Mathematics, 24.12.2019 00:31 criser1987zach

In 2006, the florida poll conducted by florida international university asked whether current environmental regulations are too strict or not too strict. of 1200 respondents, 229 said they were too strict. find and interpret a (a) 95%, (b) 99% confidence interval for a relevant parameter at the time of that survey.

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a) The 95% confidence interval for the true proportion of respondents who think current environmental regulations are too strict or not too strict is (0.1678, 0.2122). This means that we are 95% sure that the true proportion of respondents who think current environmental regulations are too strict or not too strict is between 0.1678 and 0.2122.

b) The 99% confidence interval for the true proportion of respondents who think current environmental regulations are too strict or not too strict is (0.1608, 0.2192). This means that we are 99% sure that the true proportion of respondents who think current environmental regulations are too strict or not too strict is between 0.1608 and 0.2192.

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 interval $1-\alpha$ , we have the following confidence interval of proportions.

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

In which

Z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 1200, \pi = \frac{229}{1200} = 0.19$

(a) 95% confidence interval.

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

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 - 1.96\sqrt{\frac{0.19*0.81}{1200}} = 0.1678$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 + 1.96\sqrt{\frac{0.19*0.81}{1200}} = 0.2122$

The 95% confidence interval for the true proportion of respondents who think current environmental regulations are too strict or not too strict is (0.1678, 0.2122). This means that we are 95% sure that the true proportion of respondents who think current environmental regulations are too strict or not too strict is between 0.1678 and 0.2122.

(b) 99% confidence interval.

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so Z = 2.575 .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 - 2.575\sqrt{\frac{0.19*0.81}{1200}} = 0.1608$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 + 2.575\sqrt{\frac{0.19*0.81}{1200}} = 0.2192$

The 99% confidence interval for the true proportion of respondents who think current environmental regulations are too strict or not too strict is (0.1608, 0.2192). This means that we are 99% sure that the true proportion of respondents who think current environmental regulations are too strict or not too strict is between 0.1608 and 0.2192.

Answer from: Quest

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function $y=f(x)$ the average rate of change from point $a(a,f(a))$ to point $b(b,f(b))$ can be calculated as

$\text{average rate of change}=\dfrac{f(b)-f(a)}{b-a}.$

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,

$\text{average rate of change}=\dfrac{2-8}{10-2}=\dfrac{-6}{8}=-\dfrac{3}{4}.$

The graph below shows the number of houses sold over x days. what is the average rate of change from

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

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