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
chubhunter [2.5K]
3 years ago
11

Repeated student samples. Of all freshman at a large college, 16% made the dean’s list in the current year. As part of a class p

roject, students randomly sample 40 students and check if those students made the list. They repeat this 1,000 times and build a distribution of sample proportions.
(a) What is this distribution called?

(b) Would you expect the shape of this distribution to be symmetric, right skewed, or left skewed? Explain your reasoning.

(c) Calculate the variability of this distribution.

(d) What is the formal name of the value you computed in (c)?

(e) Suppose the students decide to sample again, this time collecting 90 students per sample, and they again collect 1,000 samples. They build a new distribution of sample proportions. How will the variability of this new distribution compare to the variability of the distribution when each sample contained 40 observations?
Mathematics
1 answer:
Dima020 [189]3 years ago
0 0

Answer:

a) p-hat (sampling distribution of sample proportions)

b) Symmetric

c) σ=0.058

d) Standard error

e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

Step-by-step explanation:

a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.

b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.

This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.

c) The variability of this distribution, represented by the standard error, is:

\sigma=\sqrt{p(1-p)/n}=\sqrt{0.16*0.84/40}=0.058

d) The formal name is Standard error.

e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:

\frac{\sigma_{90}}{\sigma_{40}}=\frac{\sqrt{p(1-p)/n_{90}} }{\sqrt{p(1-p)/n_{40}}}}= \sqrt{\frac{1/n_{90}}{1/n_{40}}}=\sqrt{\frac{1/90}{1/40}}=\sqrt{0.444}= 0.667

If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).

You might be interested in
The number of bacteria, B, in a refrigerated food is given by the function b(t) = 15t2 - 60t + 125, where t is the temperature o
Nimfa-mama [501]

Answer: b(t(h))=135h^2+180h+125


Step-by-step explanation:

Given: The number of bacteria, B, in a refrigerated food is given by the function  b(t)=15t^2-60t+125 , where t is the temperature of food in degrees Fahrenheit.

The function t(h)=3h+4 gives the temperature, t, of the food h hours after being removed from the refrigerator.

Now, the number bacteria in the food in h hours is given by:-

b(t(h))=15(3h+4)^2-60(3h+4)+125\\=15(9h^2+16+24h)-180h-240+125\\=135h^2+240+360h-180h-240+125\\=135h^2+180h+125

So, The number bacteria in the food in h hours is given by:

b(t(h))=135h^2+180h+125


4 0
3 years ago
Convert 2,060 milliters to liters
Anettt [7]

2.06 liters is your answer.

3 0
3 years ago
Read 2 more answers
Please help
dem82 [27]

Answer:

Step-by-step explanation:

1) we have to solve the associated equation

-16x^2 + 24x + 16 = 0

-2x^2 + 3x + 2 = 0

2x^2 -3x -2 = 0

Δ = 9 + 16 = 25

x1 = (3 + 5)/4= 2

x2 = (3 - 5)/4 =-1/2

the x intercepts are -1/2 and 2

2) a maximum because the parabola opens downwards (the first term is negative)

V(x) = -b/2a = -24/-32 = 3/4

V(y) = -16(9/16) + 24(3/4) + 16 = -9+18 + 16 = 25

V(3/4,25)

3) for draw a parabola is are necessary the coordinates of the vertex and of two points: one that lies to left of the vertex, and one that lies on the right to the vertex.

So we already have the necessary informations to draw it.

4 0
3 years ago
A science class has 5 girls and 7 boys in the seventh grade and 5 girls and 5 boys in the eighth grade. The teacher randomly sel
Taya2010 [7]

We have a total of 10 boys & 8 Girls, then the sample space consist of 18 elements.

P(selecting 1 boy) = (total number of boys/by 18) = P(boy)=10/18=5/9

5 0
3 years ago
Read 2 more answers
Extra Credit: A company sells two different safes. The safes have different dimensions, but the same volume. What is the height
Leviafan [203]

Answer:

4 ft

Step-by-step explanation:

I am estimating for the points lol

6 0
3 years ago
Read 2 more answers
Other questions:
  • Using the x intercept method what are all the real solutions of the equation x^3-8x^2+9x+18=0
    7·1 answer
  • What is the value of the x variable in the solution to the following system of equations?
    13·2 answers
  • On your family trip, you used 14 gallons of gas.
    10·1 answer
  • 3x + 2y = 5 5x + 2y = 7 Based on the given system of equations, which of the following is not true? 2x = 2 8x = 12 4y = 4
    5·1 answer
  • Someone help me please?
    6·1 answer
  • What is the area of this figure?
    14·1 answer
  • Square root of -6 times square root of -12 times square root of -5
    11·1 answer
  • PLEASE HELP 30 points!!!!!<br> Find the length of each segment<br> CD and AD
    9·1 answer
  • Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape
    11·1 answer
  • Pls help, will give brainlist if u give me the answer!!
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!