Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.
Before 13 22 65 123 56 63
After 14 21 43 84 75 72
1. The article included the statement "A paired t-test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. (Note: The relevant normal probability plot shows a substantial linear pattern.)
a. State and test the appropriate hypotheses. (Use α = 0.05.)
b. Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)
t = _____
p-value = _____
c. State the conclusion in the problem context.
A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
B. Reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
C. Fail to reject H0. The data suggests a significant mean difference in the average number of accidents after information was added to road signs.
D. Reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.
2. If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in the number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)

Answers

Answer 1

Answer:

Test statistic = 0.63

Pvalue = 0.555

A. Fail to reject H0. The data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.

Step-by-step explanation:

Given :

Before 13 22 65 123 56 63

After_ 14 21 43 84 75 72

To perform a paired t test :

H0 : μd = 0

H1 : μd ≠ 0

We obtain the difference between the two dependent sample readings ;

Difference, d = -1, 1, 22, 39, -19, -9

The mean of difference, Xd = Σd/ n = 33/6 = 5.5

The standard deviation, Sd = 21.296 (calculator).

The test statistic :

T = Xd ÷ (Sd/√n) ; where n = 6

T = 5.5 ÷ (21.296/√6)

T = 5.5 ÷ 8.6940555

T = 0.6326

The Pvalue : Using a Pvalue calculator ;

df = n - 1 = 6 - 1 = 5

Pvalue(0.6326, 5) = 0.5548

Decision region :

Reject H0 ; If Pvalue < α; α = 0.05

Since 0.5548 > 0.05 ; we fail to reject the Null and conclude that the data does not suggest a significant mean difference in the average number of accidents after information was added to road signs.


Related Questions

the diameter of a circle is 8 cm what is its area?

Answers

A = πr^2 and d = 2r.

So r = 8/2 = 4 cm.

Now use the first formula

A = π(4 cm)^2 = 50.265 cm^2

p(X)=x²+50 then p(2)=
a) 6
b)7
c)8
d)9​

Answers

Answer:

54

Step-by-step explanation:

p(x)=x^2+50, p(2)=2^2+50=54

P(x) = x² + 50

P(2) = 2² + 50

= 54

P(6) = 6²+50

= 86

P(7) = 7²+ 50

= 99

P(8) = 8²+50

= 114

P(9) = 9²+50

= 131

Answered by Gauthmath must click thanks and mark brainliest

3 lawns in 9 hours.what was the rate of mowing in hours per lawn

Answers

Answer:

3

Step-by-step explanation:

3 = 9 \:th \\ 1 = 3 \\ 3 \times 3 = 9 \\ 9 \div 3 = 3 \\ so \: that \: answer \: is \: 3

3 because 3x3 = 9 and that just makes more sense then to put anything other unless I’m missing something it’s 3

What is the distance from point Yto wx in the figure below?
W 16 Z
30
X
1612
34
O A. 4
O B. 162
O C. 16
O D. Cannot be determined
E. 16/3
F. 8

Answers

The length of YZ in the similar triangle given is calculated using Pythagoras theorem which gave us 16√3

What are Similar Triangle

Similar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and corresponding sides that are proportional.

In this problem, we need to use the concept of ratio and proportions to find the length of YZ

However, we can simply use Pythagoras theorem to determine the length.

According to Pythagoras' Theorem, the square of the hypotenuse, or side opposite the right angle, in a right-angled triangle, is equal to the sum of the squares of the other two sides.

It is expressed as the equation a² + b² = c².

This is because the triangles forms a right angled triangle and we can easily apply that here.

YZ² = 16² + (16√2)²

YZ² = 768

YZ = √768

YZ = 16√3

The length or distance from point Y to WX which is the same as the length of YZ is calculated as 16√3.

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Answer:

C. 16

Step-by-step explanation:

I hope this helps :)

A 90% confidence interval is found to be (120,140). What is the margin of error?

Answers

Answer:

There is 10% error in both minimum and extreme values i.e. 120 & 140 , Error in 120 is 10% i.e. = 12, Since value can be more or less in error ∴ Error in 120 is ±12.

