A scientist is interested in whether there is a linear relationship between the amount of mercury in a lake and the surface area of the lake. The scientist collected data on 22 lakes of a similar type selected at random and used the data to test the claim that there is a linear relationship. The following hypotheses were used to test the claim.

H0:β=0

Ha:β≠0

The test yielded a t-value of 2.086 with a corresponding p-value of 0.05. Which of the following is the correct interpretation of the p-value?

a. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05
b. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05.
c. If there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 or greater is 0.05.
d. If there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05.
e. If there is not a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic as extreme as 2.086 or more extreme is 0.05.

Answers

Answer 1

Answer:

b. If there is a linear relationship between the amount of mercury in a lake and the surface area of the lake, the probability of observing a test statistic of 2.086 is 0.05.

( the null is rejected and alternate is accepted)

Step-by-step explanation:

Here the critical value is t≥ t∝/2(n-2) = ± 2.086

The significance level is ∝= 0.05 and  the p- value is also 0.05

Which indicates that there is no correlation between the dependent and the independent variable.

If the p - value is less than 0.05 the null hypothesis is rejected.

There is a 5% chance that the  hypothesis is true.

So the null hypothesis should be rejected.

Given these options

a) if------as 2.086 or more extreme is 0.05

2.086 or 0.05 is the same in this case one cannot be more extreme.

c)  of 2.086 or greater is 0.05.

b). If there is a linear relationship ------.

This is the alternate hypothesis.

0.05 is not greater than 2.086 in the given question

d)  If there is not a linear relationship between the amount of mercury in-----.

This is the claim which is formulated as null  hypothesis.

e) if----  2.086 or more extreme is 0.05.

0.05 is the same as 2.086

At p- value 0.05 we reject the null hypothesis and accept the alternate hypothesis


Related Questions

In which number is the value of the 5 ten times the value of the 5 in 10.059?
50.16
6.025
15.31
12.57

Answers

In which number is the value of the 5 ten times the value of the 5 in 10.059?
50.16
6.025
15.31
12.57


Answer is 6.025

Find the slope of the line passing through the points (6,6) and (6, -7).
slope: 1

Answers

Answer:

The line is a vertical line, which does not have a slope.

Step-by-step explanation:

Slope of a line:

Suppose we are given two points in the format (x,y) of a line. The slope is given by the change in y divided by the change in x.

(6,6) and (6, -7).

Change in y: -7 - 6 = -13

Change in x: 6 - 6 = 0

Slope is a division by 0, which means that the line is a vertical line, which does not have a slope.

Connor is splitting of ice cream with members of the team. If the ice cream is split​ evenly, how many will each person​ get? Explain.

Answers

Answer:

each person gets 1/4

Step-by-step explanation:

An object changes speed from 10 m/s to 18 m/s in the course of 4 seconds. What is its acceleration? HURRY PLEASE IM TAKING A TEST ASAP 50 points and brainliest

Answers

Answer:

2

Step-by-step explanation:

Velocity/Time, or 8/4 equals 2.

Hope this helps!

Need the measurements for 1 2 and 3

Answers

Answer:

m, c, and l

Step-by-step explanation:

81 people passed and 27 failed their Functional Skills Level 2 exams.
Write this as a ratio in its simplest form.

Answers

Answer:

The ratio of approved and disapproved people in its simplest form is 3:1.

Step-by-step explanation:

Since 81 people passed and 27 failed their Functional Skills Level 2 exams, to write this as a ratio in its simplest form, the common greatest divisor of both numbers must be obtained:

27 is divisible by 1, 3, 9 and 27

81 is divisible by 1, 3, 9, 27 and 81

Therefore, the common greatest divisor of both numbers is 27. So, since 27/27 is equal to 1, and 81/27 is equal to 3, the ratio of approved and disapproved people in its simplest form is 3 :1.

The ratio in its simplest form is 1 : 3.

Definition of ratio

Ratio expresses the relationship between two numbers. It is the frequency with which a number is contained in another number. The sign used to represent ratio is ':'.

Expressing in the simplest form

In order to express the given number of people that passed and failed the exam, we have to divide both numbers by the highest common factor until both numbers cannot be divided further to yield a whole number.

Common factor of 27 and 81 = 1, 3, 9, 27

Highest common factor = 27

Expressing in the simplest form = 1 : 3

To learn more about ratios, please check: https://brainly.com/question/25927869

Q7. What is the sum of the first 50 terms of the
series 2 +17 +32 +47 +...?​

Answers

Answer:

18475

Step-by-step explanation:

given sequence is in A.P.

sum of n terms of an A.P. is =

[tex] \frac{n}{2} \times (2a + (n - 1) \times d)[/tex]

here n = 50

a = 3

d= 15

ans is 18,475

Evaluate the expression if x = 3.
5x – (4 + x)

-

do not post any links.

