Some transportation experts claim that it is the variability of speeds, rather than the level of speeds, that is a critical factor in determining the likelihood of an accident occurring (Update, Virginia Department of Transportation, Winter 2000). One of the experts claims that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)2. On a heavily traveled highway, a random sample of 55 cars revealed a mean and a variance of speeds of 62.5 mph and 94.7(mph)2, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)
1. Set up the competing hypothesis to test wxpert,s claim.
2. At the 5% significance level find the critical value and state the decision rule.
3. Can you conclude that driving conditions are dangerous on this highway? explain.
Answer:
Explained below.
Step-by-step explanation:
The claim made by an expert is that driving conditions are dangerous if the variance of speeds exceeds 75 (mph)².
(1)
The hypothesis for both the test can be defined as:
H₀: The variance of speeds does not exceeds 75 (mph)², i.e. σ² ≤ 75.
Hₐ: The variance of speeds exceeds 75 (mph)², i.e. σ² > 75.
(2)
A Chi-square test will be used to perform the test.
The significance level of the test is, α = 0.05.
The degrees of freedom of the test is,
df = n - 1 = 55 - 1 = 54
Compute the critical value as follows:
[tex]\chi^{2}_{\alpha, (n-1)}=\chi^{2}_{0.05, 54}=72.153[/tex]
Decision rule:
If the test statistic value is more than the critical value then the null hypothesis will be rejected and vice-versa.
(3)
Compute the test statistic as follows:
[tex]\chi^{2}=\frac{(n-1)\times s^{2}}{\sigma^{2}}[/tex]
[tex]=\frac{(55-1)\times 94.7}{75}\\\\=68.184[/tex]
The test statistic value is, 68.184.
Decision:
[tex]cal.\chi^{2}=68.184<\chi^{2}_{0.05,54}=72.153[/tex]
The null hypothesis will not be rejected at 5% level of significance.
Conclusion:
The variance of speeds does not exceeds 75 (mph)². Thus, concluding that driving conditions are not dangerous on this highway.
Three times a number minus 5 plus the same number
Answer:
15
Step-by-step explanation:
Angle 3 and angle 4 are supplementary angles angle 3 is 88° what is the measure of angle 4?
Answer:
92°
Step-by-step explanation:
Supplimentary angle = 180°
So, 180° - 88° = 92°
out of 50 students,34 joined the journalism class and 25 joined the robotics club.If 16 students joined both clubs,how many students are in neither club
Dave cleans pools at a constant rate of 2/5 pools per hr what is the ratio of the number of pools he cleans to the number of hours
How many pools can dave clean in 20 hrs
Answer:
For every 1 hour he cleans 2/5 pools, so the ratio of pools to hours is 0.4:1
In 20 hours, Dave can clean 2/5 • 20 = 8 pools.
I need help fast
help me please
help me with ten please
Answer:
H
Step-by-step explanation:
The linear equation has 5(x + 2) = 5x + 2 A) no solution. B) one solution. C) two solutions. D) infinitely many solutions
it's A it has no solution
3(2h + 7) = 4(9 – h)
Answer:
h=−2
Step-by-step explanation:
car rental agency charges a base rate plus a certain amount per day (d) and can be modeled using the expression 15+ 18d. What is the meaning of 18d in the expression? *
4 points
It is the base rate to rent a car.
It is the cost of renting a car for a day.
It is the total number of days a car can be rented.
It is the portion of the cost based on renting a car for d days.
Answer:
It is the portion of the cost based on renting a car for d days
Step-by-step explanation:
Given:
Total cost = 15 + 18d
Total cost = fixed cost + variable cost
Fixed cost are cost that do not change.
Fixed cost = base rate = 15
Variable cost changes during production process. The variable cost in the above varies with the number of days (d)
Therefore, 18d is the portion of the cost based on renting a car for d days.
If you rent the car for 1 day
Total cost = 15 + 18d
= 15 + 18(1)
= 15 + 18
= 33
I mark as brainliest
Answer:
.1
Step-by-step explanation:
Answer:
Point Q is represented by the ordered pair (-2,9)
Question 1
Select ALL expressions that are equivalent to 4x + 2(2x - 5) - (3 - 5x).
A
82 - 10 - 3 - 52
B
3.2 - 13
С
13 – 13
82 - 10 - 3 + 5%
E
83 - 5 - 3 - 5x
Answer:
B
Step-by-step explanation:
Round the numbers to the nearest ten thousands.
62 389-
65 405-
51 330-
343 021-
102 779-
Answer:
60,00070,00050,000340,000100,000
6(5−8v)+12=−54 can you help me with this?
Answer:
v=2
Step-by-step explanation:
6(5-8v)+12=-54
6(5-8v)=-66
(6(5-8v))/6=-66/6
5-8v=-11
-8v=-11-5
-8v=-16
What is the quotient of (-55) divide by 5?
Answer:
11
Step-by-step explanation:
✨Answer:✨
-11
✨Step-by-step explanation:✨
-55 ÷ 5 = -11
(Just take the negative sign away and divide)
Michelle can type 120 words in 3 minutes. How many words can she type in 1 minute at this rate? A. 30 words B. 40 words C. 50 words D. 60 words
pls answer i cant figure it out pls don't type random things for points
Answer:
B
Step-by-step explanation:
THe answer is b because you have to divide 3 by whatever the answer is so just divide all answers until you get one thats 120 so b
Answer:
B.40 words
Step-by-step explanation:
120÷3=40
40×3=120
what is 917 divided by 63
Answer:
14.55
Step-by-step explanation:
11. Use an inequality symbol (<, >, 2, =) to compare -26
O A.
O B. =
O C.<
O D.>
Answer:
c. <
Step-by-step explanation:
-26 < (less than) 54
I think I know the answer but I just want to double check.
