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
Rom4ik [11]
3 years ago
11

A public health official is planning for the supplyof influenza vaccine needed for the upcoming flu season. She wants to estimat

e the proportion p who plan to get the vaccine.
How large does the sample size n need to be for X/n, the sample proportion of people who plan to get the vaccine, to have an 90% chance of lying within 0.04 of probability?
Mathematics
1 answer:
Marizza181 [45]3 years ago
5 0

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25  

And rounded up we have that n=421

Step-by-step explanation:

We know that the sample proportion have the following distribution:

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

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 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.05. And the critical value would be given by:

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64

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)  

We assume that a prior estimation for p would be \hat p =0.5 since we don't have any other info provided. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.64})^2}=420.25  

And rounded up we have that n=421

You might be interested in
what is the answer to the multiplication problem. Jhon has 20 fish if he lets 6 fish go how many fish dose Jhon have?
spayn [35]
Isn't this a subtraction problem, not a multiplication problem?

If John starts out with 20 fish and lets 6 go, he still has (20-6), or 14, fish.
6 0
3 years ago
What single transformation was applied to triangle AAA to get triangle BBB?
UkoKoshka [18]
I assume c, because usually to get to the opposite you reflect the line or figure on the x axis
4 0
3 years ago
the profit of a company is modeled by p = 4t + 15,500, where p is the profit and t is the time in months. what is the dependent
posledela
The dependent variable is the profit because that is what you're measuring
6 0
3 years ago
Read 2 more answers
Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Oksana_A [137]

Answer:

option 2

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Which Function is represented by the Graph
Marysya12 [62]

Answer:b

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the greatest common factor of 25x^2 and 20b^4
    11·1 answer
  • Find the slope and y-intercept of the line that is parallel to y=-x-3and passes through the point (3,-2)
    8·1 answer
  • Marie Hernandez’s checking account balance is $250.65. She then writes check #346 on July 14 in the amount of $21.95 for a bathi
    11·1 answer
  • Solve 5x+2y=4 x-y=5 (by elimination)I really need help
    15·1 answer
  • Find the distance between the two points (4,-5) and (-1,7) In units
    15·1 answer
  • Needs Clarification Please! Explain how the graph of each given function is a transformation of the graph of y = x^2
    13·1 answer
  • I need help with solving this derivative please (check for picture)
    13·1 answer
  • in 1996 there were approximately 275 students in the Delaware high school band in 2002 that number increased to 305 find the ann
    9·1 answer
  • Mark mows lawns for 2.25 an hour if he spends 7 hours mowing lawns during one weekend how much money will he earn
    6·1 answer
  • In which situation could the quotient of -24 divided by 3 be used to answer the question?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!