The National Transportation Safety Board publishes statistics on the number of automobile crashes that people in various age groups have. A researcher claims the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%. Her study examined 1000 young drivers ages 18 – 24 and found that 134 had an accident this year. Test at α = .05. a) State H0 and Ha b) Find the critical value, show work c) Find the appropriate test statistic, show work d) Do a P - value test e) Make a decision to reject or fail to reject the null hypothesis and interpret the results.
Answers
Answer:
a) Null hypothesis:\(p\leq 0.12\)
Alternative hypothesis:\(p > 0.12\)
b) \( z_{\alpha}=1.64\)
c) \(z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362\)
d) \(p_v =P(z>1.362)=0.0866\)
e) For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12
Step-by-step explanation:
Information given
n=1000 represent the random sample selected
X=134 represent the number of young drivers ages 18 – 24 that had an accident
\(\hat p=\frac{134}{1000}=0.134\) estimated proportion of young drivers ages 18 – 24 that had an accident
\(p_o=0.12\) is the value that we want to verify
\(\alpha=0.05\) represent the significance level
Confidence=95% or 0.95
z would represent the statistic
\(p_v{/tex} represent the p value
Part a
We want to verify if the population proportion of young drivers, ages 18 – 24, having accidents is greater than 12%:
Null hypothesis:\(p\leq 0.12\)
Alternative hypothesis:\(p > 0.12\)
The statistic would be given by:
\(z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}\) (1)
Part b
For this case since we are conducting a right tailed test we need to find a critical value in the normal standard distribution who accumulates 0.05 of the area in the right and we got:
\( z_{\alpha}=1.64\)
Part c
For this case the statistic would be given by:
\(z=\frac{0.134 -0.12}{\sqrt{\frac{0.12(1-0.12)}{1000}}}=1.362\)
Part d
The p value can be calculated with the following probability:
\(p_v =P(z>1.362)=0.0866\)
Part e
For this case since the statistic is lower than the critical value and the p value higher than the significance level we have enough evidence to FAIL to reject the null hypothesis so then we don't have information to conclude that the true proportion is higher than 0.12
Related Questions
Mr.Salazar assigns the same Number of homework Question each
Answers
Answer:
ur question isnt complete... ?
Step-by-step explanation:
3 in.
1 in.
2 in.
4 in.
Answers
Answer:
The volume would be 12 inches.
Step-by-step explanation:
Volume is LxWxH
for the lower box, I did
4x2x1=8
For the top half
2x2x1=4
Then i added them together
8+4= 12
Charlotte owns two entertainment websites. Here are some details about those websites for one entire month:
Website A
Website B
Number of writers
Number of posts posted
Average number of words of post
Average likes per post
Average comments per post
Number of new subscribers
Revenue
Expenses
Profit (Revenue -Expenses)
5
110
100
3500
500
9000
$30,000
$20,000
$10,000
11
200
170
3500
450
20,000
$75,000
$47,000
$28,000
Charlotte wants to know which website has more user engagement per a single dollar expense.
1) Charlotte thought of two different ways to define this quantity. Identify these two definitions among the following options.
Choose 2 answers:
Answers
Answer:B & D
B
Step-by-step explanation:
100 POINTS!
Use the difference quotient with a limit to show the derivative of f(x)=9/(5x-4) is equal to f’(x)=-45/(5x-4)^2
Answers
By using the difference quotient with a limit, the derivative of f(x) = \(\frac{9}{5x - 4}\) is equal to f'(x) = \(\frac{-45}{(5x -4)^2}\) has been proved
What is differentiation?
Differentiation is a method of finding the rate of change of a function at any given point. It involves taking the derivative of a function and calculating the tangent at a given point on the graph of the function. Differentiation can be used to calculate the slope of a line, the rate of change of a function, and to solve problems related to the rate of change. Differentiation is an important tool in calculus and is used to calculate the maximums, minimums, and points of inflection of a function. It can also be used to find the area under a curve and to solve certain differential equations. Differentiation is the fundamental tool of calculus and can be used to find the derivatives of most functions.
f(x) = \(\frac{9}{5x - 4}\)
f'(x) = \(\lim_{h \to 0} \frac{f(x+h) - f(x)}{h}\)
\(\lim_{h \to 0} \frac{\frac{9}{5(x + h)-4} - \frac{9}{5x - 4}}{h}\\\\ \lim_{h \to 0} \frac{9(5x-4)-9(5x+5h -4)}{(5(x + h)-4)(5x -4)h}}\\\\ \lim_{h \to 0} \frac{-45h}{(5(x + h)-4)(5x -4)h}}\\\\\frac{-45}{(5x -4)^2}\)
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Anyone know the answer to this?
