Answer:
There is insufficient statistical evidence to prove that the companies stated color distribution is not correct therefore, the overall proportions of the colors are correctly stated as above
Step-by-step explanation:
We have that
H₀: 0.24 blue, 0.13 brown, 0.20 green, 0.16 orange, 0.13 red and 0.14 yellow
The Data given are as follows;
Hₐ: The stated distribution of M&M is incorrect
Blue Brown Green Orange Red Yellow Total
Observed: 105 72 89 84 70 80 500
Expected: 120 65 100 80 65 70
We have;
[tex]\chi ^{2}=\dfrac{\left (105-120 \right )^{2}}{120}+ \dfrac{\left (72-65\right )^{2}}{65} + \dfrac{\left (89-100\right )^{2}}{100} + \dfrac{\left (84-80\right )^{2}}{80} + \dfrac{\left (70-65\right )^{2}}{65} + \dfrac{\left (80-70\right )^{2}}{70} = 5.85[/tex]
At 6 - 1 = 5 degrees of freedom we find the p-value from the chi squared table as follows
P(0.05) at 5% degrees of freedom =11.070 hence our P-value is larger than 0.05 and we fail to reject the null hypothesis, hence there is insufficient statistical evidence to prove that the companies stated color distribution is not correct.
A line contains the points (3,1) and (-6,4). What is the equation for this line in slope-intercept form?
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Equation of line in slope-intercept form is given by
y = mx +c
where m is the slope of line
c is y intercept
Slope of line having points (x1, y1) and (x2,y2) is given by (y2-y1)/(x2-x1)
_________________________________________________
let the equation of required line be y = mx +c
Since points given are (3,1) and (-6,4)
Then, its slope is
m = 4-1/-6-3 = 3/-9 = -1/3
Thus, slope of line is m = -1/3
lets use m = -1/3 in place of m in equation y = mx +c
y = (-1/3)x + c
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation.
hence lets plug 3 in place of x and 1 in place of y
1 = (-1/3)3 + c
=> 1 = -1 + c
=> c = 1 +1 = 2
Thus, intercept is 2.
Thus, Equation of line in slope-intercept form is y = (-1/3)x + 2.
How can you convert the Heun’s Method into the Implicit Heun’s Method? Show an example
Answer:
Heun's method is also known by its other name called Modified Euler methods. This method is used in computational or mathematical science.
Step-by-step explanation:
Euler method is the method that is also pronounced in two similar stages such as Runge- Kutta methods. This method has been named after Dr. Heun.
This method is used for the solution of ordinary differential equations with its given values. There is some method to calculate this method. The improved Runge Kutta methods are also called the Butcher tableau method, the other methods are also called the Ralston methods.
How many numbers can you make between 0-99 using exactly four 4s and the operations $$ +,−,×,÷?
Answer:
37
Step-by-step explanation:
I find 37 numbers in that range:
{0, 1/16, 1/8, 1/5, 1/3, 1/2, 3/4, 4/5, 1, 5/4, 4/3, 2, 3, 7/2, 15/4, 4, 17/4, 9/2, 5, 6, 7, 8, 9, 12, 15, 16, 17, 20, 24, 28, 32, 36, 48, 60, 64, 68, 80}
For these numbers we have used only the indicated operations. No minus signs were used.
_____
Additional comment
Of the 320 ways the numbers can be combined, 15 result in division by zero. Many other results are outside the 0-99 range of interest. In total, there are 56 unique rational results.
A motorboat moves across the lake at a constant speed when it begins it is which function describes the motor boats distance from the shore a Y equals 4X +50 PY equals 9X +50 CY equals negative 9X +50 DY equals negative 4X +50
Triangle 1 is similar to triangle 2.
what is the question? is there an image
Country financials, a financial services company, uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. In February 2012, a sample of 1000 adults showed 410 indicating that their financial security was more that fair. In Feb 2010, a sample of 900 adults showed 315 indicating that their financial security wwas more than fair.1. State the hypothesis that can be used to test for a significant difference between the population proportions for the two years?2. What is the sample proportion indicating that their financial security was more that fair in 2012?In 2010?3. Conduct the hypothesis test and compute the p-value.At a .05 level of significance what is your conclusion?4. What is the 95% confidence interval estimate of the difference between the two population proportion?
Answer:
1) The null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
Subindex 1: 2012 population proportion and Subindex 2: 2010 population proportion.
2) The sample proportion for 2012 is p1=0.41.
The sample proportion for 2010 is p2=0.35.
3) There is enough evidence to support the claim that there is significant difference between the population proportions of the two years.
4) The 95% confidence interval for the difference between proportions is (0.016, 0.104).
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that there is significant difference between the population proportions of the two years.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2\neq 0[/tex]
The significance level is 0.05.
The sample 1, of size n1=1000 has a proportion of p1=0.41.
