A regional office of the Internal Revenue Service randomly distributes returns to be audited to the pool of auditors. Over the thousands of returns audited last year, the average amount of extra taxes collected was $356 per audited return. One of the auditors, Jeffrey Jones, is suspected of being too lenient with persons whose returns are being audited. For a simple random sample of 30 of the returns audited by Mr. Jones last year, an average of $340 in extra taxes was collected.

Required:
Assuming a normal population of extra taxes collected with a standard deviation of $90, do the suspicions against Mr. Jones appear to be justified?

Answers

Answer 1

Answer:

The decision rule is

   Fail to reject the null hypothesis

The conclusion is  

     There is sufficient evidence to conclude that the justification against Mr. Jones appears not  to be justified

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu  =  \$ 356[/tex]

    The sample  size is n  =  30  

     The sample mean is [tex]\= x = \$340[/tex]

    The standard deviation is  [tex]\sigma =  \$ 90[/tex]

    The  null hypothesis is [tex]H_o  :  \mu =  \$ 35 6[/tex]

     The alternative hypothesis is   [tex]H_a  :  \mu \ne  \$ 35 6[/tex]

Let assume the significance level is [tex]\alpha = 0.05[/tex]

Generally the test statistic is mathematically represented as

     [tex]t = \frac{\= x - \mu }{\frac{\sigma }{\sqrt{n} } }[/tex]

=>  [tex]t = \frac{ 340 - 356 }{\frac{90 }{\sqrt{30} } }[/tex]

=>  [tex]t =-0.9737 [/tex]

Generally the sample size from the question is  small that it is not greater than 30  hence we use t-test

Now the degree of freedom is mathematically represented as

     [tex]df =  n- 1[/tex]

=>   [tex]df =  30- 1[/tex]

=>   [tex]df= 29[/tex]

Generally the p-value is mathematically represented as

      [tex]p-value =  2 P (t >  -0.9737 )[/tex]

Generally from the t-distribution table , the probability of -0.9737 at a degree of freedom of  [tex]df= 29[/tex] for a two -tailed  test  is

     [tex]P (t >  -0.9737 ) =  0.33825793[/tex]

Hence p-value  is  

     [tex]p-value =  2*0.33825793[/tex]

      [tex]p-value =  0.676 [/tex]

From the value we obtained we see that  [tex]p-value  >  \alpha[/tex] hence

The decision rule is

   Fail to reject the null hypothesis

The conclusion is  

     There is sufficient evidence to conclude that the justification against Mr. Jones appears not  to be justified


Related Questions

FOR EXAMPLE:

Christa and her family went out for pizza and it cost $28. In Tennessee we have a sales tax that is 7% which has to be paid along with $28. What is the sales tax on $28?

Answers

7% of 28$ is $1.96. Hope that helps

Find the slope of the line passing through the points (8,-4) and (-6,-3).

Anybody know this ?

Answers

Answer:

= -1/14

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -3 - -4)/( -6 -8)

   = ( -3+4)/( -6-8)

   1/-14

= -1/14

1 5/16 divided by 7/12

Answers

2.25 this is the correct answer

Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far are the divers from each other?

Answers

Answer:

66.25 ft

Step-by-step explanation:

25.5 + 40.75

66.25

They are 66.25 feet away from each other.

Please let me know if I'm wrong!

How much mixed spice will she need for 6 spice

Answers

Answer:

who

Step-by-step explanation:

Increased by 175%, the number of 24 becomes what?

Answers

Answer:

66

Step-by-step explanation:

increase the number by 175% of its value.

percentage increase = 175% × 24

new value =

24 + percentage increase =

24 + (175% × 24) =

24 + 175% × 24 =

(1 + 175%) × 24 =

(100% + 175%) × 24 =

275% × 24 =

275 ÷ 100 × 24 =

275 × 24 ÷ 100 =

6,600 ÷ 100 =

66

An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability that it will not be enough seats to accommodate all passengers. Assume that the probability that a randomly selected passenger shows up to the airport is 0.96. Find the probability using the normal distribution as an approximation to the binomial distribution.

