find discrepancies if null was true.

In the question however, since the null is true, the discrepancies we will be expecting will thus be small and common.

simplify 4x+3y please

Answers

Answer:

[tex]\boxed{4x + 3y}[/tex]

Step-by-step explanation:

Hey there!

Well 4x + 3y cannot be added together because they are 2 different variables.

4x + 3y = 4x + 3y

So 4x + 3y simplified is,

4x + 3y

Hope this helps :)

In the following studies, state whether you would use a one-sample t test or a two-independent-sample t test.
A. A study testing whether night-shift workers sleep the recommended 8 hours per day.
B. A study measuring differences in attitudes about morality among Democrats and Republicans.
C. An experiment measuring differences in brain activity among rats placed on either a continuous reward schedule (rewarded every time behavior is exhibited) or an intermittent reward schedule (rewarded after every few times behavior is exhibited).

Answers

Answer:

A) one-sample t-test

B) two sample t-test

C) two sample t-test

Step-by-step explanation: The one - sample t-test is used to determine the existence of a statistical difference between a sample mean and a given population mean. The one sample t test is only capable of making comparison between a singular sample mean and an established value. Such is the case in (A) where the aim is to determine if a group of night workers sleep for 8 hours.

The other two cases however, involves making comparison between the sample means of two different groups, this requires the use of a two independent sample t-test

For a one-sample t test:

(Sample mean - population mean) / standard error.

Sample mean = s

Population mean = p

Sample size = n

For a two sample t-test :

[(s2 - s1) - (p2 - p1)] ÷ √[(sd1^2/n1) + (sd2^2/n2)]

PLEASE HELP!!! TIMED QUESTION!!! FIRST CORRECT ANSWER WILL BE BRAINLIEST!!!

The bar graph shows the number or each item sold at a bake sale. Which statement about the graph is true?​

Answers

The answer is 2. You can see from the graph that 10 cookies were sold. If you take 1% of 10 and add it to 10, you get 11, which is exactly how many cupcakes were sold
Number 1 is correct.
Let me know if you need the working out. Hope it helps :)

Kaliska is jumping rope. The vertical height of the center of her rope off the ground R(t)R(t)R, left parenthesis, t, right parenthesis (in \text{cm}cmstart text, c, m, end text) as a function of time ttt (in seconds) can be modeled by a sinusoidal expression of the form a\cdot\cos(b\cdot t)+da⋅cos(b⋅t)+da, dot, cosine, left parenthesis, b, dot, t, right parenthesis, plus, d. At t=0t=0t, equals, 0, when she starts jumping, her rope is 0\text{ cm}0 cm0, start text, space, c, m, end text off the ground, which is the minimum. After \dfrac{\pi}{12} 12 π ​ start fraction, pi, divided by, 12, end fraction seconds, it reaches a height of 60\text{ cm}60 cm60, start text, space, c, m, end text from the ground, which is half of its maximum height

Answers

Answer:

Step-by-step explanation:

Janet has 12 more cookies than Cody. If Janet has 60 cookies, write and solve to determine the number of cookies Cody has.

Answers

Answer:

48

Step-by-step explanation:

Janet - 12 = Cody

60 - 12 = Cody

60 - 12 = 48

The answer to your question is Cody has 48

You are given the sample mean and the population standard deviation. Use this information to construct the​ 90% and​ 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sample of business​ days, the mean closing price of a certain stock was ​$. Assume the population standard deviation is ​$. The​ 90% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.) The​ 95% confidence interval is ​( nothing​, nothing​). ​(Round to two decimal places as​ needed.) Which interval is​ wider? Choose the correct answer below

Answers

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The 90% confidence interval is  [tex][108.165 ,112.895][/tex]

The  95%  confidence interval is [tex][107.7123 ,113.3477][/tex]

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  48

     The sample  mean is  [tex]\= x = \$ 110.53[/tex]

    The standard deviation is  [tex]\sigma = \$ 9.96[/tex]

Considering first question

  Given that the confidence level is  90% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 90)\%[/tex]

           [tex]\alpha = 0.10[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.365[/tex]

The  90% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]

=>    [tex]108.165 < \mu < 112.895[/tex]

Considering second question

  Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 95)\%[/tex]

           [tex]\alpha = 0.05[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.8177[/tex]

The  95% confidence interval is  

       [tex]\= x - E < \mu < \= x + E[/tex]

=>    [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]

=>    [tex]107.7123 < \mu < 113.3477[/tex]

Consider the following. (Assume that the coins are distinguishable and that what is observed are the faces or numbers that face up.) Three coins are tossed; the result is at most one head. Which of the following sets of elements are included in the sample space
HHTHTTTTHTTTTHTHHHTHHHTH
List the elements of the given event. (Select all that apply.)
HHT
HTT
TTH
TTT
THT
HHH
THH
HTH
List the elements of the given event. (select all that apply)
HTT
TTH
HTH
THH
THT
HHH
TTT
HHT

Answers

Answer:

Even set = {HTT, THT, TTH, TTT}

Step-by-step explanation:

We are given that three coins are tossed; the result is at most one head.

And we have to find the sets of elements that are included in the sample space.

Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.

Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.

So, the sample space so formed is;

S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}

Now, our event is at most one head. So, the sample space for the favorable event is given by;

Even set = {HTT, THT, TTH, TTT}

In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.

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