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
Lady_Fox [76]
3 years ago
9

A manufacturer reported a sample mean = 22.0 g and a sample standard deviation = 2.5 g based on a sample of 20 of their products

. They hope to design future quality control tests to satisfy several criteria:  The calculated error for a sample set (the error is the difference between the true mean and mean of the sample set) does not exceed 2.0 g.  To save money on those tests, they want to collect as few samples as possible.  They want more than 90% of the confidence intervals they calculate to include the true mean. What value of n would you recommend for future tests?
Mathematics
1 answer:
tester [92]3 years ago
6 0

Answer:

n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5

So the answer for this case would be n=5 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=22 represent the sample mean

\mu population mean (variable of interest)

s=2.5 represent the sample standard deviation

n represent the sample size  

ME = 2 represent the margin of error accepted

Solution to the problem

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

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

The margin of error is given by this formula:

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

And on this case we have that ME =2 and we are interested in order to find the value of n, if we solve n from equation (2) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (3)

We can use as estimator for the population deviation the sample deviation \hat \sigma = s

The critical value for 90% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.05;0;1)", and we got z_{\alpha/2}=1.640, replacing into formula (3) we got:

n=(\frac{1.640(2.5)}{2})^2 =4.2 \approx 5

So the answer for this case would be n=5 rounded up to the nearest integer

You might be interested in
I need help doing thsi
Naily [24]
True! Because T is the defining letter of the line, so it would be true!

Hope this helps!! :)
7 0
3 years ago
In which expression does g have a coefficient of 8 <br> 8g <br> 8 + g <br> g - 8 <br> g/8
belka [17]

Answer:

8g

Step-by-step explanation:

In 8g, g has the coefficient 8:  we multiply g by 8.

3 0
2 years ago
Read 2 more answers
Write the equation in slope intercept form?
aleksandr82 [10.1K]

Answer: y = 1/3 x - 2

Step-by-step explanation:

6 0
3 years ago
Steven earns extra money babysitting. He charges $31.25 for 5 hours and $50 for 8 hours..
Maru [420]
$6.25 × h = c
h = hours, c = total cost

$31.25 for 5 hours. $6.25 per hour

$50 for 8 hours. $6.25 per hour
3 0
3 years ago
On a map, 1
chubhunter [2.5K]
You can write this as a proportion
inch over miles = inch over miles
1/14.5 = 4.5/x
cross multiply
x = 65.25

They are actually 65.25 miles apart.

Hope this helps
6 0
3 years ago
Read 2 more answers
Other questions:
  • Find the surface area and volume of each figure. Round each answer to the nearest hundredth.
    6·1 answer
  • A recipe for 4 dozen cookies calls for 3/4 cup of sugar how much sugar is needed to Make 2 dozen cookies
    12·1 answer
  • Harvey has a 3qt container and a 5qt container. How can he measure 4 qt of water
    7·1 answer
  • Two angles in a triangle add up to 108 degrees what is the size of the third angle
    8·1 answer
  • The slopes of LM and HN both equal 0. What can you conclude about the segments
    9·2 answers
  • 1089<br> 141°<br> Next Question<br> Check Answer
    7·1 answer
  • Write the expression 14(x+8) one other way.
    7·1 answer
  • Suppose 60% of the graduating class in a certain high school goes on to college. If 126 students from this graduation class are
    9·1 answer
  • Solve for Y MUST SHOW WORK<br> 2(Y+7) = 28
    9·2 answers
  • To the nearest tenth, what is the value of x?<br>A. 3.5<br>B. 4.8<br>C. 5.9<br> D. 7.3<br>E. 9.8 ​
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!