Answers

Answer:

The probability is   [tex]P(X  >300 ) = 0.97219 [/tex]

Step-by-step explanation:

From the question we are told that

 The capacity of  an Airliner  is  k =  300 passengers

 The sample size n =  320 passengers

  The probability the a randomly selected passenger shows up on to the airport

    [tex]p = 0.96[/tex]

Generally the mean is mathematically represented as

    [tex]\mu  =  n*  p[/tex]

  => [tex]\mu  =  320 *  0.96[/tex]

    => [tex]\mu  = 307.2[/tex]

Generally the standard deviation is  

    [tex]\sigma =  \sqrt{n *  p *  (1 -p ) }[/tex]

=>  [tex]\sigma =  \sqrt{320  *  0.96 *  (1 -0.96 ) }[/tex]

=> [tex]\sigma =3.50 [/tex]

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

  [tex]P(X  > k ) =  P( \frac{ X -\mu }{\sigma }  >  \frac{k - \mu}{\sigma } )[/tex]

Here [tex]\frac{ X -\mu }{\sigma }  =Z (The \ standardized \  value \  of  \ X )[/tex]

=>[tex]P(X  >300 ) =  P(Z >  \frac{300 - 307.2}{3.50} )[/tex]

Now applying  continuity correction we have

    [tex]P(X  >300 ) =  P(Z >  \frac{[300+0.5] - 307.2}{3.50} )[/tex]    

=>    [tex]P(X  >300 ) =  P(Z >  \frac{[300.5] - 307.2}{3.50} )[/tex]

=>    [tex]P(X  >300 ) =  P(Z >  -1.914 )[/tex]

From the z-table  

    [tex]P(Z >  -1.914 ) =  0.97219[/tex]

So

    [tex]P(X  >300 ) = 0.97219 [/tex]

The slope of a line is 15 and the point (3, -1) lies
on the line. Write an equation of the line in
point-slope form.

Answers

Answer:

The answer is

[tex] \huge y + 1 = 15(x - 3) \\ [/tex]

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

m is the slope

( x1 , y1) is the point

From the question we have the final answer as

[tex]y + 1 = 15(x - 3)[/tex]

Hope this helps you

12% of 72 is what number

Answers

Answer:

8.64

Step-by-step explanation:

8.64

[tex]12\;percent\;of\;72=8.64[/tex]

write in standard form -4 + y +2x = 0

Answers

Answer:

the answer is 2x+y=4

Step-by-step explanation:

2x+y=4

Answer:

y = -2x + 4

Step-by-step explanation:

Ten less than a number is twice the same number​

Answers

Answer:Less ten a number; 20 - 10.10 ×2 = 20

Meaning lees 10 from 20 and multiply

Hi there!

First of all, let the unknown number be z.

Now, subtract 10:

z-10

This expression is equal to twice the same number:

z-10=2z

Solve this equation:

z-2z=10

-z=10

Divide both sides by -1 in order to get rid of the minus sign:

z=-10

Hope everything is clear.

Let me know if you have any questions!

#KeepLearning

:-)

pwease help!! i need help to put the answers in the box c:

Answers

Answer:

6 months is: 15675

2 months is: 5172.75

1 month is: 2586.37

15 months is: 38795.62

the missing number is: 12 months

Step-by-step explanation:

Lines E, F, and G are parallel lines cut by transversal H as shown below. What is the value of
a+b+c+d?

Answers

Answer:

okay now i get it its not easy at first but look at it for a bit and yoll get it

7(10x+5-9x)=70
I rly need help on this

Answers

Answer:

x = 5

Step-by-step explanation:

1. Combine like terms

2. Multiply by 1

3. Distribute

4. Subtract  3

5  from both sides of the equation

5. Simplify

6. Divide both sides of the equation by the same term

7. Simplify

Answer: x=5

Step by Step Explanation:
7(10x+5-9x)=70 distributive property
70x+35-63x=70 subtract common terms
7x+35=70 subtract both sides by 35
7x=35 divide both sides by 7
x=5

Find the surface area of a right cone with a diameter of 6 inches and a slant height of 5 inches.

