A researcher wishes to estimate, with 90% confidence, the population proportion of likely U.S. voters who think Congress is doing a good or excellent job. Her estimate must be accurate within 2% 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 28% of the respondents said they think Congress is doing a good or excellent job.
(c) Compare the results from parts (a) and (b).


Answer 1

The sample size just be 752.

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The degree of confidence, sample size, and sample variability are all factors that might affect the width of the CI. A larger sample would result in a narrower confidence interval if all other factors remained constant. A wider confidence interval would also be required by a higher confidence level and would be produced by a sample with  (1.645 / 0.03)2 * 0.5 * 0.5


Sample size = 752

= 1 - 0.42 = 0.58

margin of error = E =3 % = 0.03

At 90% confidence level z

Hence, The sample size just be 752.

Learn more about confidence interval, by the following link.



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Can someone help me solve this please?



Hope this helps!

Please help me 80% of what number is 16 What is the part?
What is the total?
What is the percent?
What is the answer?​



80 percent of 16 is 12.8 I'm sorry but that's all I know

Luis is doing his math homework. He has 30 problems in all. After an hour, he only has 1/6 of those problems left. How many problems does he have left?




Step-by-step explanation:

Luis has 30 problems and after one hour, (1)/(6) of those problems are left. This means that the total number of problems left will be 30 \cdot (1)/(6).

Multiplying by a fraction is the same as dividing by a whole. The denominator of (1)/(6) is 6, so we can divide 30 by 6.

30 / 6 = 5

Hope this helped!

Answer: 25

Step-by-step explanation: 1/6 of 30 is 5, so 30 minus 5 equals 25.

Find the slope of the line through each pair of point11. (-4, -3) and (7, 1)
12. (-2, -1) and (8, -3)



11) 4/11

12) -0.2

Step-by-step explanation:

Write the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point. (Let x be the independent variable and y be the dependent variable.)Vertex: (−3, 4); point: (0, 13)


The standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point is;

y = x² + 6x + 13

We are given;

Vertex coordinate; (-3, 4)

A point on the graph; (0, 13)

The vertex form of a quadratic equation is given by;

y = a(x - h)² + k

Where h, k are the coordinates of the vertex.

a is the letter in general form of quadratic equation which is;

y = ax² + bx + c

Thus, at point (0, 13) at the vertex of (-3, 4), we have;

13 = a(0 - (-3))² + 4

⇒ 13 - 4 = 9a

9a = 9  

a = 9/9

a = 1  

Since y = a(x - h)² + k is the vertex form, let us put the vertex values for h and k as well as the value of a to get the quadratic equation;

y = 1(x - (-3))² + 4

y = x² + 6x + 9 + 4

y = x² + 6x + 13

Read more at; brainly.com/question/17546421


The formula for this quadratic function is x*2 +6x+13

Step-by-step explanation:

If we have the vertex and one point of a parabola it is possible to find the quadratic function by the use of this

y= a (x-h)*2 + K

Quadratic function looks like this

y= ax*2 + bx + c

So let's find the a

y= a (x-h)*2 + K where

y is 13, x is 0, h is -3 and K is 4

13= a (0-(-3))*2 +4

13=9a +4




The quadratic function will be

y= 1(x+3)*2 + 4

Let's get the classic form

(x+3)*2 = (x+3)(x+3)


x*2 +6x+13

f(0) = 13

A survey of 800 students yielded the following information: 519 were seniors, 430 were commuters, and 300 of the seniors were commuters. How many of the 800 surveyed students were seniors or were commuters?



The number is  (S \ u \  C  ) = 649

Step-by-step explanation:

From the question we are told that  

      The sample size is  n =  800

       The number of seniors is  S  =  519

         The number of  commuters is  C =  430

         The number of of seniors that are commuters is  (S\  n \ C )=  300

Generally the number of 800 surveyed students who were seniors or were commuters is  mathematically evaluated as

     (S \ u \  C  ) =  S + C  -  ( S \  n  \  C )

=>   (S \ u \  C  ) =  519  + 430   - 300

=>   (S \ u \  C  ) = 649