2(8+7)=(_×8)+(_×7)
Use the distributive property to fill in the blanks
Answers
Answer:
Just fill in the blanks with the number 2
Step-by-step explanation:
Since we are using the distributive property, 2(8+7) = (2x8)+(2x7)
value of 6 in 2,016?
Answers
Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.
Given, a number 2,016
we have to find the place and face value of 6 in the given number 2,016.
So, the Place value of 6 in the given number is ones.
Ones is the place value of the digit 6 in the number 2,016
Also, the Face value of 6 in the given number is 6.
6 is the face value of the digit 6 in the number 2,016
Hence, Ones is the place value of the digit 6 in the number 2,016 and 6 is the face value of the digit 6 in the number 2,016.
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PLEASE HELP WILL MARK BRAINLIEST!!!!!!!!! EXPLAIN
Answers
Answer:
devide the circle into 16 (8 above and 8 below)
The figure below is a net for a right rectangular prism.
11 m
13 m
11 m
7 m
11 m
11 m
What is the surface area of the right rectangular prism, in square meters?
Answers
The surface area of the right rectangular prism is given as follows:
358 m².
How to obtain the surface area?The surface area of a prism is obtained with the sum of the areas of each part of the prism.
The parts that compose the prism are given as follows:
Two rectangles of dimensions 7 ft and 12 ft.Two rectangles of dimensions 5 ft and 12 ft.Two rectangles of dimensions 5 ft and 7 ft.The area of a rectangle is given by the multiplication of each of the dimensions of the rectangle.
Hence the surface area of the prism is calculated as follows:
S = 2 x (7 x 12 + 5 x 12 + 5 x 7) = 358 m².
(multiplication by two due to the two rectangles with each of the dimensions).
Missing InformationThe prism is given by the image shown at the end of the answer.
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I need help asap thank you..
Answers
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
if you invest $550.00 and your annual interest is 4%, what will be the interest
Answers
The annual interest is $22.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Given;
Amount invested= $550
Annual interest= 4%
SI= 550*4*1/100
=5.5*4
=22
Therefore, the simple interest will be $22.
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find the exact value of each of the remaining trigonometric functions of 0. rationalize denominators when applicable.
sin 0 = v3/6 given that cos 0 = 0
Answers
Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).
sin^2(0) + cos^2(0) = 1
sin^2(0) = 1 - cos^2(0)
sin^2(0) = 1 - 0^2
sin^2(0) = 1
So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.
However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.
trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.
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What is 5 1/2 +2 1/7 due in one hour help please
Answers
Answer:
7 9/14
Step-by-step explanation:
1/2=7/14
1/7=2/14
7/14+2/14=9/14
5+2=7
Answer:
7.64285714286
Step-by-step explanation:
You may not need all those numbers so your answer may be 7.64 or something near it, but that is the approximate answer.
a+36=11
a+2b=8
using elimination
Answers
Answer:
a= -25
b = 16.5
,.............
.........
Answer:
a = -25
b = \(\frac{33}{2}\)
Step-by-step explanation:
Step 1 - Subtract 36 from both sides of the first equation:
a + 36 = 11
a + 36 - 26 = 11 - 36
a = -25
Step 2 - Substitute in the known a value:
a + 2b = 8
-25 + 2b = 8
Step 3 - Add 25 to both sides:
-25 + 2b + 26 = 8 + 25
2b = 33
Step 4 - Divide both sides by 2:
2b ÷ 2 = \(\frac{33}{2}\)
b = \(\frac{33}{2}\)
Hope this helps!
An MP3 player is on sale for $162.00 after a 10% discount. What was the original price?
Answers
Answer:
The original price is 180$
Answer:
Step-by-step explanation:
If there is a 10 percent discount, that means that this is 90 percent of the total.
So, let us find 10 percent is made up of how many dollars.
$162/9=$18 (do note that the slash sign means divide! When you write down the equation on a paper, please write the actual divide sign. Sorry for the inconvenience)
Since the original price is 100 percent, and we have 10 percent, that means we can just multiply the 10 percent by 10, to get 100 percent, as 10 times 10 is hundred.