Answers

Answer:

about 172.82

Step-by-step explanation:

Answer:

83.23

Step-by-step explanation:

to work out surface area of a  right cone u

A=πr(r+h2+r2)

hope this helps

im not sure if its right tho

Find the mean of these numbers:
2,57, 38, 42,6

Answers

Answer:no

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

add all of those numbers and divide it by the value of how many numbers there are in total.

In a group of 80 people, 50 can speak Nepali, 45 can speak English and 7 of them do not
speak both languages.
a) Find the number of people who speak both languages.
b) Also illustrate the above information in Venn diagram.​

Answers

Answer:

Universal set is 80

Number of people that speak Nepali is 50

Number of people that speak English is 45

Number of people that do not speak both is 7

a. Number of people that speak both languages is 22

b. As above

Step-by-step explanation:

a. Let make number of people that speak both languages x

To get x

(50-x) + (45-x) + x + 7 = 80

(50-x) + (45-x) + x = 80 - 7

(50-x) + (45-x) + x = 73

Open bracket

50-x+45-x+x= 73

50+45-2x+x = 73

95 - x = 73

-x = 73 - 95

-x = -22

x = 22

Therefore, number of people that speak both languages is 22

b. To get venn diagram

Number of people that speak Nepali is 50 - 22 = 28

Number of people that speak English is 45 - 22 = 23

Therefore, total = 28+23+22+7 = 80

Olga has $40 in her wallet. She has one more $5 bill than $10 bills, and two more $1 bills than $5 bills. If Olga has only three types of bills, how many bills of each denomination does she have?

Answers

Answer:

Number of $10 bills = 2

Number of $5 bills = 3

Number of $1 bills  = 5

Step-by-step explanation:

Given:

Total amount = $40

Number of $10 bills = x

Number of $5 bills = x + 1

Number of $1 bills = x + 1 + 2 = x + 3

Find:

Number of each bills

Computation:

10(x) + 5(x+1) + 1(x+3) = 40

10x + 5x + 5 + x + 3 = 40

16x = 32

x = 2

Number of $10 bills = x = 2

Number of $5 bills = x + 1 = 3

Number of $1 bills  = x + 3 = 5

Answer:

# of $10 bills = 2

# of $5 bills = 3

# of $1 bills  = 5

Step-by-step explanation:

t> -5
can someone show step by step how to solve this equation?

Answers

Answer: The equation cannot be simplified any further.

Explanation: The variable(t) is greater than any number than negative five.

Plz mark brainliest:)

Which expression is equivalent to |-5| + |-3|

Answers

Answer:

5+3

Step-by-step explanation:

5+3

Answer:

5+3=8

Step-by-step explanation:

What is the value of the expression -7+-4

Answers

-11 cuz 7+4 is 11 and since they both negative, 11 will be negative

Answer:

-11

Step-by-step explanation:

This is the answer because:

1) First, multiply the negative sign with the positive sign.

Negative x Positive = Negative

Equation: -7 - 4

2) Now, multiply the negative sign with the negative sign.

Negative x Negative =  Positive  

Equation: 7 + 4 = 11

3) Finally, add the greater number's sign (-7) in front of the number.

-11

Hope this helps! :D

Find atleast 5 numbers between 1/2 and 1/3.

Answers

Answer:

12.2 12.3 12.4 12.5

Step-by-step explanation:

Express the number 7,980 in scientific notation.

Answers

Answer:

7.98x10^3

Step-by-step explanation:

10^3=1000

Answer:7.980 × 10^3

Step-by-step explanation:

Never Going To Give You Up never going to let you down never gonna run around baby nor desert you Rick roll.. ​

Answers

yeeeeeeeeeer eeee ee e e we. we e e we e e eeeee e e e e e e e e e e e

Answer:

we're no strangers to love

Step-by-step explanation:

you know the rules, and so do I

What do you know about the slope of two parallel lines? *
They have the opposite sign of each other
They are reciprocals of each other
They have the same slope
They have negative reciprocal slopes

Answers

Answer:

same slope

Step-by-step explanation:

if it has the same slope then the you will know the two lines are parallel

hope this helps

brainliest?

to be proportional, there must be a constant of proportionality

true or false

Answers

Answer:

True

Step-by-step explanation:

There must be a constant of proportionality.

