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3 years ago

Pro

Mathematics

1 answer:

Firdavs [7]3 years ago

8 0

Answer:

C. Both (1, 11) and (-1, -5)

Step-by-step explanation:

The missing options are:

A. Only (1, 11)

B. Only (-1, -5)

C. Both (1, 11) and (-1, -5)

D. Neither

To check if an ordered pair is a solution of an equation, replace one variable into the equation an calculate the other one.

Replacing x = 1, we get:

y = 8(1) + 3

y = 11

then (1, 11) is a solution

Replacing x = -1, we get:

y = 8(-1) + 3

y = -5

then (-1, -5) is a solution

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a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

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Step-by-step explanation:

Previous concepts

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Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

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Part a

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

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