$18x10=$180
Hope this helped! If you need another method, along with a different explanation, or separate, do comment below, so I can know. Any part you do not understand, please don't be afraid to tell me. If you think I can improve my answer, or change any parts to perhaps make it clearer, i'm open to suggestions!
3^x = 27^a+b and a^2-b^2/(a-b)=5 What is x?
Answers
Selena started her dog walking service in June to earn a little extra cash during the summer.If Selena made $255.30 after 30 days, how much did she make daily.
Answers
Using the unitary method we found that the amount Selena earned daily when she was a part of the dog walking service is $8.51.
What is meant by the unitary method?
The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
It comes in two different variations.
Direct variationInverse variationWhen there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other.
When there is an indirect variation, if we enhance one quantity, another item's value decreases.
Given,
Number of days worked = 30
Cash earned in 30 days = $255.30
We are asked to find the cash that Selena made daily when she did dog walking.
For this, we use the unitary method.
We know 30 days = $255.30
Then for one day = 255.30/30 = $8.51
Therefore the amount Selena earned daily when she was a part of the dog walking service is $8.51.
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What is the constant of proportionality in the equation y=25X?
Answers
Answer:
Step-by-step explanation:
y = kx
If y = 25x , then k = 25
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
Answers
Answer:
x² = 9/16 = 3/4
x² = 36/25 = 6/5
x³ = 64/125 = 4/5
x³ = 1/729 = 1/9
Step-by-step explanation: Just trust me. :)
A phone is £78 after a 35% discount how much was the original price.
Answers
Answer:
120
Step-by-step explanation:
Let's say the original price was 100x. After a 35% discount, the final price reduces to 65x. We know that 65x equals £78.
So if 65x= £78,
1x=78/65
If we multiply both sides by 100,
we get 100x=\(\frac{78}{65}\)*100
The original price was 100x and it is equal to 120.
Answer:
Price with discount: £78
Original price: x (we will give this the letter x, as we don't know the answer)
Decreased percentage: 35%
In this case, we subtract 35 from 100 (as percentage is out of 100), which will give us 65%.
Next, we make a table which shows £ and %, as shown in the picture. Then, we enter our details according to the headings which are "£" and "%".As shown in the picture, we then cross-multiply. We multiply 100 by 78 and x by 65.The workings must be something like the steps 1, 2 and 3 shown in the picture.Answer is, £120.
The zero of this function is 3 . What do you think "zero of a function" means?
Answers
The zeros of a function are the values of x that, when evaluated in the function, make the output of the function to be zero.
What doe the "zero of a function" means?A function is written in general form as y = f(x)
That notation says that, when we use the input "x" in a given function, that function "transforms" that input x into an output "y"
So y = f(x) is the value that the function takes for the input x.
A zero is an input of the function such that:
0 = f(x)
So the zeros are the inputs that have an output of zero, in this case you know that the function has a zero at 3, and as you can see, when x = 3, the function intercepts the x-axis, which is the axis defined by y = 0.
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Write an equation of the line perpendicular to the given line that contains P.
P(4, -7); y = 1/5x +2
Write an equation for the line in point-slope form.
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
Answers
Answer:
Step-by-step explanation:
perp. -5
y + 7 = -5(x - 4)
y + 7 = -5x + 20
y = -5x + 13
Mario compared the slope of the function graphed below to the slope of the linear function that has an x-intercept of 1 and a y-intercept of -2.
Find the slope of both lines. In the answer box give the slope of the steeper line.
Answers
Answer:
The linear equation in the slope-intercept form will be:
\(y\:=\:\frac{2}{3}x+64\)
Step-by-step explanation:
From the line graph, taking two points
(21, 78)(27, 82)Finding the slope between (21, 78) and (27, 82)
\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)
\(\left(x_1,\:y_1\right)=\left(21,\:78\right),\:\left(x_2,\:y_2\right)=\left(27,\:82\right)\)
\(m=\frac{82-78}{27-21}\)
\(m=\frac{2}{3}\)
We know that the slope-intercept of the line equation is
\(y = mx+b\)
where m is the slope and b is the y-intercept
substituting (21, 78) and m = 2/3 in the slope-intercept of the line
\(y = mx+b\)
\(78=\frac{2}{3}\left(21\right)+b\)
switch sides
\(\frac{2}{3}\left(21\right)+b=78\)
\(14+b=78\)
\(b=64\)
substituting b = 64 and m = 2/3 in the slope-intercept of the line
\(y = mx+b\)
\(y\:=\:\frac{2}{3}x+64\)
Therefore, the linear equation in the slope-intercept form will be:
\(y\:=\:\frac{2}{3}x+64\)
Albinism in humans is autosomal and fully recessive to normal color. A couple, who are both normal, have a daughter who is albino and a son who is normal. The couple wants to have 3 more children. What is the probability that they will have 3 normal girls?
