1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Dmitriy789 [7]
3 years ago
11

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

r district.
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.)
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.
Mathematics
1 answer:
UkoKoshka [18]3 years ago
4 0

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.

You might be interested in
A factory has two types of employees line workers and Mananger
denis-greek [22]

Step-by-step explanation:

Read this article to learn about the types, functions, advantages and conflicts of line and staff organisation.

Types of Staff:

1. Personal Staff:

Personal staff is attached to individual line officers. The Personal Assistant or the Private Secretary etc. form personal staff of line managers. These persons help their bosses in every possible way. The routine work of line officers is mostly handled by the personal staff. They fix routine meetings, open the post, maintain diaries and accompany the boss on official visits. The line officers are spared of routine works and are able to devote much time for planning and execution.

2. Specialist Staff:

These are technically qualified persons who provide service to the whole organisation. They serve line and other staff in planning, organizing and coordinating their work. Their specialized knowledge is an asset to the organisation. The appointment of a legal advisor may be helpful to every department where his advice is required.

3. General Staff:

ADVERTISEMENTS:

This staff consists of persons attached to the key executives. They have the same background as that of line officers. They are attached to important functionaries as their deputies, etc. They may be appointed as Deputy Managers, Assistant Managers, Special Assistants, etc.

Functions of Staff Authority:

The staff authority is assigned the following functions:

1. Agency of Control:

It has to discharge the functions such as:

(a) Organisation;

ADVERTISEMENTS

3 0
3 years ago
A pizza delivery shop averages 20 minutes per delivery with a standard deviation of 4 minutes. What is the probability that a pi
Vlada [557]
... ......... . .........
4 0
3 years ago
Read 2 more answers
Answer the question for a normal random variable x with mean μ and standard deviation σ specified below. (Round your answer to o
vladimir2022 [97]

Answer:

x = 63.6

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X and also the area to its left. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X, which is the area to its right.

In this problem, we have that:

\mu = 38, \sigma = 11

Find a value of x that has area 0.01 to its right

This is x when Z has a pvalue of 1-0.01 = 0.99. So it is X when Z = 2.3267.

Z = \frac{X - \mu}{\sigma}

2.3267 = \frac{X - 38}{11}

X - 38 = 11*2.3267

X = 63.6

So x = 63.6

6 0
3 years ago
X^2 - 36 = 0.
strojnjashka [21]

Answer:

(x+6)(x−6)=0

x=-6 or x=6

Step-by-step explanation:

X^2 - 36 = 0

Solve by Square Root

add 36 both sides

x^2−36+36=0+36

x^2=36

square root

x=±√36

x=6 or x=−6

You can do that or for 2nd option

Solve by factoring

x^2-36=0

(x+6)(x−6)=0

Set factors equal to 0

x+6=0 or x−6=0

x=-6 or x=6

PLEASE NOTE: 36 is the square of 6

and

x2  is the square of  x1

8 0
3 years ago
Need help right now!!!!!
Irina18 [472]

Answer:

I just took the test and the correct answer is -6 is not in the domain of f g

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • A DVD has a diameter of 34 centimeters. What is the area of the DVD? Round your answer to the nearest
    6·2 answers
  • -3/2 to a decimal form
    13·1 answer
  • Find the measure of the missing angle. 122,79,90,Z
    5·1 answer
  • Gary had $230. he spent 45% of the money on a wallet. how much money did he have left?​
    10·2 answers
  • How many solutions do the following equations have?
    7·1 answer
  • Plz help 52 points
    10·2 answers
  • HELP I NEED HELP ASAP <br> HELP I NEED HELP ASAP <br> HELP I NEED HELP ASAP
    8·1 answer
  • 1. Dominic earned $23.00 at the local
    8·1 answer
  • 5/4+5/4=_ × 1/4 plz help me​
    13·1 answer
  • The diameter of the pan is 9 inches. What is the approximate circumference of a lid that will fit his frying pan? (Use 3.14 for
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!