The perimeter of a rectangle is 15x + 17y

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

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:

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

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

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

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.02\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.02}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.02})^2$

$n = 2401$

The minimum sample size is 2401.

4 0

3 years ago

Quan's last paycheck shows that he eamed $210.00 for 24 hours of work. What is his hourly rate of pay?

Mariana [72]

Answer:

8.57 explanation:

Step-by-step explanation: If Quan gets 210 dollars every 24 hours and you want to find the amount he gets every hour all you have to do is do 210 divided by 24 which you will get 8.75. So every hour he gets $8.75 every hour for his work

7 0

3 years ago

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What is the greatest common factor (GCF) of 64 and 12

neonofarm [45]

The answer: 4
64’s common factors are 2 2 2 2 2 2
12’s common factors are 2 3 2
Find the factors that 64 and 12 have in common. The answer is 2 x 2= 4

8 0

3 years ago

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A=4ℼR2 solve for R<br> SHOW ALL STEPSSSSSSSSSSSSS

GuDViN [60]

Given problem;

A = 4 π R²

To solve for R, we have to make it the subject of the expression.

Since

A = 4 π R² , follow these steps to find R;

Multiply both sides by $\frac{1}{4\pi }$