MATHEMATICS COLLEGE

In a poll conducted by the Gallup organization in April 2013, 48% of a random sample of 1022 adults in the U.S. responded that they felt that economic growth is more important than protecting the environment. We can use this information to calculate a 95% confidence interval for the proportion of all U.S. adults in April 2013 who felt that economic growth is more important than protecting the environment. Make sure to include all steps.

Answers

Answer 1

Answer:

Answer:

The 95% confidence interval is $0.449 < p < 0.48 + 0.511$

Step-by-step explanation:

From the question we are told that

The sample proportion is $\r p = 0.48$

The sample size is $n = 1022$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5 \%$

$\alpha = 0.05$

Next we obtain the critical value of $(\alpha )/(2)$ from the z-table , the value is

$Z_{(\alpha )/(2) } =Z_{(0.05 )/(2) }= 1.96$

The reason we are obtaining critical value of $(\alpha )/(2)$ instead of $\alpha$ is because

$\alpha$ represents the area under the normal curve where the confidence level interval ( $1-\alpha$ ) did not cover which include both the left and right tail while $(\alpha )/(2)$ is just the area of one tail which what we required to calculate the margin of error

NOTE: We can also obtain the value using critical value calculator (math dot armstrong dot edu)

Generally the margin of error is mathematically represented as

$E = Z_{(\alpha )/(2) } * \sqrt{(\r p (1- \r p ))/(n) }$

substituting values

$E = 1.96* \sqrt{(0.48 (1- 0.48 ))/(1022) }$

$E = 0.03063$

The 95% confidence interval is mathematically represented as

$\r p - E < p < \r p + E$

substituting values

$0.48 - 0.03063 < p < 0.48 + 0.03063$

$0.449 < p < 0.48 + 0.511$

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Answers

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined. The range is the set of all valid y values.

Step-by-step explanation:

since x=4 is a vertical line,there is no y-intercerpt and the slope is undefined.

Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?

Answers

The equation that represents an inequality in the system of inequalities shown in the graph is;

y < 2x + 2

The point that is a solution to the system is; (-1, -2)

Graph Inequalities

The image of the graph is missing and so i have attached it.

From the graph, we see one broken line passing through the points x = -1 and y = 2.

We also see an unbroken line passing through the points x = ½ and y = -1

Now, when we use a broken line it means greaterthan or less than but when we use a thick line which is unbroken it means y ≤ or y ≥.

Now, if we shade below the line, it is (y< or y≤) but if we shade above the line, it is (y> or y≥).

Now, we see that the solution will be in between the broken line and the thick line.

Thus, the equation is;

y < 2x + 2 with the solution as coordinates as (-1, -2)

Read more about graph inequalities at;brainly.com/question/11234618

Answer:

y<2x+2

(-1,-2)

explanation:

person above gets credit, hope it helps!

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Answers

Answer:

56, 57, and 58.

Step-by-step explanation:

The circumference of a circle is22 cm find the radiusof the circle

Answers

Answer:

3.5cm

Step-by-step explanation:

$C = 22cm\nr = ?\n\nC = 2\pi r\n\nr = (C)/(2\pi) \n\nr = (22)/(2(3.14))\n \nr = (22)/(6.28) \n\nr = 3.5$

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Answers

Answer:

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Step-by-step explanation:

The area of a parallelogram is given by the formula ...

A = bh

Substituting the given values for the length of the base (b) and the height (h), we have ...

A = (4 in)(3 in)

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Answer:

D 12

Step-by-step explanation:

I just did the lesson and got it right.

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