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
goldfiish [28.3K]
3 years ago
11

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Norm

al distribution with standard deviation σ = 100.
You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for μ is found to be 512.00 ± 25.76."

What was the confidence level used to calculate this confidence interval?
Mathematics
1 answer:
Vlad1618 [11]3 years ago
8 0

Answer:

Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

Step-by-step explanation:

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".

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The distribution for the sample mean is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

\bar x =512 represent the sample mean

\sigma=100 represent the population standard deviation

n= 100 sample size selected.

The confidence interval is given by this formula:

\bar X \pm z_{\alpha/2} \frac{\sigma}{\sqrt{n}}   (1)

The marginof error for this case is given by Me=25.76. And we know that the formula for the margin of error is given by:

Me=z_{\alpha/2} \frac{\sigma}{\sqrt{n}}

25.76=z_{\alpha/2} \frac{100}{\sqrt{100}}

And we can find the critical value z_{\alpha/2} like this:

z_{\alpha/2}=\frac{25.76(\sqrt{100})}{100}=2.576

And we know that on the right tail of the z score =2.576 we have \alpha/2 of the total area. We can find the area on the right of the z score using this excel code:

"=1-NORM.DIST(2.576,0,1,TRUE)" or using a table of the normal standard distribution, and we got 0.004998=\alpha/2, so then \alpha=0.00498*2=0.009995 \approx 0.01, and then we can find the confidence like this:

Confidence =1-\alpha=1-0.01=0.99

And then the confidence level would be given by 99%

You might be interested in
What is 80% of 72 ? pls help due today
Leni [432]

Answer:

Step-by-step explanation:

57.6

3 0
3 years ago
Read 2 more answers
Worth 20 points Il will mark brainiest! :)
Alex73 [517]

A. Perpendicular!

Because they cross with a 90 degree angle :]

8 0
3 years ago
Read 2 more answers
Find the missing side and round to the nearest tenth
mario62 [17]
65 degrees is right
8 0
3 years ago
(a + b)(a ² - ab + b ²) Please help!
kvasek [131]
Hey there :)

( a + b )( a² - ab + b² )
Let us distribute ( a + b )

a ( a² ) + a ( - ab ) + a ( b² ) + b ( a² ) + b ( - ab ) + b ( b² )
a³ - a²b + ab² + a²b - ab² + b³

We can simplify further:
- a²b + a²b = 0
ab² - ab² = 0

a³ + b³

You can see in the picture I have attached that this is the 7th formula

4 0
3 years ago
Read 2 more answers
Help me pretty please...
OleMash [197]

Answer:

the answer to your question is C

4 0
3 years ago
Other questions:
  • Lexi runs the snack stand at Belleview Community Pool. This morning, she withdrew $150 from the stand's bank account to buy supp
    6·1 answer
  • The diagonals of a rhombus are _____.
    15·2 answers
  • -2/5y =4<br><br> photo show above. please explain answer aswell.
    12·1 answer
  • What is the length, in dekameters, of 1073.4 centimeters?​
    5·2 answers
  • Use the substitution method to solve the system of equations. Choose the correct ordered pair.
    15·1 answer
  • Algebra 2 I need this for my test tomorrow can someone help me pls
    15·1 answer
  • Adam is going to make concrete. He is going to use 180 kg of cement. 375 kg of sand. 1090 kg of stone. Cement, sand and stone ar
    14·1 answer
  • Simplify (3x-21)/(7x-x²)<br>with working pls​
    10·1 answer
  • (64x44)/11x2^7<br> please reply it is exponents question
    5·1 answer
  • 5. A carton of ice cream holds 5 cups of ice cream. One serving of ice cream is 1 cups.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!