[tex]p_1=X_1/n_1=410/1000=0.41[/tex]
The sample 2, of size n2=900 has a proportion of p2=0.35.
[tex]p_2=X_2/n_2=315/900=0.35[/tex]
The difference between proportions is (p1-p2)=0.06.
[tex]p_d=p_1-p_2=0.41-0.35=0.06[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{410+315}{1000+900}=\dfrac{725}{1900}=0.3816[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.3816*0.6184}{1000}+\dfrac{0.3816*0.6184}{900}}\\\\\\s_{p1-p2}=\sqrt{0.0002+0.0003}=\sqrt{0.0005}=0.0223[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.06-0}{0.0223}=\dfrac{0.06}{0.0223}=2.69[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as (using a z-table):
[tex]P-value=2\cdot P(z>2.69)=0.007[/tex]
As the P-value (0.007) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is significant difference between the population proportions of the two years.
We want to calculate the bounds of a 95% confidence interval.
For a 95% CI, the critical value for z is z=1.96.
The margin of error, using the results previously calculated, is:
[tex]MOE=z \cdot s_{p1-p2}=1.96\cdot 0.0223=0.0437[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=(p_1-p_2)-z\cdot s_{p1-p2} = 0.06-0.0437=0.016\\\\UL=(p_1-p_2)+z\cdot s_{p1-p2}= 0.06+0.0437=0.104[/tex]
The 95% confidence interval for the difference between proportions is (0.016, 0.104).
image 30 points) math
Answer:
[tex]\pi =\frac{C}{d}[/tex]
Step-by-step explanation:
[tex]C=\pi d[/tex]
[tex]\pi =\frac{C}{d}[/tex]
Answer:
I'm not 100%sure but i'm think that it is c
Step-by-step explanation:
Hope this helps! May have gotten it wrong really sorry if I did
Which of the following describe an angle with a vertex at Y?
Check all that apply.
Answer:
X
Step-by-step explanation:
X and Y make up a graph
you secure a mortgage to buy a house with a loan of $140,000 at 8.5% for 20 years. answer the following questions about that loan for the first two months of payments: a) what is the monthly payment? b)how much of the monthly payment goes toward interest when you submit your first payment? c)what is your balance after the first payment? d) how much of the monthly payment goes toward interest when you submit your second payment? e) what is your balance after the second payment?
Answer:
monthly payment $1214.951st month's interest $991.67balance after 1st payment $139,776.722nd month's interest $990.09balance after 2nd payment $139,551.86Step-by-step explanation:
The monthly interest rate is ...
[tex]\dfrac{8\%}{12}=0.00708\overline{3}[/tex]
a) The monthly payment is given by the amortization formula:
A = Pr/(1 -(1+r)^-n)
where r is the monthly interest rate on a loan of amount P for n months.
A = $140,000(0.0070833)/(1 -(1.0070833^-240)) = $1214.95
The monthly payment is $1214.95.
__
b) The amount to interest is the product of the remaining principal and the monthly interest rate.
first month's interest = $140,000·0.0070833 = $991.67
__
c) The balance after the first payment is ...
new balance = $140,000 +991.67 -1214.95 = $139,776.72
__
d) The amount to interest for the second payment is computed the same way:
second month's interest = $139,776.72·0.00708333 = $990.09
__
e) The balance after the second payment is computed the same way:
new balance = $139,776.72 +990.09 -1214.95 = $139,551.86
If p=(-3,-2) and q=(1,6) are the endpoints of the diameter of a circle find the equation of the circle
Answer:
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Step-by-step explanation:
Given points end Points are p(-3,-2) and q( 1,6)
The distance of two points formula
P Q = [tex]\sqrt{x_{2} - x_{1})^{2} + ((y_{2} -y_{1})^{2} }[/tex]
P Q = [tex]\sqrt{1 - (-3)^{2} + ((6 -(-2))^{2} }[/tex]
P Q = [tex]\sqrt{16+64} = \sqrt{80}[/tex]
The diameter 'd' = 2 r
2 r = √80
= [tex]\sqrt{16 X 5}[/tex]
= [tex]4 \sqrt{5}[/tex]
r = 2√5
Mid-point of two end points
[tex](\frac{x_{1} + x_{2} }{2} , \frac{y_{1} +y_{2} }{2} ) = (\frac{-3+1}{2} ,\frac{-2 +6}{2} )[/tex]
= (-1 ,2)
Mid-point of two end points = center of the circle
(h,k) = (-1 , 2)
The equation of the circle
(x -h )² +(y-k)² = r²
(x -(-1) )² +(y-(2))² = (2(√5))²
x² + 2 x + 1 + y² - 4 y + 4 = 20
x² + 2 x + y² - 4 y = 20 -5
x² + 2 x + y² - 4 y = 15
Final answer:-
The equation of the circle (x +1) )² +(y-(2))² = (2(√5))²
or
The equation of the circle x² + 2 x + y² - 4 y = 15
Answer:
-1 , 2 , 20Step-by-step explanation:
( x - -1 ) ² + ( y - 2 ) ² = 20Which type of reasoning allows you to use observation to find the next three
values in the number pattern 1,4,7,10....?
