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
Agata [3.3K]
3 years ago
6

3. The average age of online consumers a few years ago was 23.3 years with a standard deviation of 5.3 years. It is believed the

average has changed since older individuals gained more confidence with internet use. Recently a random sample of 20 online shoppers were selected. The sample had an average age of 26.2. Determine whether or not the average age of online consumers has changed over the last few years, use α =0.01. What is the p-value of the result?
Mathematics
1 answer:
Slav-nsk [51]3 years ago
8 0

Answer:

We cant say, with α =0.01, that the average age changed. The p-value is 0.014

Step-by-step explanation:

As a consecuence of the Central Limit Theorem, the mean sample has a distribution approximately normal, with unknown mean and standard deviation \sigma = 5.3/\sqrt{20} = 1.1851 (the standard deviation of one single sample divided by the  sqaure root of the sample lenght).

The null hypothesis H₀ is that the average age is still 23.3 (the mean is 23.3). The alternative hypothesis is that the mean is different. We want to see if we can refute H₀ with significance level α =0.01.

Lets call X the mean of a random sample of 20 online shoppers. As we discuse above, X is approximately normal with unknown mean and standard deviation equal to 1.1851 . If we take the hypothesis H₀ as True, then the mean will be 23.3, and if we standarize X, we have that the distribution

W = \frac{X - 23.3}{1.1851}

Will have a distribution approximately normal, with mean 0 and standard deviation 1.

The values of the cummulative ditribution of the normal function can be found in the attached file. Since we want a significance level of 0.01, then we need a value Z such that

P(-Z < W < Z) = 0.99

For the symmetry of the standard Normal distribution, we have that Φ(Z) = 1-Φ(-Z), where Φ is the cummulative distribution function of the standard Normal random variable. Therefore, we want Z such that

Φ(Z) = 0.995

If we look at the table, we will found that Z = 2.57, thus,

0.99 = P(-2.57 < W < 2.57) = P(-2.57 < \frac{X-23.3}{1.1851} < 2.57)\\ = P(-2.57*1.1851 + 23.3 < X < 2.57*1.1851 + 23.3) = P(20.254 < X < 26.345)

Thus, we will refute the hypothesis if the observed value of X lies outside the interval [20.254, 26.345].

Since the observed value is 26.2, then we dont refute H₀, So we dont accept that the number average age of online consumers has changed.

For us to refute the hypothesis we need Z such that, for the observed value, |W| > Z. Replacing X by 26.2, we have that [tex] W = \frac{26.2-23.3}{1.1851} = 2.4470. We can observe that Φ(2.447) = 0.993, substracting that amount from 1 and multiplying by 2 (because it can take low values too), we obtain that the p-value is 0.014.  

Download pdf
You might be interested in
Whar does7^or other numbers like it mean?
likoan [24]
7^0=1

7^1=7

7^2=7*7=49

7^3=7*7*7=343

etc... etc...
4 0
2 years ago
Read 2 more answers
HELP DO NOT UNDERSTAND THIS QUESTION AT ALL THE BEST ONE WILL BE MARKED AS BRAINLIEST
Murrr4er [49]

Step-by-step answer:

A line with slope (or gradient) m, passing through a point (x0,y0) can be represented by the equation:

(y-y0) = m(x-x0)  ......................(1)

Here,

(x0,y0) = (1,7), and

slope/gradient = -2

Substitute values into (1) above gives

(y-7)=2(x-1)

Expand and simplify

y-7 = 2x-2

y =2x -2 + 7

y=2x+5

is the final answer.

5 0
3 years ago
4.2×9.35 please show the work
valentina_108 [34]
Here ya go. I hope this helps! :) (It was much easier to do this than to try and type it out, in my opinion)

5 0
3 years ago
Read 2 more answers
Consider the angle. Which TWO statements are true?
svetoff [14.1K]

Answer:

C, E

Step-by-step explanation:

A. INCORRECT

A is wrong because a reflection across the x-axis DOES move the position of the figure (as it is flipped, so the position changes), but it DOES NOT change the angle (since a shift in position doesn't equal to a change in angle measure)

B. INCORRECT

Although a reflection across the x-axis does change the position of the angle, it DOES NOT change the measure of the angle.

C. CORRECT

A reflection across the x-axis does in fact move the position of the figure and does not change the angle measure. Reflections only deal with flipping a figure, not changing it's shape/distorting it so that the angle will change.

D. INCORRECT

A translation right will change the position of the figure but will not change the measure of the angle.

E. CORRECT

Yes, a translation right WILL change the position of the figure but will NOT change the measure of the angle. This is because a translation is simply moving a figure up and down; it has nothing to do with changing the shape of the figure/distorting it so that the angle is different.

8 0
3 years ago
The cleaning service requires $39 in variable costs for cleaning materials. The fixed costs of labor, the company's truck, and a
user100 [1]

The average cost per cleaning service call charge by the company is $184.5.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the total cost for x number of service calls in a year. Hence:

y = 39x + 349200

For 200 service call, in a year, x = 200 * 12 = 2400

y = 39(2400) + 349200 = $442800

Average cost = $442800 / 2400 = 184.5

The average cost per cleaning service call charge by the company is $184.5.

Find out more on equation at: brainly.com/question/2972832

#SPJ1

8 0
2 years ago
Other questions:
  • A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. to test this claim, a random sampl
    13·2 answers
  • A division of a company produces income tax apps for smartphones. Each income tax app sells for $9. The monthly fixed costs incu
    13·1 answer
  • Can I please have help on 9-11?
    15·1 answer
  • A boat travels 8 km upstream and 8 km back. The time for the round trip is 2 hrs. The speed of the stream is 4 ​km/hr. What is t
    6·1 answer
  • How is a variable defined
    6·2 answers
  • In the process of making a financial forecast, Farid has been looking closely at his
    14·2 answers
  • Solve for x using the<br> distributive property.<br> 3(x + 4) = 6
    5·1 answer
  • Please helpppp i will brainlisy anyone who helps
    10·1 answer
  • Reese claims that if 60% of the registered voters cast 273,600 votes, there would be fewer registered voters than above. Is he c
    5·1 answer
  • Given the figure below find the values of x and z
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!