What is the image of (3, -12) after a dilation by a scale factor of į centered
at the origin?

Answers

Answer:

9 is. ................m.m..mk

Keith is trying to figure out the area of his pool section in his backyard he knows that his pool is 20 feet long and 9 feet wide he also knows the sidewalk is 3 feet wide all around the floor what is the total area of the pool section of Keith’s backyard?

Answers

Answer:

The total area of the pool section of Keith's backyard is 390 square feet.

Step-by-step explanation:

Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:

(20 + 3 + 3) x (9 + 3 + 3) = X

26 x 15 = X

390 = X

Therefore, the total area of the pool section of Keith's backyard is 390 square feet.

What is a corresponding pair for f(-7)=5

Answers

Answer:

An ordered pair for a function f(x) looks like (x, f(x)). So the ordered pair here would be (5, f(5)) or (5, 7). Either one would work, as they are the same.

What is |1-8i|?

A.
B.
C
D

Answers

9514 1404 393

Answer:

  (b) √65

Step-by-step explanation:

The modulus of a complex number is the root of the sum of the squares of the real and imaginary parts.

  |1 -8i| = √(1² +(-8)²) = √(1+64) = √65

The BBQ club meets every Thursday. The meetings last 2 1/2 hours. There were 5 Thursdays in
September. How many hours did the BBQ club meet in September?


A.2 1/2 hours
B.5 hours
C.12 1/2 hours
D.10 hours

Answers

Answer:

12 1/2

Step-by-step explanation:

2 x 5 = 10

1/2 x 5 = 2 1/2

10 + 2 1/2 = 12 1/2

Which equation has the same solution as 10(x) - x + 5 = 41

Answers

Step-by-step explanation:

if that is truly the full problem description, then we have

10x - x + 5 = 41

=>

9x = 36

our simply

x = 4

so, I am not sure, what your teacher wants to see as result.

there is an infinite number of equations I could find, all with the solution x = 4.

A lottery ticket has a grand prize of $30.1 million. The probity of winning the grand prize is .000000038
Deteman the expected value of the lottery ticket

Answers

Answer:

$30.1 million * .000000038

$1.14

did the question say how much the ticket cost?

if it was $1 then you would have to subtract $1 so the expected value would be 14 cents

Step-by-step explanation:

Help me please --------------------

Answers

9514 1404 393

Answer:

  139.39 in

Step-by-step explanation:

The length of a semicircle of diameter D is ...

  C = (1/2)πD

For the given diameter of 27 inches, the length of the curved edge of the figure is ...

  C = 1/2(3.14)(27 in) = 42.39 in

__

The perimeter of the figure is the sum of the side lengths. Clockwise from left, that sum is ...

  P = 27 + 35 + 42.39 + 35 = 139.39 . . . inches

The perimeter of the figure is 139.39 inches.

Find the length of the arc.
A. 21/π4 in
B. 18π in
C. 45/π8 in
D. 1890π in

Answers

Answer:

we know that all Lenght of circle is 2πr so 2*π*7=14π

Step-by-step explanation:

14π equal to 360°

but we need just 135° so we should write it kind of radian(π)

if 14π=360°

x=135°

14π*135=360°*x 14π*27=72*x ........= 14π*3=8*x

7π*3=4*x ....... X=21π/4

The length of the arc is 21/π4 in

An answer is an option A. 21/π4 in

What is the arc of the circle?

The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.

⇒angle= arc/radius

 ⇒  135°=arc/7

⇒ arc =135°*7

  ⇒arc=135°*π/180° *7in

⇒arc = 21/π4 in

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find each measurement indicated round your answers to the nearest tenth. Part 1d. NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Answers

Answer:

see explanation

Step-by-step explanation:

Using the Sine rule in all 3 questions

(1)

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values , firstly calculating ∠ B

[ ∠ B = 180° - (78 + 49)° = 180° - 127° = 53° ]

[tex]\frac{a}{sin78}[/tex] = [tex]\frac{18}{sin53}[/tex] ( cross- multiply )

a sin53° = 18 sin78° ( divide both sides by sin53° )

a = [tex]\frac{18sin78}{sin53}[/tex] ≈ 22.0 ( to the nearest tenth )

