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
harina [27]
3 years ago
14

An advertising agency that manages a major radio station wants to estimate the mean amount of time that the station’s audience s

pends listening to the radio on a daily basis. From past studies, the standard deviation is assumed to be 20 minutes. What sample size is needed if the agency wants to have a 95% confidence interval with a margin of error equal to 5 minutes?
Mathematics
1 answer:
Kazeer [188]3 years ago
7 0

Answer:

n=(\frac{1.960(20)}{5})^2 =61.46 \approx 62

So the answer for this case would be n=62 rounded up to the nearest integer

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".

\bar X represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=20 represent the population standard deviation

n represent the sample size  

Solution to the problem

The margin of error is given by this formula:

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} \sigma}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, replacing into formula (b) we got:

n=(\frac{1.960(20)}{5})^2 =61.46 \approx 62

So the answer for this case would be n=62 rounded up to the nearest integer

You might be interested in
A trapezoid and a rectangle are both quadrilaterals. This means they both have_____ sides and_______ angles. The angles in a rec
Yanka [14]

Answer:

both have equal sides and equal Angel's

the angels In a rectangle 4 sides

the angles in a trapezoid is 4 sides

4 0
3 years ago
I need help with this please pls pls
Masja [62]

Answer:in what ?

Step-by-step explanation:

7 0
3 years ago
Please help!!!!! Will give brainliest!!
valkas [14]

2.57*10^4 is 1,000,000 times more than 2.57*10^-1

Why?

4-(-1)=5 2

2.57*10^4=25700

2.57*10^-1=0.0257

and

25700

÷ 0.0257

=1000000

and 1000000=10^6

6 0
3 years ago
X - (-20) = 5 _________________
tamaranim1 [39]

X - (-20) = 5

When you subtract a negative, change it to addition:

X + 20 = 5

Subtract 20 from both sides:

X = -15

8 0
3 years ago
Read 2 more answers
90% on a test. If he answered 135 questions correctly, how many questions were on the test?
USPshnik [31]

Answer:

150

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • What is 2/3 divided by 4/5 please show work
    13·2 answers
  • Solve, using linear combination. <br> 3x + y = 4<br> 2x + y = 4
    11·1 answer
  • Solve for x<br> 3 tan' x = tan x
    9·1 answer
  • The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y ≤ −2x + 10 y &gt; 1 over
    8·1 answer
  • The figure below shows triangle XYZ and some of its transformed images on a coordinate grid: Which of the four triangles was for
    11·2 answers
  • If 3/10 of the flowers are green and 3/4 of the rest are yellow. And the rest are purple. How many flowers do you have if you ha
    15·2 answers
  • HELLLPPPPPPPP PLEASEEE use the image
    6·2 answers
  • The length of a rectangle is 4 times its width. The perimeter of the rectangle is 50 cm long. What is the area of the rectangle?
    9·1 answer
  • Donna is putting money into a savings account. She starts with $450 in the savings account, and each week she adds $70.
    8·1 answer
  • Simplify 79.5-2.58 x (3.63-1.63) to the third power
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!