Mathematics, 21.05.2020 22:58, Jsquad8879

A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think the president of their country can control the price of gasoline. Her estimate must be accurate within 3% of the true proportion. a) No preliminary estimate is available. Find the minimum sample size needed. b) Find the minimum sample size needed, using a prior study that found that 26% of the respondents said they think their president can control the price of gasoline. c) Compare the results from parts (a) and (b).

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answered: aylin5044

a) $n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849$

And rounded up we have that n=1849

b) $n=\frac{0.26(1-0.26)}{(\frac{0.03}{2.58})^2}=1422.99$

And rounded up we have that n=1423

c) For this case we can see that if we have a prior estimate the minimum sample size required for the margin of error desired would be less as we can see in part b we reduce the sample size compared to the part a

Step-by-step explanation:

Part a

The critical value for a confidence level of 99% is for this case $z_{\alpha/2} =2.58$

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 $ME =\pm 0.03$ 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 know any estimate for the true proportion we can use $\hat p =0.5$ as a godd estimator. And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.03}{2.58})^2}=1849$

And rounded up we have that n=1849

Part b

For this case we have a prior estimate $\hat p =0.26$ and replacing we got:

$n=\frac{0.26(1-0.26)}{(\frac{0.03}{2.58})^2}=1422.99$

And rounded up we have that n=1423

Part c

For this case we can see that if we have a prior estimate the minimum sample size required for the margin of error desired would be less as we can see in part b we reduce the sample size compared to the part a

answered: Guest

linear pair postulates

answered: Guest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1