Answers

Answer:

the answer is 8

Step-by-step explanation:

5 times 3 is 15

4 plus 3 is 7

15 minus 7 is 8

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 2 of 2 : Suppose a sample of 884 floppy disks is drawn. Of these disks, 831 were not defective. Using the data, construct the 98% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answers

Answer:

CI = ( 0, 042 ;  0,079 )

Step-by-step explanation:

If from 884 , 831  disks were OK  then  884  - 831  = 53 were defective

x  =  53

p = 53/884    p  = 0,0599     or p = 5,99 %   p ≈ 6 %

and q =  1  - 0,06       q = 0,94

p*n  and q*n   are big enough

For CI 98 %  significance level is α = 2 %   α/2 = 0,01

z(score) for α/2 = 0,01 is

z(c) ≈ 2,324

CI  =  p ±  z(c) *√p*q/n

√p*q/n   =  √ ( 0,94*0,06)/884

√p*q/n   =  √ 0,0564/884

√p*q/n   =  0,00799

CI  =  ( 0,06  ±  2,324*0,00799)

CI  =  ( 0,06  - 0,0185 ; 0,06 +  0,0185 )

CI = ( 0, 042 ;  0,079 )

help please

Find the x-intercepts for the parabola defined by the equation below.
y= x^2-9x+ 18
A. (-3,0) and (-6,0)
B. (0, -3) and (0, -6)
c. (0,3) and (0,6)
D. (3, 0) and (6.0)

Answers

Answer:

The answer correct (D).

The x-intercepts for the parabola defined by the equation y= x²-9x+ 18 are (3, 0) and (6.0)

What is quadratic equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

We have to find the  x-intercepts for the parabola y= x²-9x+ 18

We have to make y as zero to find the x intercepts

x²-9x+ 18 = 0

This equation is in the form of quadratic equation

x² -6x-3x+18=0

x(x-6)-3(x-6)=0

(x-3)(x-6)=0

x=3 or x=6

Hence, the x-intercepts for the parabola defined by the equation y= x²-9x+ 18 are (3, 0) and (6.0)

To learn more on Quadratic equation click:

https://brainly.com/question/17177510

#SPJ7

Pam wants to put a banner across her garage door to congratulate her son on his college graduation. The garage door is 9 feet high and 12 feet wide. How many feet long should the banner be to fit the garage door?

Answers

9514 1404 393

Answer:

  15 feet

Step-by-step explanation:

The diagonal of a 9 ft by 12 ft rectangle is given by the Pythagorean theorem as ...

  d = √(9² +12²) = √225

  d = 15 . . . . feet

The banner should be 15 feet long to match the length of the door diagonal.

you have a spinner divided into 5 equal sections each section is number with a number 1 through 5 theoretically what is the probability of spinning and landing on a five​

Answers

Answer:

20%

Step-by-step explanation:

1/5 = 20/100 = 20%

Answer:

1/5

Step-by-step explanation:

probability- number of favorable outcomes/ number of total outcomes

in this question,

number of favorable outcomes is 1.

and, the number of total outcomes is 5.

so, probability of spinning and landing on 5 is 1/5.

An 84-square foot tabletop is starting to bow in the middle. Using only the scrap wood in her shop, a carpenter
adds a diagonal support piece to the square shaped tabletop. Which of the following lengths of scrap wood is
closest to the length the diagonal support piece?

Answers

Answer:

13.5

Step-by-step explanation:

Answer:

13.5

Step-by-step explanation:

8x+5
3x+8
Find the measurement of x!!

Answers

Answer:

Step-by-step explanation: look at the picture

The size your dog and the number of times you take it to the vet, The amount your drive to school and the amount you have to pay for gas, The number of people at your party and the number of sodas you have in the refrigerator. What correlation are all of these separately. None, Positive, or Negative thanks so much and tell me which one thanks!

Answers

1. No correlation

Those things don't really relate to each other.

2. Positive correlation

The more you drive your car, the more you'll have to pay for gas.

3. Negative correlation

More people = less soda.

please help i wanna pass
A wildlife society is taking a sampling of the lengths of bluegill fish at a local lake.


If the survey resulted in the data above, the distribution of fish lengths would be best described as...
A.
symmetrical with multiple modes.
B.
symmetrical with one mode.
C.
skewed to the right.
D.
skewed to the left.

Answers

Answer:

it was skewed to the right

Step-by-step explanation:

i just answered the quistion and D was not the answer

If -x = 20, then x = ?

Answers

Answer:

[tex] - x = 20 \\ so \: x \: will \: be \: = - 20[/tex]

Hope it helps!

Answer: x = -20

Step-by-step explanation:

Question: If -x = 20, then x = ?

Multiply both sides of the equation by -1

(-1)(-x) = (-1)(20)

Simplify (remember that multiplying two negative numbers equals a positive number)

x = -20

ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP ASAP NEED HELP​

Answers

Answer:

21) Scalene - Right triangle, 22) Scalene - Right triangle, 23) Equilateral - Acute triangle, 24) Isoceles - Obtuse triangle, 25) Scalene - Right triangle.

