Mathematics, 15.04.2020 03:20 jnelso5437

A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national parks. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%

Answers: 3

Show answers

Answers

The size of the sample that is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5% is; n = 271

We are given;

Confidence level of 90%

Margin of error; E = 5% = 0.05

We are not given the population proportion but we will assume that it is 0.5

Formula for margin of error here is;

E = z(√(p(1 - p)/n)

where z is the critical value at the confidence level

n is the sample size

Now, z at CL of 90% is 1.645

Making n the subject gives;

n = z²(p(1 - p)/E²

Plugging in the relevant values gives;

n = 1.645²(0.5(1 - 0.5))/0.05²

n ≈ 271

Read more about confidence intervals with proportion at; link

Answer from: maleah12x

We need a sample size of at least 271

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 level of $1-\alpha$ , 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 $1 - \frac{\alpha}{2}$ .

The margin of error is:

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

90% confidence level

So $\alpha = 0.1$ , z is the value of Z that has a pvalue of $1 - \frac{0.1}{2} = 0.95$ , so Z = 1.645 .

How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%

We need a sample size of at least n, in which n is found when M = 0.05

We do not know the true proportion, so we use $\pi = 0.5$ , which is when we are going to need to use the largest sample size.

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

$0.05 = 1.645\sqrt{\frac{0.5*0.5}{n}}$

$0.05\sqrt{n} = 1.645*0.5$

$\sqrt{n} = \frac{1.645*0.5}{0.05}$

$(\sqrt{n})^{2} = (\frac{1.645*0.5}{0.05})^{2}$

n = 270.6

Rounding up

We need a sample size of at least 271

Answer from: Quest

in the attachment. i didn't see your choices. the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.

Which graph represents the same relation as the set (-3,,,-2)?

Answer from: Quest

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0

the value of x is equal to 0.

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Evaluate 4 a for a = 5 2/3 . express your answer in simplest form.

Answers: 1

Answer

Mathematics, 21.06.2019 16:30

If your annual gross income is $62,000 and you have one monthly car payment of $335 and a monthly student loan payment of $225, what is the maximum house payment you can afford. consider a standard 28% front-end ratio and a 36% back-end ratio. also, to complete your calculation, the annual property tax will be $3,600 and the annual homeowner's premium will be $360.

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Which of the expressions (on the photo document i inserted) together represent all solutions to the following equation? 8cos(12x)+4=-4 *the answer should be in degrees.* > i would like for someone to explain the process to find the solutions for this.

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

You are shooting hoops after school and make 152 out of a total of 200. what percent of shots did you make? what percent did you miss? show proportion(s).

Answers: 1

Answer

You know the right answer?

A private opinion poll is conducted for a politician to determine what proportion of the population...

Questions