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
Which expression is equivalent to (x Superscript 27 Baseline y) Superscript one-third?
alexgriva [62]

Answer:

x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)

OR x^9/(∛y)

Step-by-step explanation:

Given the indicinal equation

(x^27/y)^1/3

To find the corresponding expression, we will simplify the equation as shown:

(x^27/y)^⅓

= (x^27)^⅓/y⅓

= {x^(3×9)}^⅓/y⅓

= x^9/y⅓

= x^9/(∛y)

The right answer is x Superscript 9 Baseline (RootIndex 3 StartRoot y EndRoot)

6 0
3 years ago
Read 2 more answers
Which of these expressions can you simplify by combining like terms
Tom [10]

Answer:

top right bottom left

Step-by-step explanation:


7 0
3 years ago
Read 2 more answers
∆ABC is mapped onto ∆A'B'C' which is then mapped onto ∆A"B"C". ∆ABC and ∆A"B"C" are shown in the diagram.
hram777 [196]

Answer:

1rotation translation dilation

2dilation

3the relationship is the shapes are the same just dilated and in different spots. The shapes are in different spots and are different sizes ut they are the same shape making them related.

Step-by-step explanation:

6 0
2 years ago
37:35-(32:24-10).2+√289=
Mkey [24]

Answer:

to simplify this it is 1295/1804

Step-by-step explanation:

3 0
2 years ago
A cube has a volume of 125 cubic inches. What is the length of each edge?
Bingel [31]

The formula for the volume of a cube is V = a^3.

We know the volume is 125 cubic inches.

125 = a^3

Take the third square root

5 = a

The length of each edge is 5 inches

3 0
2 years ago
Read 2 more answers
Other questions:
  • Are my answer correct
    12·2 answers
  • What is the whole number 13 as an improper fraction
    14·1 answer
  • Write mixed number as a fraction 5 1/2​
    12·2 answers
  • Sunflower produce approximately 50 seeds per flower. If one ounce of sunflower seeds contain an average of 72 seeds, how many fl
    13·1 answer
  • 30 POINTS!!!
    7·1 answer
  • Find the length of AB on the kite?
    12·1 answer
  • P(take the bus) seniors =
    15·1 answer
  • What is the remainder when f(x) = 2x4 + x3 – 8x – 1 is divided by x - 2?
    6·1 answer
  • Find the volume of the cone.
    12·1 answer
  • which of the following is an example of stratified sampling? in order to assess students' satisfaction with the food establishme
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!