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
Gnoma [55]
3 years ago
12

In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.

Mathematics
1 answer:
inn [45]3 years ago
4 0

Answer:

a) The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.

b) The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.

c) The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).

d) The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

Standard error:

The standard error is:

s = \sqrt{\frac{\pi(1-\pi)}{n}}

Margin of error:

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}} = zs

The confidence interval is:

Sample proportion plus/minus margin of error. So

(\pi - M, \pi + M)

In a simple random sample of 1500 young Americans 1305 had earned a high school diploma.

This means that n = 1500, \pi = \frac{1305}{1500} = 0.87

a. What is the standard error for this estimate of the percentage of all young Americans who earned a high school diploma?

s = \sqrt{\frac{\pi(1-\pi)}{n}} = \sqrt{\frac{0.87*0.13}{1500}} = 0.0087

0.0087*100% = 0.87%.

The standard error for this estimate of the percentage of all young Americans who earned a high school diploma is 0.87%.

b. Find the margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma.

95% confidence level

So \alpha = 0.05, z is the value of Z that has a p-value of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Then

M = zs = 1.96*0.0087 = 0.0171

0.0171*100% = 1.71%

The margin of error, using a 95% confidence level, for estimating the percentage of all young Americans who earned a high school diploma is of 1.71%.

c. Report the 95% confidence interval for the percentage of all young Americans who earned a high school diploma.

87% - 1.71% = 85.29%

87% + 1.71% = 88.71%.

The 95% confidence interval for the percentage of all young Americans who earned a high school diploma is (85.29%, 88.71%).

d. Suppose that in the past, 80% of all young Americans earned high school diplomas. Does the confidence interval you found in part c support or refute the claim that the percentage of young Americans who cam high school diplomas has increased? Explain.

The lower bound of the confidence interval is above 80%, which means that the confidence interval supports the claim that the percentage of young Americans who cam high school diplomas has increased.

You might be interested in
Subtract 7x+3 from 2x-7
AysviL [449]

Subtract 7x+3 from 2x-7

(2x - 7) - (7x + 3) =

2x - 7 - 7x + 3

-5x -4

6 0
3 years ago
She puts the gifts into a box. She puts a label on one side of the box.How many faces do not have labels?faces.
Kisachek [45]
A closed box has 6 faces.

There is 1 label on 1 face.

Subtract 1 from 6

6 - 1 = 5

5 faces is your answer


Hope this helps
3 0
3 years ago
Find the annual interest rate. Round your answer to the nearest hundredth of a percent. I=$160.67, P=$2000, t=8 months
FinnZ [79.3K]
Let would be the annual interest rate such that,
                              I = P x r^t
For the 1st
                            160.67 = (2000) x r*8/12    ; r = 0.02277
The second case is just  the same. 
3 0
3 years ago
Find.<br> 12/18 = n/36<br><br> n = (Blank)
Orlov [11]

Solve for n by simplifying both sides of the equation, then isolating the variables.

n=54

Hope I helped

4 0
3 years ago
Caleb and his classmates are making felt dog toys for a local animal shelter.
TEA [102]
Not really sure how to answer this hope someone helps you!
3 0
3 years ago
Other questions:
  • Please help!!!!!!! I forgot how to do this !!
    13·2 answers
  • If y varies directly as x, and y is 12 when x is 1.2, what is the constant of variation for this relation?
    6·2 answers
  • Please answer ASAP worth 20 points!
    15·2 answers
  • What is the decimal form of -4 7/8
    6·1 answer
  • Fill in the blanks below in order to justify whether or not the mapping
    6·1 answer
  • The amplitude of y = -2 sin 3x is
    10·1 answer
  • Inverse function details
    12·1 answer
  • What can you say about the function that generated the following table of values? O A. the function has no x-intercepts O B. the
    10·1 answer
  • SELECT ALL MODELS I WILL GIVE BRAINLIEST 6TH GRADE MATH
    9·1 answer
  • Which equation and solution can be used to solve this problem?
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!