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
olga_2 [115]
3 years ago
9

Sample Size for Proportion As a manufacturer of golf equipment, the Spalding Corporation wants to estimate the proportion of gol

fers who are left0handed. (The company can use this information in planning for the number of right0handed and left0 handed sets of golf clubs to make.) How many golfers must be surveyed if we want 99% confidence that the sample proportion has a margin of error of 0.025?
Mathematics
1 answer:
Dima020 [189]3 years ago
6 0

Answer:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

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

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

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:

t_{\alpha/2}=-2.58, t_{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 0.025 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 can assume an estimated proportion of \hat p =0.5 since we don't have prior info provided. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.025}{2.58})^2}=2662.56  

And rounded up we have that n=2663

You might be interested in
The tax rate for new york is 7.45%.if nicolas earns 36,000 this year,how much will he pay taxes
Arlecino [84]

\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7.45\% of 36000}}{\left( \cfrac{7.45}{100} \right)36000}\implies 2682

4 0
3 years ago
fond two consecutive odd integers whose sum is 36 which of the following equations could be used to solve the problem
Travka [436]

Answer:

17 is the answer.

Step-by-step explanation:

4 0
3 years ago
Determine whether the data in the table can be modeled by a linear equation. Explain.
kotykmax [81]

Answer:

yes, because they're varying in a constante rate

y = -1/2x +3.5

7 0
2 years ago
1520 divided by 83 it has r
Amanda [17]
18 with a remainder of 26 I got this by using a long division calculator I hope this helps you
7 0
3 years ago
Read 2 more answers
PLEASE HELP!!! WILL MARK BRAINLIEST!!<br> Use the diagram to solve for x
bearhunter [10]

Answer: 3

Step-by-step explanation:

Set them equal because they are the same so 15x+5=16x+2 so x+2=5 so x=3

3 0
3 years ago
Other questions:
  • 20 POINTS!!!!!! help asap
    7·2 answers
  • Please Help! Brainiest!
    14·2 answers
  • Help with this question ??
    7·1 answer
  • The moon is about 240,000 miles from earth . What is the distance written as a whole number multiplied by a power of ten
    7·2 answers
  • What is the slope of the line represented by 7y − 15x = 14?
    5·1 answer
  • Which expression is equivalent to the area of metal sheet required to make this square-shaped traffic sign? (5 points) A square
    13·2 answers
  • Rename the quadratic function f(x)=-2(x+4)^2-5 in standard form.
    13·1 answer
  • What is the missing term? 4/5 = 2/3 = 4/5 x
    15·1 answer
  • A bag contains 40 red and green marbles. The number of green marbles, g, is 9 times the number of red marbles, r.
    5·1 answer
  • how would you solve 4c + 11 = -25? explain how in complete sentences and list the solution. (yall im so lost in class rn, i need
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!