Answers
The probability that the couple will have 3 normal girls is approximately 0.422
Since both parents are normal, they both have to be heterozygous carriers for the recessive allele that causes albinism. We can represent the normal allele with the letter N and the albino allele with the letter n. Then, we can write the genotypes of the parents as Nn x Nn.
The daughter is albino, so her genotype must be nn. The son is normal, so his genotype must be Nn.
We want to find the probability that the couple will have 3 normal girls. We can use the multiplication rule of probability to find this probability:
P(3 normal girls) = P(normal girl) x P(normal girl) x P(normal girl)
The probability of having a normal girl is 3/4 since there are three possible genotypes that result in a normal phenotype (NN, Nn, Nn) out of a total of four possible genotypes. The probability of having a normal boy is also 3/4, for the same reason.
Therefore, the probability of having 3 normal children (in this case, girls) is:
P(3 normal girls) = (3/4) x (3/4) x (3/4) = 27/64 ≈ 0.422
So, the probability that the couple will have 3 normal girls is approximately 0.422, or about 42.2%.
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Tania has a roll of cloth that is
52.5
52.5 feet long. She uses the cloth to make scarves that are each
3.75
3.75 feet long. How many scarves can Tania make?
Answers
Answer:
Tania can make 14 scarves.
Step-by-step explanation:
You get this answer by dividing 52.5 by 3.75.
find the exact value of cosine theta given that sin theta equals -12/13 and theta is in the quadrant three
Answers
Answer:
cos θ = -5/13
Step-by-step explanation:
sin θ = -12/13
Use Pythagorean identity.
sin²θ + cos²θ = 1
(-12/13)² + cos²θ = 1
144/169 + cos²θ = 1
cos²θ = 25/169
cos θ = ±5/13
θ is in the 3rd quadrant, so cos θ < 0.
cos θ = -5/13
Find the surface area of the figure
a. 150 square cm
b. 228.4 square cm
c. 78.4 square cm
d. 210 square cm
Answers
Answer:
c
Step-by-step explanation:
One side of a triangle is three times the shortest side.
"The third side is 7 feet more than the shortest side. The
perimeter is 62 feet. Find all three sides.
Answers
Answer:
The lengths of the sides are - 11, 18, 33
Step-by-step explanation:
Shortest side = x
Second side = 3x
Third side = 7 + x
Perimeter = sum of all three sides
62 = x + 3x + x + 7
62 = 5x + 7
55 = 5x
x = 11
Shortest side = x = 11
Second side = 3x = 33
Third side = 7 + x = 18
Movie executives want to know if a movie watcher’s heart rate increases when they watch certain types of movies. Subjects in the experiment were given a free movie ticket and randomly assigned to watch one of four movies: an action-adventure film, a horror film, a romantic comedy, or an animated children’s film. They measured the average heart rate of all subjects while watching the assigned film.
Which of the following is the most appropriate statistical test to use to test if the average heart rate of the movie watchers was different for the four types of movies?
A. Matched pairs t-test
B. Chi-squared test for independence
C. ANOVA
D. Two-sample t-test
E. Inference for regression
Answers
Answer:
The correct option is C
Step-by-step explanation:
ANOVA is the correct option because it can be used to carry out comparison of average of more than two groups
answer asap..........
Answers
Answer:
Quadrant I: (⅓, 2⅓)
Quadrant II: (-1⅓, 3⅓)
Quadrant III: (-3, -10) (-3⅓, -1⅓)
Quadrant IV: (9, -1)
Step-by-step explanation:
If it is (+, +), it is in quadrant I.
If it is (-, +), it is in quadrant II.
If it is (-, -), it is in quadrant III.
If it is (+, -), it is in quadrant IV.
Write the logarithmic expression as a single logarithm with coefficient , and simplify as much as possible. Assume that all variable expressions represent positive real numbers.
1/2ln(b^2+1)-1/2ln(b+1)
Answers
Answer:
hope you can understand
