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
77julia77 [94]
2 years ago
11

A university planner wants to determine the proportion of spring semester students who will attend summer school. Suppose the un

iversity would like a 0.90 probability that the sample proportion is within 0.112 or less of the population proportion.
a) What is the smallest sample size to meet the required precision? (There is no estimation for the sample proportion.) (Enter an integer number.)
Mathematics
1 answer:
ss7ja [257]2 years ago
3 0

Answer:

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

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".  

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by \alpha=1-0.90=0.1 and \alpha/2 =0.005. And the critical value would be given by:

z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.112 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

Since we don't have prior estimation for the population proportion we can use the value \hat p =0.5. And replacing into equation (b) the values from part a we got:

n=\frac{0.5(1-0.5)}{(\frac{0.112}{1.64})^2}=53.60  

And rounded up we have that n=54

You might be interested in
Need help ASAP. Question in photo. Will mark brainliest if correct
ioda

Answer:

C

Step-by-step explanation:

I did this question today, pls lmk if u get it right

5 0
2 years ago
Write the equation of the line that passes through (-6,0) and is parallel to the line y=5x-43
AVprozaik [17]

The equation of the line that passes through (-6,0) and is parallel to the line y = 5x - 43 in slope intercept is y = 5x + 30

<em><u>Solution:</u></em>

Given that line that passes through (-6, 0) and is parallel to the line y = 5x - 43

We have to find the equation of line

Let us first find slope of line having equation y = 5x - 43

<em><u>The slope intercept form of line is given as:</u></em>

y = mx + c  ------- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

On comparing equation of line y = 5x - 43 with slope intercept form y = mx + c,

we get m = 5

Thus slope of given line is 5

We know that slopes of parallel lines are equal

Thus the slope of line parallel to given line is also 5

Now let us find equation of line having slope "5" and passes through (-6, 0)

Substitute m = 5 and (x, y) = (-6, 0) in eqn 1

y = mx + c

0 = 5(-6) + c

<h3>c = 30</h3>

<em><u>Thus the required equation is:</u></em>

Substitute c = 30 and m = 5 in eqn 1

y = 5x + 30

Thus the required equation of line is found

8 0
2 years ago
In what temperature range can mercury be found as a liquid
Varvara68 [4.7K]
Some metals melt at lower temps than others. Tin becomes liquid at 231.8˚C (447.8˚F); at the other end of the spectrum, tungsten has the highest melting point of any metal: 3,422˚C (6,192˚F). Somewhere in the middle is mercury, which stays in a liquid state until its temperature drops to -40.
4 0
2 years ago
Is the perpendicular bisector of . What is the length of ?
mixas84 [53]

Answer:

the answer is C. 12

Step-by-step explanation:

5 0
3 years ago
2) 4 tot he power of 3 = _______
Ghella [55]

Answer:

64

Step-by-step explanation:

4^3=64

4*4=16

16*4=64

8 0
3 years ago
Other questions:
  • A solid has faces that consist of two squares and four congruent rectangles. What type of solid is it?
    5·2 answers
  • Write an expression that says "Nine plus a number times 14"
    15·2 answers
  • The difference of two numbers is 3. their sum is 14. find the two numbers. (show work please)
    5·1 answer
  • ASAP
    15·1 answer
  • 2. Suppose the temperature that most foods can stay bacteria free in restaurants varies approximately according to a normal dist
    11·1 answer
  • The owner of a flower shop on H street sells 28 roses for $140. What is the cost in dollars per rose?
    14·2 answers
  • Lillian is going to invest in an account paying an interest rate of 5.7% compounded continuously. How much would Lillian need to
    7·1 answer
  • NEED ANSWER QUICK PLSSSS​
    13·1 answer
  • I am doing home<br> work and need help due day
    10·1 answer
  • #18. estimate the perimeter and the area of the shaded figure to the nearest tenth
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!