Advanced Placement (AP), 10.04.2020 07:52, tyaniahawarren

A survey was given to a random sample of 400 people living in a certain community. The people were asked whether they supported the construction of walking trails in the community park. The results are shown in the following table.

Response Frequency
Yes, support 210
No, do not support 90
No opinion 100
Total 400

A follow-up study will be conducted with a sample of 20 people from the 300 people who responded yes (support) and no (do not support). Two sampling methods have been proposed: a simple random sample and a stratified random sample with the survey response as strata.

(b) If the stratified random sample is used, what is the number of people that will be selected from those who responded yes? Support your answer by showing your work.

Answers: 3

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Answers

Using simple random sampling for the follow up data will involve making a random selection of 20 participants from the 300 people such that each of the 300 participants have an equal chance of being selected. A random number generator could be employed in making a simple random sample in this scenario.

For Stratified random sampling, participants are first divided into stratas, in this case, the stratas are (Yes and No responses). Then a random sample of participants is are chosen from each strata based on the number of participants in each strata.

If a stratified random sampling is employed, the number of 'Yes' respondents which will be chosen can be calculated thus :

(Number of yes respondent / total) × sample size

(210 / 300) × 20

0.7 × 20 = 14 people.

Therefore, 14 people would be selected from those who responded 'yes' to be a part of the sample.

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answered: annaharmon693

The total number of people that will be selected is 14.

Explanation:

In the case of stratified random sampling, we first need to split the population into several strata and then select a sample from each. For a given question, the solution type is

Sample size of strata = (Scale of whole sample by population size) multiply strata size

= (20 by 300) multiply 210

After we have resolved, 14 or 14 persons will be chosen.

One value is that here, as we split all the data into strata and then pick samples from them so that they can be used as a protection against unnecessary samples and to have more precise sample measurements. Here, because we needed samples from the population that provided yes and no opinion so that it is easier to use stratified sampling method then if we use simple random sampling then we can use those samples that did not offer an opinion. But since we're not using this form, we can stop it.

answered: Guest

its c because i have that test too

answered: Guest

Answer: the interval on which the curve is concave up is (-∞, -1/2)====== $\displaystyle y = \int_{0}^x \frac{1}{1 + t + t^2} \; dt$ we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \end{aligned}$ let the function f denote be the anti-derivative of the inside expression, i.e. a function such that $(d/dx)f(x) = 1/(1 + t + t^2)$ .then use the fundamental theorem of calculus: $\begin{aligned} \frac{dy}{dx} & = \frac{d}{dx} \int_{0}^x \frac{1}{1 + t + t^2} \; dt \\& = \frac{d}{dx} \big[ f(x) - f(0) \big] & & \text{\footnotesize apply ftc} \\ & = \frac{d}{dx}f(x) - 0 \\ & = \frac{1}{x + x + x^2} & & \text{\footnotesize since $\frac{d}{dx}f(x) = \frac{1}{1 + x + x^2}$ } \end{aligned}$ differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function $\begin{aligned} \frac{d}{dx} \left( \frac{dy}{dx} \right) & = \frac{d}{dx}\left(\frac{1}{1 + x + x^2} \right) \\ \frac{d^2y}{dx^2} & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot \tfrac{d}{dx}(1 + x + x^2) \\ & = \frac{-1}{\left(1 + x + x^2\right)^2} \cdot (1 + 2x) \\ & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \end{aligned}$ find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x $\begin{aligned} 0 & = \frac{-(1 + 2x)}{\left(1 + x + x^2\right)^2} \\ 0 & = -(1+2x) \\ -1 & = 2x \\ x & = -1/2 \end{aligned}$ where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation 1 + x + x² = 0results in a discriminant of $b^2 - 4ac = 1^2 - 4(1)(1) = -3$ meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = -1} & = \frac{-(1+2(-1))}{\left(1+(-1)+(-1)^2\right)^2} \\ & = \frac{-(1-2)}{1} \\ & = 1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get $\begin{aligned} \left.\frac{d^2y}{dx^2}\right|_{x = 0} & = \frac{-(1+2(0))}{\left(1+(0)+(0)^2\right)^2} \\ & = \frac{-(1)}{1} \\ & = -1 \end{aligned}$ so the since the 2nd derivative of the curve is positive on the interval (-∞, -1/2), the curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is (-∞, -1/2)