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
Studentka2010 [4]
3 years ago
14

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour

of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.
Mathematics
1 answer:
Lesechka [4]3 years ago
4 0

Answer:

54-1.64\frac{21}{\sqrt{16}}=45.39    

54 +1.64\frac{21}{\sqrt{16}}=62.61    

So on this case the 90% confidence interval would be given by (45.39;62.61)    

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=54 represent the sample mean  

\mu population mean (variable of interest)

\sigma=21 represent the sample standard deviation

n=16 represent the sample size  

Solution to the problem

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=1-0.9=0.1 and \alpha/2 =0.05, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.05,0,1)".And we see that z_{\alpha/2}=1.64

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

54-1.64\frac{21}{\sqrt{16}}=45.39    

54 +1.64\frac{21}{\sqrt{16}}=62.61    

So on this case the 90% confidence interval would be given by (45.39;62.61)    

You might be interested in
Help anyone. I want to be good at math
dybincka [34]
Practice, practice, practice.  And ask questions.
5 0
3 years ago
Read 2 more answers
bill furrier marks up mink coats $3000. This represents 50% markup on cost. what is the cost of the coats?
MrRissso [65]
40 dollars each I believe.
3 0
3 years ago
Find the total surface area for the following. <br>height-3m, length-300 cm and width- 2 cm.​
Delvig [45]

Answer:

Step-by-step explanation:

So the Dimensions are:

Height: 300cm

Length: 300cm

Width: 2cm

SA = 2(H*L)+2(H*W)+2(L*W)

= 180000 + 1200 + 1200

= 182400 cm^{2} OR 18.24m^{2}

6 0
3 years ago
Read 2 more answers
A. y=82x + 998<br> b. y=247.7x - 335<br> c. y=743x - 1647<br> d. y=998x + 82
MrMuchimi
A is the answer for the question
3 0
3 years ago
Read 2 more answers
A rectangular cracker has a length of 5 centimeters and an area f 20 square centimeters. Find its perimeter.
iren [92.7K]

Answer:

18cm

Step-by-step explanation:

We have the length of the rectangle but we need to find the width which we'll call w. Area is a, l is length.

a = l * w

20 = 5 * w

divide both sides by 5 to cancel the multiplication by 5 on the right side

4 = w

The rectangle is going to have two sides that are the length of l, and two sides that are the the length of w. We're looking for the perimiter p.

p = 2l + 2w

p = (2 * 5) + (2 * 4)

p = 18

4 0
2 years ago
Other questions:
  • In a quadrilateral MNOP the length of side MN is (4x − 7) units and the length of side ON is (7 − 3x) units. What value of x wil
    8·1 answer
  • particles of mass 2m and m are fixed at the extreme of a light string of lenght l.find the centre of mass and the moment of iner
    8·1 answer
  • Suppose the diameter of a circle is 4, What is its circumference?
    7·1 answer
  • Four times the sum of x and 6 is equal to 32.<br> what is the algebraic expression?
    6·1 answer
  • Drag and drop a statement or reason to each box to complete the proof.
    9·2 answers
  • I need help finding a polynomial in factored form for the shaded area
    7·2 answers
  • a six sided die is rolled once what is the probability of rolling the die and landing on number 5 first and then rolling it agai
    5·1 answer
  • If a van traveled 200 miles in 5 hours how far would it travel in 8 hours
    7·2 answers
  • How do i Write (3x^3)^2 without exponents
    8·1 answer
  • When liquid silver nitrate and liquid sodium chloride are combined, solid silver chloride forms along with a new liquid, sodium
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!