answer.
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
atroni [7]
2 years ago
14

A marketing firm wants to estimate how much root beer the average teenager drinks per year. A previous study found a standard de

viation of 1.12 liters. How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval
Mathematics
1 answer:
Verdich [7]2 years ago
4 0

Answer:

At least 832 teenargers must be interviewed.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.99}{2} = 0.005

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

How many teenagers must the firm interview in order to have a margin of error of at most 0.1 liter when constructing a 99% confidence interval

At least n teenargers must be interviewed.

n is found when M = 0.1.

We have that \sigma = 1.12

So

M = z*\frac{\sigma}{\sqrt{n}}

0.1 = 2.575*\frac{1.12}{\sqrt{n}}

0.1\sqrt{n} = 2.575*1.12

\sqrt{n} = \frac{2.575*1.12}{0.1}

(\sqrt{n})^{2} = (\frac{2.575*1.12}{0.1})^{2}

n = 831.7

Rounding up

At least 832 teenargers must be interviewed.

You might be interested in
A survey found that 89% of a random sample of 1024 American adults approved of cloning endangered animals. Find the margin of er
Kobotan [32]

Answer:

The margin of error for the survey is 0.016

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1024

Sample proportion:

\hat{p} = 89\% = 0.89

We have to find the margin of error associated with a 90% Confidence interval.

Formula for margin of error:

z_{stat}\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.10} = 1.64

Putting the values, we get:

M.E = 1.64\times (\sqrt{\dfrac{0.89(1-0.89)}{1024}})\\\\M.E=0.016

Thus, the margin of error for the survey is 0.016

3 0
2 years ago
A report from a Gallup poll 1 in 2011 started by saying, "Forty-five percent of American adults reported getting their health in
snow_tiger [21]

Answer:

The interval estimate for the population proportion of American adults who got their health insurance from an employer is (0.43, 0.47).

Step-by-step explanation:

The confidence interval is the interval estimate of the population parameter.

The confidence interval has a certain probability that the true value of the parameter is contained in the interval.

The general form of the confidence interval is:

CI=SS\pm MOE

Here,

SS = sample statistic.

MOE = margin of error

The sample statistic is an unbiased estimator of the population parameter. If the sample size is large enough then the sample statistic can be used to estimate the population parameter value.

In this case the parameter of interest is the population proportion of American adults who got their health insurance from an employer.

The information provided is:

<em>SS = p = </em>0.45.

<em>MOE</em> = 0.02.

Compute the confidence interval for the population proportion <em>p</em> as follows:

CI=p\pm MOE\\=0.45\pm 0.02\\=(0.43, 0.47)

Thus, the interval estimate for the population proportion of American adults who got their health insurance from an employer is (0.43, 0.47).

3 0
2 years ago
Lila wrote an equation of the cost for printing brochures, where x represents the number of brochures and y represents the total
Elena L [17]

Answer:

The answer is C. Lila made an error in Step 3 when she did not use the x- and y-coordinates from the same ordered pair.

Hope this helps!

Stay safe at home :)

(those of you doing edge hang in there!)

5 0
2 years ago
Read 2 more answers
Dave drives to work each morning at about the same time. his commute time is normally distributed with a mean of 45 minutes and
Paladinen [302]
The normal distribution curve is shown in the diagram below

<span>The percentage of time that his commute time exceeds 61 minutes is equal to the area under the standard normal curve that lies to the RIGHT of X=61

Standardising X=61 to find z-score
</span>z= \frac{61-45}{5} =3.2
<span>
from the z-table
</span>P(Z\ \textgreater \ 3.2) = 1 - P(Z\ \textless \ 3.2) = 1 - 0.9993 = 0.0007 = 0.07%<span>
</span>

8 0
2 years ago
A motorboat covers the distance from one pier to the other pier in 4 hours and the way back in 5 hours. What is the speed of the
stiv31 [10]
Speed of current ------ y km/h 

<span>distance with the current = 4(x+y) </span>
<span>distance against the current = 5(x-y) </span>

<span>we know that 3.5(x+y) = 70 </span>
<span>x+y = 20 </span>

<span>but 4(x+y) = 4(20) = 80 </span>
<span>then 5(x-y) = 80 </span>
<span>x-y = 16 </span>

<span>x+y=20 </span>
<span>x-y=16 </span>
<span>add them </span>
<span>2x = 36 </span>
<span>x = 18 , then y = 2 </span>
5 0
2 years ago
Other questions:
  • Susan wants to buy a paddle boat for $840. She will pay 20% down and pay the rest in six monthly installments. What will be the
    6·1 answer
  • The area of a square is tripled by adding 10 cm to one dimension and 12 cm to the other. Determine the side length of the square
    15·1 answer
  • Erica is given the diagram below and asked to prove that ab df. What would be the missing step of the proof? I only need the ans
    7·2 answers
  • Tim throws a stick straight up in the air from the ground. The function h = –16t2 + 48t models the height, h, in feet, of the st
    13·2 answers
  • W(t)W, left parenthesis, t, right parenthesis models the daily water level (in \text{cm}cmstart text, c, m, end text) at a pond
    12·2 answers
  • Andre is making paper cranes to decorate for a party. He plans to make one large papercrane for a centerpiece and several smalle
    10·1 answer
  • Keisha estimates 259+372 by rounding each number to the nearest 10. What is Keisha's estimate of the sum?
    10·1 answer
  • The surface area S of a single-celled organism may be found by multiplying 4π times the square of the radius r of the cell. Expr
    10·1 answer
  • For what values of h and k does the linear system have infinitely many solutions? 2x1 + 5x2 = −1 hx1 + kx2 = 7
    8·1 answer
  • Easton is working two summer jobs, making $18 per hour tutoring and $9 per hour clearing tables. Last week Easton worked 4 times
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!