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
solong [7]
3 years ago
10

An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driv

ing permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least _______.
Mathematics
1 answer:
nlexa [21]3 years ago
8 0

Answer:

n=1041  or higher

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})

2) Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by \alpha=1-0.99=0.01 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.04 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have a prior estimation for th proportion of interest, we can use this value as an estimation \hat p =0.5 And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{2.58})^2}=1040.06  

And rounded up we have that n=1041  or higher.

You might be interested in
Fix the sentence by following the apostrophe rule.
Anika [276]
<span>Strong children's education is essential to the progress of any nation.
</span>
7 0
2 years ago
Read 2 more answers
Sboob wohs dna ten.esaelpemetaD ot og FG evah i naC
emmainna [20.7K]

Answer:

Ummmm no thanks. I am not going there.

Step-by-step explanation:

6 0
3 years ago
5 peas equals 1 pod. 4 pods equals 1/2 ping. 3 pings equals how many peas? Please give me the full explanation so I can know for
salantis [7]

Answer:

120 peas in 3 pings

Step-by-step explanation:

(5x8)3

5 0
3 years ago
A group of 15 teenagers owes $75 at a pizza parlor. If they split the bill evenly, how much will each person owe?
Kipish [7]

Answer:

$5 each teenager

Step-by-step explanation:

divide 75 by 15

7 0
1 year ago
Read 2 more answers
Lucy wants to make a different types of cheesecake it's cheesecake uses 2/3 pound of cream cheese she has 2 lb of cream cheese h
slava [35]

3 would be your answer

4 0
3 years ago
Other questions:
  • How many reasons must your thesis contain and which reason is first
    9·1 answer
  • Addition and __?___ are operations you can use to join __?____?
    14·1 answer
  • What is 100.360 rounded to the nearest whole number plz help
    13·2 answers
  • Camila and her children went into a bakery and she bought $35 worth of cupcakes and brownies. Each cupcake costs $3.75 and each
    12·2 answers
  • A company's revenue (in dollars) can be modeled by the function
    10·1 answer
  • Evaluate the following expressions for x = -4
    11·1 answer
  • May you run 7 miles in 50 minutes at the same rate how many miles would she run in 75 minutes​
    8·1 answer
  • An African elephant weighs 2 tons. How many pounds are in a herd with 26 elephants?
    7·2 answers
  • How r u so good at this
    5·2 answers
  • The mean distance from the Earth to the Sun is c gigametres (Gm), where c = 150 and 1 Gm = 10⁹ m. The mean distance from Pluto t
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!