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
Step2247 [10]
3 years ago
12

If Upper X overbar equals 62​, Upper S equals 8​, and n equals 36​, and assuming that the population is normally​ distributed, c

onstruct a 99 % confidence interval estimate of the population​ mean, mu.
Mathematics
1 answer:
marishachu [46]3 years ago
3 0

Answer:

The 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

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=62 represent the sample mean

\mu population mean (variable of interest)

s=8 represent the sample standard deviation

n=36 represent the sample size  

Part a: Confidence interval

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=36-1=35

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,35)".And we see that t_{\alpha/2}=2.72

Now we have everything in order to replace into formula (1):

62-2.72\frac{8}{\sqrt{36}}=58.373    

62+2.72\frac{8}{\sqrt{36}}=65.627    

So on this case the 99% confidence interval would be given by (58.373;65.627)    

We are 99% confident that the true mean for the variable of interest is between 58.373 and 65.627.

You might be interested in
In a candy mix there are 4 green bars for every 3 red bars. How many red bars are there if there are 200 green bars?
UkoKoshka [18]

150 red bars

4/3=200/150

3 0
3 years ago
Read 2 more answers
The term –18xy and which other term are like terms?
alexgriva [62]
So,

We know that we cannot add or subtract quantities of the same kind.

-18xy can only be added/subtracted to 4yx, which is the same as 4xy.  The result would be -14xy, or -14yx.

The correct option is B.
6 0
3 years ago
The value of N is both 5 times as much as the value of M and 36 more than the value of M. What are the values of N and M? Explai
vlabodo [156]
180 just multiply 36*5= 180

Thank you, i would be happy to have more questions
 
7 0
2 years ago
Help Please!!!!!!!!!!!<br><br> Questions 9 and 10
Sphinxa [80]

Answer:

Step-by-step explanation:

9

1. ∠ACB ≅∠ECD ; vertical angles are congruent (A)

2. C is midpoint of AE ; given

3. AC ≅CE; midpoint divides the line segment in 2 congruent segments (S)

4.AB║DE; given

5. ∠A≅∠E; alternate interior angles are congruent (A)

6. ΔABC≅ΔEDC; Angle-Side-Angle congruency theorem

10

1. YX≅ZX; given (S)

2. WX bisects ∠YXZ; given

3. ∠YXW≅∠ZXW; definition of angle bisectors (A)

4. WX ≅WX; reflexive propriety(S)

5. ΔWYX≅ΔWZX; Side-Angle-Side theorem

3 0
2 years ago
Bill and Eugene left the airport at the same time. They traveled in opposite directions. Eugene traveled 21.1 km/h faster than B
gizmo_the_mogwai [7]

Answer:

56.3 kilometers per hour

Step-by-step explanation:

We know D = RT

where

D is distance

R is rate (speed)

T is time

Let's Bill's rate be "x". Thus using equation we can write:

D = xt

We know Eugene travelled 21.1 faster than Bill, so Eugene's rate is 21.1 + x. So we can write:

D = (21.1 + x)t

D = 21.1t + xt

Now, putting t = 1 in both since after 1 hour given, we have:

D = x(1)

D = x

and

D = 21.1(1) + x(1)

D = 21.1 + x

We know the sum of both the distance is 133.7, so we can write:

x + 21.1 + x = 133.7

Solving for x:

2x = 133.7 - 21.1

2x = 112.6

x = 112.6 / 2

x = 56.3 km/hr

This is Bill's rate: 56.3 kilometers per hour

8 0
2 years ago
Other questions:
  • On the coordinate plane below, what is the length of AB?
    11·1 answer
  • Rounded 121580 to the nearest thousand
    6·1 answer
  • A painter painted 7/8 of a house. What percentage is equivalent to the fraction of the house painted?​
    10·2 answers
  • To celebrate ratios, Mrs. Johnson’s class will make pizzas. Julio is in charge of bringing in the sauce. There are 30 students i
    12·2 answers
  • What is 0x+5=2x+4? Since quarantined can't ask teacher for help with this problem.
    12·1 answer
  • Janet's has X dollars Henny has $8 less than Janet which expression shows how to find how many dollars Hanley has
    14·1 answer
  • Find the 11th term of the arithmetic sequence -2x,-8,-9x,-11,-16x,-14
    15·1 answer
  • Which point represents the opposite of -2?
    5·2 answers
  • Area of a composite figure​
    6·1 answer
  • The table shows a relation between x and y.<br><br> is the relation a function, and why?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!