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
Lena [83]
3 years ago
10

The mean income per person in the United States is $44,500, and the distribution of incomes follows a normal distribution. A ran

dom sample of 16 residents of Wilmington, Delaware, had a mean of $52,500 with a standard deviation of $9,500. At the .05 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
(a) State the null hypothesis and the alternate hypothesis.



H0: µ =

H1: µ >


--------------------------------------------------------------------------------



(b) State the decision rule for .05 significance level. (Round your answer to 3 decimal places.)


Reject H0 if t >


(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)


Value of the test statistic
Mathematics
1 answer:
Artist 52 [7]3 years ago
5 0

Answer:

We conclude that the residents of Wilmington, Delaware, have higher income than the national average

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $44,500

Sample mean, \bar{x} = $52,500

Sample size, n = 16

Alpha, α = 0.05

Sample standard deviation, s =  $9,500

a) First, we design the null and the alternate hypothesis

H_{0}: \mu = 44,500\text{ dollars}\\H_A: \mu > 44,500\text{ dollars}

We use one-tailed(right) t test to perform this hypothesis.

c) Formula:

t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }

Putting all the values, we have

t_{stat} = \displaystyle\frac{52500 - 44500}{\frac{9500}{\sqrt{16}} } = 3.37

b) Rejection rule

If the calculated t-statistic is greater than the t-critical value, we fail to accept the null hypothesis and reject it.

Now,

t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753

Since,                    

t_{stat} > t_{critical}

We fail to accept the null hypothesis and reject it. We accept the alternate hypothesis. We conclude that the residents of Wilmington, Delaware, have higher income  than the national average

You might be interested in
Discounts and what is the outcome
Pachacha [2.7K]

Answer:

with discount+tax= $23.15

Step-by-step explanation:

board game is 25

discount: 15%

tax: 7.5%

discount means you take off that amount

tax means you add that amount

discount: 15% off

tax: +7.5%

to find 15% of 25 multiply 25 by 15% (15/100=0.15)

25*0.15

= 3.75

then subtract that from 25

25-3.75

=21.25

tax:

0.075*25

=1.875

~1.9

21.25+1.9

=23.15

5 0
3 years ago
Prove that the triangle EDF is isosceles. Give reasons for your answer.
Gekata [30.6K]

Answer:

\triangle EDF is isosceles.

Step-by-step explanation:

Please have a look at the attached figure.

We are <u>given</u> the following things:

\angle EDF = y

\text{External }\angle DFG = 90 +\dfrac{y}{2}

Let us try to find out \angle E and \angle DFE. After that we will compare them.

<u>Finding </u>\angle DFE<u>:</u>

Side EG is a straight line so \angle GFE = 180

\angle GFE is sum of internal \angle DFE and external \angle DFG

\angle GFE = 180 = \angle DFE  + \angle DFG\\\Rightarrow 180 = \angle DFE + (90+\dfrac{y}{2})\\\Rightarrow \angle DFE = 180 - 90 - \dfrac{y}{2}\\\Rightarrow \angle DFE = 90 - \dfrac{y}{2} ....... (1)

<u>Finding </u>\angle E<u>:</u>

<u>Property of external angle:</u> External angle in a triangle is equal to the sum of two opposite internal angles of a triangle.

i.e. external \angle DFG = \angle E + \angle EDF

\Rightarrow 90+\dfrac{y}{2} = \angle E + y\\\Rightarrow \angle E = 90+\dfrac{y}{2}  -y\\\Rightarrow \angle E = 90-\dfrac{y}{2} ....... (2)

Comparing equations (1) and (2):

It can be clearly seen that:

\angle DFE = \angle E =90-\dfrac{y}{2}

The two angles of \triangle EDF are equal hence \triangle EDF is isosceles.

8 0
3 years ago
What is the answer to this math question?
Andrews [41]

Answer:

2x+a=5bx

Step 1: Add -2x to both sides.

a+2x+−2x=5bx+−2x

a=5bx−2x

Answer:

a=5bx−2x

Step-by-step explanation:

8 0
3 years ago
Find the values of x and y in the given figure below.<br> 30°<br> 45<br> х<br> y<br> 35
Alex17521 [72]

ill do ur hw for cashapp

insta

kk_iwi

txt and ill give u the deatails

8 0
3 years ago
Read 2 more answers
In this picture, m∠PQR = 161° and m∠SQR = 38°. If m∠PQS = (2x + 15)°, what is the value of x?
elena55 [62]

Answer:

B

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Other questions:
  • 4 is 80% of what number?
    11·1 answer
  • Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
    9·2 answers
  • What would be the least common denominator for the sum of 3/5+4/10
    14·1 answer
  • Divide a six-sided polygon into triangles to find the sum of its interior angles.
    14·2 answers
  • Help me please !!!!!!!!!
    13·1 answer
  • NEED HELP ASAP WILL GIVE BRAINLIEST
    13·2 answers
  • A circular mirror is surrounded by a square metal frame. The radius mirror is 6x the side length of the medal frame is 18x. What
    8·2 answers
  • WILL GIVE BRAINLEST
    10·1 answer
  • Identify the method that will be used to solve for x for each equation.
    11·2 answers
  • PLEASE HELP ILL GIVE BRAINLIEST!!!! I AM STUMPED AS I HAVE NOT PAYED ANY ATTENTION IN CLASS PLEASE HELP ME!!!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!