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
Vaselesa [24]
3 years ago
13

Assume that population mean is to be estimated from the sample described. Use the sample results to approximate the margin of er

ror and​ 95% confidence interval. Sample​ size, n=64​; sample​ mean, x =69.0 ​cm; sample standard​ deviation, s=4.0 cm
Mathematics
1 answer:
Vikentia [17]3 years ago
3 0

Answer:

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

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 =69 represent the sample mean for the sample  

\mu population mean

s=4.0 represent the sample standard deviation

n=64 represent the sample size  

Assuming the X follows a normal distribution

X \sim N(\mu, \sigma)

The sample mean \bar X have the following distribution:

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

The margin of error for the sample mean is given by this formula:

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

Since we have the sample standard deviation we can estimate the margin of error like this:

ME=t_{\alpha/2}\frac{s}{\sqrt{n}}

The next step would be find the value of \z_{\alpha/2}, \alpha=1-0.95=0.05 and \alpha/2=0.025

We can find the degrees of freedom like this:

df=n-1=64-1=63

And we can find the critical value with the following code in excel for example: "=T.INV(0.025,63)" and we got:

t_{\alpha/2}=\pm 1.998

And the margin of error would be :

ME=1.998 \frac{4}{\sqrt{64}}=0.999 \approx 1

You might be interested in
Y=-(x + 1) - 5<br> find domain and range
In-s [12.5K]
This is the answer ......

4 0
3 years ago
PLEASE HELP<br> ILL MARK AS BRAIN LEIST!
Talja [164]

Answer:

C. 707 cm^2

Step-by-step explanation:

8 0
2 years ago
If one potato can make 32 trench fries, can eat 3 bites per minute, and one bite equals 2 french fries How many potatoes will ea
Katen [24]

Answer:

Step-by-step explanation:

5! I think

4 0
3 years ago
Can someone help me pls thanks
allsm [11]

Answer:

x = 1/2QN^2

Step-by-step explanation:

8 0
2 years ago
Pleaseeeee help I’m begging someone I PROMISE. I will mark brainlest
Lerok [7]

Answer:


Step-by-step explanation:

a) x>0 → items can not be negative

b) c(2,000) = 5,000+1.3(2,000) = $7,600

c)5,000+1.3x<10,000

5,000-5,000+1.3x<10,000-5,000

1.3x<5,000

x<3846 items


5 0
3 years ago
Other questions:
  • 17/64 + 47/64 + 7/8 =<br>B.<br>1/16<br>134<br>151/64<br>1%<br>D.​
    10·1 answer
  • Mathematical connections
    5·1 answer
  • List A contains the numbers [20,10,30], while list B contains the numbers [10,30,20,40,30]. We choose one number from list A ran
    14·1 answer
  • The equation y-9+9=-17+9 is an example of which property of equality?
    15·1 answer
  • Pls help me I need help ASAP and PLS SHOW YOUR WORK because I don’t understand this
    5·1 answer
  • Mary and Tom were buying a present for their mother for Mother's Day. Mary spent $12 and Tom spent $28. If they want to share th
    7·2 answers
  • Joshua needs to order some new supplies for the restaurant where he works. The restaurant needs at least 378 spoons. There are c
    12·1 answer
  • Solve the system of equations. 5x−4y=−10 -4x + 5y = 8
    10·1 answer
  • 2(-3y-1)+(2y+7)<br> I need to know how to solve this equation
    8·1 answer
  • What is the additive inverse of (-2m)?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!