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
balandron [24]
3 years ago
5

The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the e

ighth grade level. Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. Using the data, construct the 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level.
Mathematics
1 answer:
Viefleur [7K]3 years ago
7 0

Answer:

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

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 zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

Suppose a sample of 1537 tenth graders is drawn. Of the students sampled, 1184 read above the eighth grade level. So 1537 - 1184 = 353 read at or below this level. Then

n = 1537, \pi = \frac{353}{1537} = 0.2297

95% confidence level

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

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 - 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2087

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2297 + 1.96\sqrt{\frac{0.2297*0.7703}{1537}} = 0.2507

The 95% confidence interval for the population proportion of tenth graders reading at or below the eighth grade level is (0.2087, 0.2507).

You might be interested in
The box-and-whisker plot below represents some data set. What percentage of the
Alex

Considering the given box-and-whisker plot, it is found that 50% of the data values are between 16 and 72.

<h3>What does a box-and-whisker plot shows?</h3>

A box and whisker plot shows five things:

  • The minimum value.
  • The 25th percentile, which is the median of the bottom 50%.
  • The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.
  • The 75th percentile, which is the median of the upper 50%.
  • The maximum value.

From this plot, we have that:

  • The 25th percentile is of 16.
  • The 75th percentile is of 72.

Hence, 50% of the data values are between 16 and 72.

More can be learned about a box-and-whisker plot at brainly.com/question/27721471

#SPJ1

5 0
2 years ago
A normal population has a mean of 12.2 and a standard deviation of 2.5. compute the z value associated with 14.3. what proportio
Citrus2011 [14]
The z-score associated with 14.3 is 0.84.  0.2995 of the population is between 12.2 and 14.3.  0.1894 of the population is less than 10.0.

The formula for a z-score is

z=(X-μ)/σ

With our data, we have:
z=(14.3-12.2)/2.5=0.84

The z-score associated with the mean is 0.5.  To find the proportion of the population between the mean and 14.3, subtract 0.7995 (the proportion of population below the z-score of 0.84, using http://www.z-table.com) and 0.5:

0.7995 - 0.5 = 0.2995.

The z-score for 10.0 is

(10.0-12.2)/2.5 = -0.88.  The proportion of the population less than this is 0.1894.
5 0
3 years ago
What is the effect of the b value in an exponential function? y-a*b^x<br> please help me
Margaret [11]

Answer:

Here's li^{}

nk to the answer:

bit.^{}

ly/3a8Nt8n

4 0
3 years ago
Write an equation in slope intercept form for a line that passed through the two points below (-4,7), (8,1)
vichka [17]
Y= -1/2x + 5
Good luck!!!!
7 0
2 years ago
A cylinder and a cone have the same radius and height. The volume of the cylinder is 639 ft ^3. what is the volume of the cone?
AURORKA [14]

The volume of the cone is: A. 213 ft³.

<h3>Volume of a Cylinder and a Cone</h3>
  • Volume of cylinder = πr²h.
  • Volume of cone = ⅓πr²h.

Given:

radius and height of both the cylinder and the cone are equal.

Volume of Cylinder = 639 ft³

Therefore:

πr²h = ⅓πr²h

This means that volume of cone would be ⅓ of the volume of the cylinder.

Volume of cone = ⅓(639) = 213 ft³

Therefore, the volume of the cone is: A. 213 ft³.

Learn more about volume of cone on:

brainly.com/question/13677400

7 0
2 years ago
Other questions:
  • The number of visitors to a park is expected to follow the function v(x) = 7(x − 1), where x is the number of days since opening
    9·2 answers
  • By decreasing each dimension by 2 units units​, the area of a rectangle decrease from 48 square feet​ (on the​ left) to 24 squar
    12·1 answer
  • A scientist mixes water (containing no salt) with a solution that contains 35% salt. She wants to obtain245 ounces of a mixture
    10·1 answer
  • Geometry question help please !!​
    14·1 answer
  • Kathleen says that quadrilaterals have right angles Gray says that quadrilaterals do not have to have right angles explain who i
    12·1 answer
  • Plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz help
    13·2 answers
  • A. Write an expression that represents the total cost of large pizza. let t = # of toppings.
    9·1 answer
  • Which unit rate corresponds to the proportional relationship shown in the graph? Drag and drop the answer into the box to match
    9·2 answers
  • Can anybody help me with this?
    6·2 answers
  • 13mm<br> 12 mm<br> 13 mm<br> 14 mm<br> 10 mm
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!