Ask question

Ask question

All categories

gayaneshka [121]

3 years ago

7

g A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam. We ar

e interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%. The test statistic is

1 answer:

BaLLatris [955]3 years ago

4 0

Answer:

The test statistic is $z = 1.25$

Step-by-step explanation:

We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%.

At the null hypothesis, we test if the proportion is 80%, that is:

$H_0: p = 0.8$

At the alternate hypothesis, we test if the proportion is more than 80%, that is:

$H_a: p > 0.8$

The test statistic is:

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, $\sigma$ is the standard deviation and n is the size of the sample.

80% is tested at the null hypothesis:

This means that $\mu = 0.8, \sigma = \sqrt{0.2*0.8} = 0.4$

A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam.

This means that $n = 100, X = \frac{85}{100} = 0.85$

The test statistic is

$z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{0.85 - 0.8}{\frac{0.4}{\sqrt{10}}}$

$z = 1.25$

The test statistic is $z = 1.25$

You might be interested in

Jonathan had to rent a car for one day while his car was getting fixed , the car rental costs $23 per day plus $2 for every mile

Drupady [299]

The answer is B. 23+2x>100

8 0

4 years ago

Read 2 more answers

The picture shows a barn door:

spin [16.1K]

C

Opposite / hypotenuse
Sin 45 degrees= 7/x

8 0

3 years ago

Read 2 more answers

Use the Divergence Theorem to evaluate S F · dS, where F(x, y, z) = z2xi + y3 3 + sin z j + (x2z + y2)k and S is the top half of

GenaCL600 [577]

Close off the hemisphere $S$ by attaching to it the disk $D$ of radius 3 centered at the origin in the plane $z=0$ . By the divergence theorem, we have

$\displaystyle\iint_{S\cup D}\vec F(x,y,z)\cdot\mathrm d\vec S=\iiint_R\mathrm{div}\vec F(x,y,z)\,\mathrm dV$

where $R$ is the interior of the joined surfaces $S\cup D$ .

Compute the divergence of $\vec F$ :

$\mathrm{div}\vec F(x,y,z)=\dfrac{\partial(xz^2)}{\partial x}+\dfrac{\partial\left(\frac{y^3}3+\sin z\right)}{\partial y}+\dfrac{\partial(x^2z+y^2)}{\partial k}=z^2+y^2+x^2$

Compute the integral of the divergence over $R$ . Easily done by converting to cylindrical or spherical coordinates. I'll do the latter:

$\begin{cases}x(\rho,\theta,\varphi)=\rho\cos\theta\sin\varphi\\y(\rho,\theta,\varphi)=\rho\sin\theta\sin\varphi\\z(\rho,\theta,\varphi)=\rho\cos\varphi\end{cases}\implies\begin{cases}x^2+y^2+z^2=\rho^2\\\mathrm dV=\rho^2\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi\end{cases}$

So the volume integral is

$\displaystyle\iiint_Rx^2+y^2+z^2\,\mathrm dV=\int_0^{\pi/2}\int_0^{2\pi}\int_0^3\rho^4\sin\varphi\,\mathrm d\rho\,\mathrm d\theta\,\mathrm d\varphi=\frac{486\pi}5$

From this we need to subtract the contribution of

$\displaystyle\iint_D\vec F(x,y,z)\cdot\mathrm d\vec S$

that is, the integral of $\vec F$ over the disk, oriented downward. Since $z=0$ in $D$ , we have

$\vec F(x,y,0)=\dfrac{y^3}3\,\vec\jmath+y^2\,\vec k$

Parameterize $D$ by

$\vec r(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath$

where $0\le u\le 3$ and $0\le v\le2\pi$ . Take the normal vector to be

$\dfrac{\partial\vec r}{\partial v}\times\dfrac{\partial\vec r}{\partial u}=-u\,\vec k$

Then taking the dot product of $\vec F$ with the normal vector gives

$\vec F(x(u,v),y(u,v),0)\cdot(-u\,\vec k)=-y(u,v)^2u=-u^3\sin^2v$

So the contribution of integrating $\vec F$ over $D$ is

$\displaystyle\int_0^{2\pi}\int_0^3-u^3\sin^2v\,\mathrm du\,\mathrm dv=-\frac{81\pi}4$

and the value of the integral we want is

(integral of divergence of <em>F</em>) - (integral over <em>D</em>) = integral over <em>S</em>

==> 486π/5 - (-81π/4) = 2349π/20

5 0

4 years ago

Which expressions are equivalent to the one below? Check all that apply.<br> 3x

noname [10]

Answer:

F and C

Step-by-step explanation:

5 0

3 years ago

Can y’all help me please !

Leviafan [203]

no because she turned it only 90 degrees not 180.

180 would be a mirror reflection

6 0

3 years ago