Hope this helps!

If you have metamorphic rock and melt it, what does it become?

A. Magma
B. Minerals
C. Sedimentary Rock
D. Soil

Answers

Answer:  Magma

Step-by-step explanation:

When metamorphic rock melts it turns into magma.

The standard height from the floor to the bull’s-eye at which a standard dartboard is hung at 5 feet 8 inches. A standard dartboard is 18 inches in diameter. Suppose a standard dartboard is hung at standard height so that the bull’s-eye is 10 feet from the wall to its left. Sasha throws a dart at the dartboard that land at point 10.25 Feet from the left wall and 5 feet above the floor. Does Sasha’s dart land on the dartboard? Drag the choices into the boxes to correctly complete the statements.

Answers

Answer:

Hello! I'm sorry I couldn't get to your question sooner. I just completed this quiz!

The equation of the circle that represents the dartboard is (x-10)^2 + (y-17/3)^2 = 9/16, where the origin is the lower-left corner of the room and the unit of the radius is feet.  

The position of Sasha's dart is represented by the coordinates (10.25,5). Sash's dart does land on the dartboard.

This quiz was completed on k12, lesson 3.03.

The question is an illustration of equation of circles.

The equation of the dartboard circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]Sasha's dart lands on the dartboard because

From the question, we understand that:

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex] ---- the height at which the dartboard was hung

[tex]\mathbf{d = 18\i n }[/tex] ---- the diameter of the dartboard

[tex]\mathbf{B = 10ft}[/tex]  --- the bull's eye

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] --- Sasha's dart

Equation of the circle

First, we convert all units to feet

This is done by dividing inches units by 12

[tex]\mathbf{h = 5\ ft\ 8\ in }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{8}{12}\ ft }[/tex]

[tex]\mathbf{h = 5\ ft\ + \frac{2}{3}\ ft }[/tex]

Take LCM

[tex]\mathbf{h = \frac{15 + 2}{3}\ ft }[/tex]

[tex]\mathbf{h = \frac{17}{3}\ ft }[/tex]

[tex]\mathbf{d = 18\i n }[/tex]

[tex]\mathbf{d = \frac{18}{12}ft}[/tex]

[tex]\mathbf{d = \frac{3}{2}ft}[/tex]

Divide by 2 to calculate radius

[tex]\mathbf{r = \frac{3}{2*2}ft}[/tex]

[tex]\mathbf{r = \frac{3}{4}ft}[/tex]

The equation of the circle is represented as:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]

In this case:

[tex]\mathbf{a = B = 10ft}[/tex] -- the distance between the bull's eye and the wall

[tex]\mathbf{b = h = \frac{17}{3}\ ft }[/tex] ---- the height at which the dartboard was hung

So, we have:

[tex]\mathbf{(x - a)^2 + (y - b)^2 = r^2}[/tex]

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = (\frac 34)^2}[/tex]

Evaluate the exponents

[tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Hence, the equation of the circle is: [tex]\mathbf{(x - 10)^2 + (y - \frac{17}3)^2 = \frac 9{16}}[/tex]

Does Sasha’s dart land on the dartboard?

Yes her dart lands on the dartboard because

[tex]\mathbf{D = (10.25ft, 5ft)}[/tex] is within the circumference of the dartboard

Read more about equation of circles at:

https://brainly.com/question/23988015

Determine the midpoint of the segment with endpoints of (-3, 8) and (-3,
-2).

Answers

Answer:

(-3,3)

Step-by-step explanation:

Please help guys this has to be do in 10:00 please help

Answers

she drank 14 ounces of her water, she has 28 ounces left, just divide 42 by 3

Answer:

1)14oz

2)28oz

Step-by-step explanation:

1) To find the amount of water is left in the bottle you want to substract 1/3 so the first thing you want to do is find what 1/3 of 42 is. So do this: (This is also 42/3)

42*1/3=14

So we now know that 14 is 1/3 of 45 which is the first answer. To find the second answer you want to substract 14 from 42 which is 28.

So that means she has 28 oz of water left when she gets there.

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