Answer:
D
Step-by-step explanation:
I think it's same with what ur thinking
the ratio of lily's programing to tina's programing speed is 3:5. lily can write six programs per day. if lily and tina work together to write 240 programs, how many days are needed
Answer:
which principle prevents a brach from abusing its power
Step-by-step explanation:
The pilot of an airplane flying at an elevation of 5000 feet sights two towers that are 300 feet apart. If the angle of depression to the tower closer to him is 30, determine the angle of depression to the second tower.
Answer: 29.2 degree
Step-by-step explanation:
Given data:
Elevation of the pilot = 50,000 feet
Elevation of the two towers = 300 feet apart.
Depression of closer tower = 30
Solution:
The angle of depression to the second tower is x
tanx = 5000/(5000*√(3)+300)
x=29.2
Therefore the angle of depression of the second tower is at 29.2 degree
Answer:
29.2°
Step-by-step explanation:
From diagram (b)
Tan θ= opp/adj
Where θ = 30°
opp = 5000ft
adj = ?
tan 30° = 5000/x
x tan30° = 5000
x = 5000/tan 30
x = 5000/0.577
x = 8665.5ft
From diagram c
tan θ = opp/adj
Where θ = ?
opp = 5000
adj = 300+x
x= 8665.5
tan θ = 5000/300+8665.5
tan θ = 5000/8965.5
tan θ = 0.55769
θ = arch tan 0.55769
θ = 29.147
θ= 29.2°
Plot the line for the equation on the graphy,−5=3/2(x−2)
Answer:
The equation of the line is:
y - 5 = 3/2 (x - 2)
Transforming the line into the slope intercept form:
y = 3x/2 - 3 + 5
y = 3x/2 + 2
The slope is 3/2 and the y-intercept is 2.
Plotting this on the graph can be done using these steps:
Locate the point (0,2) on the graph.
From (0,2), count 3 units up and 2 units to the left and indicate that point.
Finally, connect the two points and extend the line.
If you spend 540 minutes per year waiting in lines, how many hours is this?
Answer:
540 minutes in hours =540/60
=9 hours
The time 540 minutes in hours will be 9 hours.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the time is 540 minutes. The value of time in hours will be calculated as,
The time of 60 minutes is equal to 1 hour. So divide the time 540 minutes by 60 minutes.
Time = 540 / 60
Time = 9 hours
To know more about an expression follow
https://brainly.com/question/12053230
#SPJ2
( 3+√3 ) (2+√2) simplify
What is the value of the expression below? (9 divided by 3) + 4 (6 minus 7) –7 –1 7 20
PLEASE ANSWER QUiCK I’m on timer
Answer:
The answer is -1.
Step-by-step explanation:
Answer:
-1 is the answer saw it on clculator
Which expression would be easier to simplify if you used the commutative property to change the order of the numbers?
A. 30 + (-12) + 70
B. -10 + (-20) + 1/2
C. 60 +40 + (-25)
Answer:it’s A
Step-by-step explanation:
Is it carbohydrate, lipid, protein, or nucleic acid?
PLEASE HELP!!! LAST QUESTION AND IM STUCKK.
Answer:
nucleic acid
Step-by-step explanation:
Brett made a scale drawing of a rectangular room in his house.
The actual length of the room is 12 4/5 ft. The scale used to make the
drawing was 1/4 in. = 1 ft. What is the length, in inches, of the room
on the drawing?
Answer:
Step-by-step explanation:
Length of the room = 12 4/5 ft = 12.8 ft
Scale is 0.25 inches = 1 ft.
This means that every 1ft is shown as 1/4 inch on the map.
To find what 12 4/5ft on the map, you would multiply 12.8 by 0.25.
12.8 x 0.25 = 3.2 inches
The mayor of a town saw an article that claimed the national unemployment rate is 8%. They wondered if this held true in their town, so they took a sample of 200 residents to test H_0 : p = 0.08 versus H_a : p != 0.08, where p is the proportion of residents in the town that are unemployed. The sample included 22 residents who were unemployed.Identify the correct test statistic for this significance test to one decimal place.
Answer:
Z = [tex]\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }[/tex] = 1.6
we reject the Null hypothesis
Step-by-step explanation:
The correct test statistic
Assume :
Null Hypothesis : H_0 : p = 0.08
Alternative hypothesis : H_a : p ≠ 0.08
p = proportion of residents that are unemployed
x = unemployed residents = 22
n = sample size = 200
To get the sample of the population that is unemployed we use this equation
[tex]p = \frac{X}{n}[/tex] = 22 / 200 = 0.11
now we apply the test of of significance of single proportion
= Z = [tex]\frac{p - P}{\sqrt{pq/n} }[/tex]
therefore Z = [tex]\frac{0.11-0.08}{\sqrt{0.08*0.92/200} }[/tex] = 1.6
Therefore we reject the Null hypothesis
Testing the hypothesis, it is found that the test statistic used is z = 1.6.
At the null hypothesis, it is tested if the proportion is of 8%, that is:
[tex]H_0: p = 0.08[/tex]
At the alternative hypothesis, it is tested if the proportion is different of 8%, that is:
[tex]H_1: p \neq 0.08[/tex]
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion. p is the proportion tested at the null hypothesis. n is the sample size.For this problem, the parameters are: [tex]p = 0.08, n = 200, \overline{p} = \frac{22}{200} = 0.11[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.11 - 0.08}{\sqrt{\frac{0.08(0.92)}{200}}}[/tex]
[tex]z = 1.6[/tex]
A similar problem is given at https://brainly.com/question/24166849
Write using interval notation
Answer:
(-9,5]
Hope this helps!!!!!