(3)

[tex]\frac{c}{sinC}[/tex] = [tex]\frac{a}{sinA}[/tex] , substitute values

[tex]\frac{35}{sinC}[/tex] = [tex]\frac{45}{sin134}[/tex] ( cross- multiply )

45 sinC = 35 sin134° ( divide both sides by 35 )

sinC = [tex]\frac{35sin134}{45}[/tex] , then

∠ C = [tex]sin^{-1}[/tex] ( [tex]\frac{35sin134}{45}[/tex] ) ≈ 34.0° ( to the nearest tenth )

(5)

Calculate the measure of ∠ B

∠ B = 180° - (38 + 92)° = 180° - 130° = 50°

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] , substitute values

[tex]\frac{BC}{sin38}[/tex] = [tex]\frac{10}{sin50}[/tex] ( cross- multiply )

BC sin50° = 10 sin38° ( divide both sides by sin50° )

BC = [tex]\frac{10sin38}{sin50}[/tex] ≈ 8.0 ( to the nearest tenth )

If only the height of a pyramid is doubled its volume is Also doubled true or false

Answers

Answer: true

Step-by-step explanation:

Use AABC to find the value of sin B.

Answers

Answer:

35/37

Step-by-step explanation:

sin(B)=(AC)/(AB) = 35/37

Solve the above quadratic equation

Answers

Answer:

r = 1

Step-by-step explanation:

Find the intersection.

r = 1

r = 3

r = -1

r = 1

Answer:

r=3, r=1, r= -1

Step-by-step explanation:

48r^3-144r^2-48r=-144

48r^3-144r^2-48r +144 =-144 + 144

48r^3-144r^2-48r+144=0

48(r-3)(r+1)(r-1)

r-3=0 r+1=0 r-1=0

r=3, r=1, r= -1

solution 2^2x+3-7(2^2x+1)+3=0 introduce Log​

Answers

Answer:

[tex]x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Step-by-step explanation:

Given the expression

[tex]2^{2x}+3-7(2^{2x}+1)+3=0[/tex]

Let [tex]P=2^x[/tex]

Substituting into the expression, we will have:

[tex]P^2+3-7(P^2+1)+3=0\\Expand\\P^2+3-7P^2-7+3=0\\-6P^2-1=0\\6P^2=-1\\p^2=-1/6\\P=\sqrt{-1/6}[/tex]

Since:

[tex]P=2^x\\2^x=\sqrt{-1/6}\\xlog2=log(\sqrt{-1/6}) \\x = \frac{log\sqrt{-1/6}}{log2}[/tex]

Select the statement that best justifies the conclusion based on the given information.

l is in plane M,
x is on line l
Conclusion: x is in plane M.

a. A plane contains at least three points not all on the same line.
b. If two points lie in a plane, then the line containing them lies in that plane.
c. If a plane contains a line, it contains the points on the line.
d. Exactly one plane contains a given line and a point not on the line.

Answers

9514 1404 393

Answer:

  c. If a plane contains a line, it contains the points on the line.

Step-by-step explanation:

The only statement relating a point on a line to the plane containing the line is the one shown above.

_____

Additional comment

Identifying true statements is a reasonable strategy for many multiple-choice questions. Another strategy that can be employed is finding the one true statement that is relevant to the question being asked.

The equation cos(35•) = a/25 can be used to find the length of BC what is the length of BC round to the nearest tenth

Answers

Idrk tbh I need help with the same thing

A telephone service representative believes that the proportion of customers completely satisfied with their local telephone service is different between the South and the Midwest. The representative's belief is based on the results of a survey. The survey included a random sample of 1300 southern residents and 1380 midwestern residents. 39% of the southern residents and 50% of the midwestern residents reported that they were completely satisfied with their local telephone service. Find the 80% confidence interval for the difference in two proportions. Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval

Answers

Answer:

The point estimate that should be used in constructing the confidence interval is 0.11.

