With direct variation, if you increase the input, the output

In a random sample of students who took the SAT test, 427 had paid for coaching courses and the remaining 2733 had not. Calculat

Dvinal [7]

Answer:

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the z-score that has a p-value of $1 - \frac{\alpha}{2}$ .

427 had paid for coaching courses and the remaining 2733 had not.

This means that $n = 427 + 2733 = 3160, \pi = \frac{427}{3160} = 0.1351$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a p-value of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 - 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.1232$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1351 + 1.96\sqrt{\frac{0.1351*0.8649}{3160}} = 0.147$

The 95% confidence interval for the proportion of students who get coaching on the SAT is (0.1232, 0.147).

8 0

3 years ago

The first step to solve the equation x/4-3/4=16 is shown below

Sladkaya [172]

Answer:

i think it is A because that seems like the one making the most sense

Step-by-step explanation:

7 0

3 years ago

Help fast plz give me the answer

Lunna [17]

The answer is 75 degrees I believe.

45 + 60 + x = 180

I’m pretty sure I’m correct but I’m so sorry if I’m wrong.

7 0

3 years ago

The amount A of the radioactive element radium in a sample decays at a rate proportional to the amount of radium present. Given

slavikrds [6]

Answer:

a) $\frac{dm}{dt} = -k\cdot m$ , b) $m(t) = m_{o}\cdot e^{-\frac{t}{\tau} }$ , c) $m(t) = 10\cdot e^{-\frac{t}{2438.155} }$ , d) $m(300) \approx 8.842\,g$