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
cestrela7 [59]
3 years ago
15

Suppose a lawn and garden company wants to determine the current percentage of customers who use fertilizer on their lawns. How

many customers should the company survey in order to be 95% confident that the estimated (sample) proportion is within 4 percentage points of the true population proportion of customers who use fertilizer on their lawns?
Mathematics
1 answer:
marishachu [46]3 years ago
3 0

Answer:

n=601

Step-by-step explanation:

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}})

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 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The confidence interval for the mean is given by the following formula:  

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

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 the proportion we can use 0.5 as estimation. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.04}{1.96})^2}=600.25  

And rounded up we have that n=601

You might be interested in
HELP ASAP!! Linear Equations<br>x/7=3<br><br>A. 21<br>B. 3/7<br>C. 20<br>D. -21​
vredina [299]

Answer:

21

Step-by-step explanation:

put 21 were x is and then divide 21÷7=3

6 0
2 years ago
Read 2 more answers
Patrick compared the slope of the function g(x) = -2x - 8 to the slope of the linear function shown in the table below. Let m =
Zina [86]
Both slopes have the same sign
7 0
3 years ago
Write and inequality for the following statement: c is less than 6
Talja [164]

In order to solve this exercise you need to remember the following symbols in Inequalities:

1. The meaning of this symbol is "Greater than":

>

2. The meaning of this one is "Less than":

3. The following symbol means "Less than or equal to":

\le

4. And this one means "Greater than or equal to":

\ge

Knowing the above, you can determine that the statement "c is less than 6", can be written as the following inequality:

c

The answer is:

c

7 0
1 year ago
I do not know 6×8 is will you please help me with my homework
BartSMP [9]
If you multiply 6 times 8, you will get 48 as final answer
3 0
3 years ago
Read 2 more answers
Is 5 a natural whole integer or rational or irrational​
lara [203]

Answer:

Rational number

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • Amy read 8 more books than ben read. how many books did ben read
    7·2 answers
  • Explain how 50 tens x 4 hundreds = 40 tens x 5 hundreds
    6·1 answer
  • The function f(x) = RootIndex 3 StartRoot x EndRoot is reflected over the x-axis to create the graph of g(x) = Negative RootInde
    10·1 answer
  • I'm not the best at math, I could really use some help ;)
    12·1 answer
  • Zaire spent 55 hours in 2 weeks working on a science project. She worked 32 hours the first week. Write and solve an addition eq
    6·2 answers
  • Fundamental Counting:
    11·1 answer
  • What is the gcf of 42 and 60​
    6·2 answers
  • Why is math good for me?
    10·2 answers
  • If 36 men can do a piece of work in 25 days, in how many days will<br> 15 men do it?
    13·1 answer
  • What is the equation of the following line?<br><br> (-3,9)<br><br> (0,0)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!