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Midwest:

50% of 1380, so:

[tex]p_M = 0.5[/tex]

[tex]s_M = \sqrt{\frac{0.5*0.5}{1380}} = 0.0135[/tex]

South:

39% of 1300, so:

[tex]p_S = 0.39[/tex]

[tex]s_S = \sqrt{\frac{0.39*0.61}{1300}} = 0.0135[/tex]

Distribution of the difference:

[tex]p = p_M - p_S = 0.5 - 0.39 = 0.11[/tex]

So the point estimate that should be used in constructing the confidence interval is 0.11.

[tex]s = \sqrt{s_M^2+s_S^2} = \sqrt{0.0135^2+0.0135^2} = 0.0191[/tex]

Confidence interval:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].  

The lower bound of the interval is:

[tex]p - zs = 0.11 - 1.28*0.0191 = 0.0856[/tex]

The upper bound of the interval is:

[tex]p + zs = 0.11 + 1.28*0.0191 = 0.1344[/tex]

The 80% confidence interval for the difference in two proportions is (0.0856, 0.1344).

simplify using the laws of exponents (4^3)^-2 × (2^3)^4 ×(8/15)^-2​

Answers

Answer:

[tex] \dfrac{225}{64} [/tex]

Step-by-step explanation:

[tex] (4^3)^{-2} \times (2^3)^4 \times (\dfrac{8}{15})^{-2} = [/tex]

[tex]= (2^2)^{-6} \times 2^{12} \times (\dfrac{15}{8})^{2}[/tex]

[tex]= 2^{-12} \times 2^{12} \times \dfrac{225}{64}[/tex]

[tex] = \dfrac{225}{64} [/tex]

Simplify Square root (150n^2)

Answers

Answer:

12

Step-by-step explanation:

Please help me determine the general equation for the graph above as well as solve for a. Thank you.

Answers

Observe that the x coords of the roots of a polynomial are,

[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]

Which can be put into form,

[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]

with data

[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]

Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,

[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]

and a will be "lost" in the process.

If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.

Hope this helps :)

A board that measures 3/4 feet long is cut into 6 equal pieces . What is the length of each price

Answers

Step-by-step explanation:

8 cm² is the correct answer for that question

Given:

Board Length = 3/4

6 equal pieces = 3/4 ÷6

= 3/4 × 1/6

= 1/4 × 1/2

= 1/8

Therefore each equal piece will be 1/8 feet long

Answered by GauthMath if you like please click thanks and comment thanks too.

What is the equation of a line that passes through the point (5,-3) and has a slope of -2

Answers

Answer:

y=-2x+7

Step-by-step explanation:

The Slope is obviously -2, and just add a random y and play around with it until it goes through the point (5,-3)

A movie theater has a seating capacity of 187. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1338, How many children, students, and adults attended?
___ children attended.
___ students attended.
___ adults attended.

Answers

Answer:

A) children attended=98 b) students attended=60 c)adults attended=49

Step-by-step explanation:

system%28a%2Bc%2Bx=207%2Cc%2Fa=2%2C5c%2B7x%2B12a=1498%29

Simplify and solve the system.

-

a%2B2a%2Bx=207

3a%2Bx=207

x=207-3aandc=2a

-

The revenue equation can be written in terms of just one variable, a.

10a%2B7%28207-3a%29%2B12a=1498

Solve for a;

use it to find x and c.

FURTHER STEPS

-

10a%2B1449-21a%2B12a=1498

a%2B1449=1498

a=98-49

highlight%28a=49 -------adults

-

c=2a

c=2%2A49

highlight%28c=98 -------children

-

x=207-a-c

x=207-49-98

highlight%28x=60 ---------students

50T Q12 A man wants to buy bags of gravel to cover his driveway. He decides to work out the area of his driveway. 1 bag of gravel covers 14m2 3m Sketch of driveway Not to scale 3m 8m 6m What is the area of his driveway? How many bags of gravel must he buy?​

Answers

Answer:

hi amki nai patajjdkfkejd

need help pls with this question. im struggling with this question.

Answers

Answer:

i can't rn but i could explain to you how... so first put a point on 0,5 then move down one and right one... then keep moving down one and right one

and there you go thats your graph

Step-by-step explanation:

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