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
IrinaK [193]
3 years ago
14

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population pro

portion? Assume that past data are not available for developing a planning value for p*
Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

Answer:

A sample of 1068 is needed.

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}}

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.

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.03 for the estimation of a population proportion?

We need a sample of n.

n is found when M = 0.03.

We have no prior estimate of \pi, so we use the worst case scenario, which is \pi = 0.5

Then

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

0.03 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.03\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.03}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.03})^{2}

n = 1067.11

Rounding up

A sample of 1068 is needed.

You might be interested in
Find the unknown angle in the figure
Alik [6]

Answer:

Angle 125 degree

Step-by-step explanation:

mark me brainliest

6 0
2 years ago
Read 2 more answers
A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular
kap26 [50]

Answer:

  a) no

  b) 143 rectangular containers

  c) 157 cylindrical containers

  d) both (preferring rectangular for the bulk of an order)

Step-by-step explanation:

a) If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs?

  No.*

For packaging 41 candles or fewer, the cylindrical container costs less than the rectangular one.

For packaging 6400 candles, there will be 10 candles left over if rectangular containers are used for most of the packaging needs. A dollar can be saved by packaging these remaining candles in a cylindrical container.

__

b) How many rectangular containers will be necessary to package 6,400 candles?

  6400/45 = 142 10/45

If rectangular containers are used for all, then 143 are needed.

__

c) How many cylindrical containers will be necessary to package 6,400 candles?

  6400/41 = 156 4/41

If cylindrical containers are used for all, the 157 are needed.

__

d) Which container should the company use to minimize costs?

  The cost of 143 rectangular containers is 143×$16 = $2288

  The cost of 157 cylindrical containers is 157×$15 = $2355

  The cost of 142 rectangular and 1 cylindrical container is $2287

If only one shape container is used, the company should use rectangular containers to minimize cost. If either shape can be used, cost will be minimized by using one cylindrical container for the remnant of the order.

_____

* This question is directed solely at the cost of materials required for packaging. We have advocated that both rectangular and cylindrical containers be made available. As a practical matter, the cost to the company of maintaining inventory of both sizes of containers may exceed the savings associated with using a cheaper container for smaller orders.

8 0
3 years ago
If a store advertised a sale that gave customers a 1/4 discount what is the fractional part of the original price that the custo
mina [271]
It will be 3/4 of the original price
8 0
3 years ago
An exponent is also called___.
bija089 [108]

Answer:

An expression that represents repeated multiplication of the same factor is called a power.

Step-by-step explanation:

The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

8 0
3 years ago
Please Help!!!!! 30 Points!!!!
s2008m [1.1K]

Answer:

11 yards

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • 1+2=21<br>2+3=36<br>3+4=43<br>4+5=​
    10·2 answers
  • Water goes over niagra falls at a rate of 180 million cubic feet every 1/2 hour. How much water goes over the falls in 1 minute?
    14·2 answers
  • How do you solve, j+2j+3j=-20+-16
    11·1 answer
  • How do you find the markup rate?
    12·2 answers
  • I'm doing some map testing please help
    9·1 answer
  • How many flowers spaced 4in are needed to surround a circular garden with a 200 in radius use 3.14 for pie
    8·1 answer
  • ILL GIVE BRAINLIEST PLEASE HELP WITH THESE ALGEBRA QUESTIONS show work pls
    13·1 answer
  • I need help with this!! ASAP
    11·1 answer
  • Fill in the chart <br> Tons ____<br> Pounds 1187<br> Ounces_____
    8·2 answers
  • NEED HELP QUICKLY! WORTH 100 POINTS!
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!