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
RUDIKE [14]
3 years ago
11

The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

evealed an average age of 28 years with a standard deviation of 10 years. Determine a 95% confidence interval for the average all of all his customers. Specifically provide the lower limit and upper limit of the confidence interval to one decimal.
Mathematics
1 answer:
jolli1 [7]3 years ago
7 0

Answer:

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)  

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=28 represent the sample mean

\mu population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size  

Solution to the problem

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=25-1=24

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that t_{\alpha/2}=2.064

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

28-2.064\frac{10}{\sqrt{25}}=23.872    

28+2.064\frac{10}{\sqrt{25}}=32.128    

So on this case the 95% confidence interval would be given by (23.9;32.1)    

You might be interested in
HELLPPP <br> I need help asappp
sattari [20]

Answer:

(8,5)

Step-by-step explanation:

x=8

5*8-2y=30

40-2y=30 .      subtract 40 from both sides

-2y=-10 .           divide both sides by-2

y=5

3 0
2 years ago
What is the correct answer for the problem 3.12 x 4.0
ch4aika [34]

Hi Brielle the correct answer to your question is 3.12 x 4.0 = 12.48

7 0
2 years ago
Read 2 more answers
Picture of math assignment
n200080 [17]

Answer:

{5}^{ - 7}

Step-by-step explanation:

You have to use the property of quotient of powers, you subtract the power of the fraction denominator from the numerator

6 0
2 years ago
Read 2 more answers
I can't seem to find the answer for this I'm pretty sure it's non linear
Nata [24]

Answer:

  (d) No. Slope is not constant.

Step-by-step explanation:

You want to know if the given graph shows a linear function.

<h3>Linear function</h3>

The graph of a linear function is a straight line. The points on the graph shown do not form a straight line, so the function is nonlinear.

<h3>Rate of change</h3>

The rate of change of a function is the ratio of "rise" to "run" between two points in the graph. This ratio is also called the "slope." For a straight line, the rate of change (slope) is constant. That is, a linear function has a constant rate of change.

If the function is nonlinear, its rate of change is not constant. The converse is also true: if the slope is not constant, the function is nonlinear.

6 0
1 year ago
Circle D circumscribes ABC and ABE. Which statements about the triangles are true? Statement I: The perpendicular bisectors of A
mestny [16]

Answer:

The correct option is;

B. I and II

Step-by-step explanation:

Statement I: The perpendicular bisectors of ABC intersect at the same point as those of ABE

The above statement is correct because given that ΔABC and ΔABE are inscribed in the circle with center D, their sides are equivalent or similar to tangent lines shifted closer to the circle center such that the perpendicular bisectors of the sides of ΔABC and ΔABE are on the same path as a line joining tangents to the center pf the circle

Which the indicates that the perpendicular the bisectors of the sides of ΔABC and ΔABE will pass through the same point which is the circle center D

Statement II: The distance from C to D is the same as the distance from D to E

The above statement is correct because, D is the center of the circumscribing circle and D and E are points on the circumference such that distance C to D and D to E are both equal to the radial length

Therefore;

The distance from C to D = The distance from D to E = The length of the radius of the circle with center D

Statement III: Bisects CDE

The above statement may be requiring more information

Statement IV The angle bisectors of ABC intersect at the same point as those of ABE

The above statement is incorrect because, the point of intersection of the angle bisectors of ΔABC and ΔABE are the respective in-centers found within the perimeter of ΔABC and ΔABE respectively and are therefore different points.

6 0
2 years ago
Read 2 more answers
Other questions:
  • What is 4 tens and 6 tenths as a decimal
    15·2 answers
  • Find a common denominator for 1/3 and 1/12 by dividing each whole into the same ​
    15·1 answer
  • A customer buys 17.01 in gas and requests one five dollar [$5] lottery ticket, two one dollar [$1] lottery tickets, and one [$3]
    10·1 answer
  • Polygon ABCD is rotated 90° counterclockwise about the origin to create polygon A'B'C'D'. natch each set of coordinates to the v
    15·1 answer
  • Jake gives his dog 4 chew bones and 1 dog toy each month. How many chew bones and toys with Jake give his dog in 5 months?
    6·1 answer
  • Suki rode her bike 6/7 mile. Claire rode her bike 1/3 mile. They want to compare how far they each rode their bikes using benchm
    15·1 answer
  • Always true, sometimes true, never true.
    8·1 answer
  • Can u help with 11 pls. Thank u so much. P.S. sorry it's a little blurry.
    9·1 answer
  • Graph f(x) = -|x-3| - 6
    15·1 answer
  • Solve for p:
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!