Step-by-step explanation:

21) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.

22) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.

23) This triangle has three sides of same length and three acute angles: Equilateral - Acute triangle.

24) This triangle has two sides of same length and an obtuse angle and two acute angles: Isoceles - Obtuse triangle.

25) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.

Your answer should be  :1) Scalene - Right triangle, 22) Scalene - Right triangle, 23) Equilateral - Acute triangle, 24) Isosceles - Obtuse triangle, 25) Scalene - Right triangle.Step-by-step explanation:21) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.22) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.23) This triangle has three sides of same length and three acute angles: Equilateral - Acute triangle.24) This triangle has two sides of same length and an obtuse angle and two acute angles: Isosceles - Obtuse triangle.25) This triangle has three sides of distinct length and a right angle and two acute angles: Scalene - Right triangle.Step-by-step explanation:hope this help

A pizzeria sells 1 pizza pie for $13, 2 for $23, 3 for $33, and 5 for $53.
Is that a proportional relationship? yes or no?

Answers

Answer:

Yes, 10 dollars are added each time

Step-by-step explanation:

A goliath grouper at the local aquarium ate 112 fish over the course of 8 hours. At this rate how many fish can he eat in 3.5 hours

Answers

Answer is 49

112 divided by 8 is 14
14 multiplied by 3.5 is 49

How can you find the area of a quadrilateral

Answers

Answer:

(½) × diagonal length × sum of the length of the perpendiculars drawn from the remaining two vertices.

Step-by-step explanation:

or you can solve for the area of the rectangle then the area of the triangle and add them together

Find the measure of angles 1-7(please help)

Answers

Answer:

Step-by-step explanation:

1. 70 deg (compliment angle of 110 deg.)

2. 65 deg (compliment angle of 115 deg.)

3. 65 deg (corresponding angle of angle 2)

4. 115 deg (corresponding angle of 115 deg.)

5. 45 deg (angles 1+3+5 = 180 deg. as sum of internal angles in a triangle)

6. 45 deg (alternate angle of angle 5)

7. 45 deg (corresponding angle of angle 5)

Please help me with these, find the missing side. Thank yu only if you know

Answers

Answer:

7.48m (3s.f.)

Step-by-step explanation:

Let the missing side be x m.

Applying Pythagoras' Theorem,

x² +5²= 9²

x² +25= 81

x²= 81 -25 (-25 on both sides)

x²= 56

[tex]x = \sqrt{56} [/tex]

[tex]x = 2 \sqrt{14} [/tex]

x= 7.48 (3 s.f.)

∴ The missing side is 7.48 m (3s.f.)

Cual es la mitad de 30.6

Answers

Answer

Supongo que estás pidiendo la mitad de 30.6 es decir, 15.3

Explanation : 15.3+15.3=30.6

or 30.6 ÷2 =30.6

The difference between -7 and a number x is no more than -2/3

Answers

Answer:

Pregunta muy difícil, no creo que pueda resolver este amigo.

Step-by-step explanation:there is no step-by-step thing because honestly don't understand what your trying to say here. Hmm...

PLEASE HELP ME RIGHT NOW

Find the range and interquartile range of the data.

23,45,39,34,28,41,26,33

The range of the data is


The interquartile range of the data is

Answers

Answer:

the answer to the range should be 22 but i do not have the interquartile range :(

Step-by-step explanation:

An aquarium has the dimensions of 36 inches wide, 10 inches long and 9 inches high. It was filled with 7 inches of water. How many cubic inches of water does the aquarium have?

Answers

Answer:

106

Step-by-step explanation:

7*10*36=106

what force would be required to accelerate a 1,100 kg car to 0.5m/s?

Answers

Answer:

550 N

Step-by-step explanation:

We can solve the problem by using Newton's second law:

[tex]F=ma[/tex]

F is the force required to accelerate the car

m is the mass of the car

a is the acceleration of the car

In this problem, the mass is m=1100 kg, while the acceleration is a=0.5 m/s^2, therefore the force required to accelerate the car is

[tex]F=ma=(1100kg)(0.5m/s^{2} )=550N[/tex]

Hope this helps!

Find the missing side of each right triangle. Side c is the hypotenuse. Sides a and b are the legs. Round your answers to the nearest tenth if necessary. b= 12 mi. C= 13 mi​

Answers

Answer:5

Step-by-step explanation:

a2+b2=c2

a2+12squared=13 squared

169-144=a2

a2=25, now that we have 25 we have to find the square root which is 5.

Find the measure of one exterior angle. Round your answer to the nearest 3 points
tenth if necessary.
Your answer
Find the measure of one exterior angle. Round your answer to the nearest tenth of necessary

Answers

Answer:

aikajwbuabsbss

abhsua w

wmhabw

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