A. Deduction
B. Induction
C. Decision making
D. Proof
Plz help me
Answer:
Induction
Step-by-step explanation:
Induction reasoning refers to conjectures which is what you will need for this
The Inductive reasoning allows to use observation to find the next three
values in the number pattern 1, 4, 7, 10, . . .
The correct answer is option (B)
What is inductive reasoning?It is a reasoning that is based on patterns you observe. By observing the pattern in the sequence, we can use inductive reasoning to decide the next successive terms of the sequence.A conclusion you reach using inductive reasoning is called a conjectureFor given example,
We have been given the number pattern 1, 4, 7, 10, . . .
Here, 4 - 1 = 3 ..................(i)
7 - 4 = 3 ..................(ii)
10 - 7 = 3 ..................(iii)
From (i), (ii) and (iii),
the common difference between consecutive terms is 3.
The next three values would be,
10 + 3 = 13
13 + 3 = 16
16 + 3 = 19
So, the number pattern would be 1, 4, 7, 10, 13, 16, 19, . . .
Therefore, an Inductive reasoning allows to use observation to find the next three values in the number pattern 1, 4, 7, 10, . . .
The correct answer is option (B)
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The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48
The correct answer is B. 24
Explanation:
If you consider the shaded part of the rectangle is a triangle the best way to calculate the area of this is by calculating the total area or space occupied by this triangle. This can be done if you multiply the base by the height and divide the result in 2 or b x h / 2.
6 squares (base) x 8 squares (height) = 48 / 2 = 24 squares
Also, the shaded area is approximately the half area of all the rectangle, in this case, you can calculate the area of the rectangle by multiplying side x side or length by width. This means 6 squares x 8 squares = 48 squares (total area), which divided by 2 (shaded area) is also equal to 24.
Answer:
B, 24.
Step-by-step explanation:
I solved it with my teacher
For each of the sequences below, find a formula that generates the sequence. (a) 4, 10, 16, 22, 28, 34, 40, . . . (b) 5, 15, 45, 135, 405, . . . (c) 10, 20, 10, 20, 10, 20, 10
Answer:
[tex](a) \: 6n-2\\(b)\: 5 \times 3^{n-1}\\(c)\: 5({-1^n}+3)[/tex]
Step-by-step explanation:
[tex]6(1)-2=4[/tex]
[tex]6(2)-2=10[/tex]
[tex]5 \times 3^{(3)-1}=45[/tex]
[tex]5 \times 3^{(4)-1}=135[/tex]
[tex]5(-1^{(5)}+3)=10[/tex]
[tex]5(-1^{(6)}+3)=20[/tex]
a) The formula that generates the sequence 4, 10, 16, 22, 28, 34, 40 is an = 4 + 6 * (n - 1)
b) The formula that generates the sequence 5, 15, 45, 135, 405 is an = 5 * 3ⁿ⁻¹
c) The formula that generates the sequence 10, 20, 10, 20, 10, 20, 10 is an = 10 + 10 * ((n + 1) % 2)
(a) The sequence increases by 6 at each step. To generate the sequence, we can use the formula: an = 4 + 6 * (n - 1), where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(b) The sequence is a geometric progression with a common ratio of 3. To generate the sequence, we can use the formula: an = 5 * 3ⁿ⁻¹ where "an" represents the nth term in the sequence, and "n" is the position of the term in the sequence.
(c) The sequence alternates between 10 and 20. To generate the sequence, we can use the formula: an = 10 + 10 * ((n + 1) % 2), where "an" represents the nth term in the sequence, and "%" represents the modulo operation, which results in 0 when n is even and 1 when n is odd. So, when n is even, an = 10, and when n is odd, an = 10 + 10 = 20.
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A cylinder with a base diameter of x units has a volume of
cubic units
Which statements about the cylinder
options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is ax? square units.
The area of the cylinder's base is nx square units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Corrected Question
A cylinder with a base diameter of x units has a volume of [tex]\pi x^3[/tex] cubic units
Which statements about the cylinder are true? Check all that apply.
The radius of the cylinder is x units. The radius of the cylinder is 2x units. The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The area of the cylinder’s base is [tex]\dfrac{1}{2}\pi x^2[/tex] square units. The height of the cylinder is 2x units. The height of the cylinder is 4x units.Answer:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius [tex]=\dfrac{x}{2}$ units[/tex]
Area of the base [tex]=\pi r^2 =\pi (\dfrac{x}{2})^2 =\dfrac{\pi x^2}{4}$ square units[/tex]
Volume =Base Area X Height
[tex]\pi x^3 =\dfrac{\pi x^2}{4} X h\\$Height, h = \pi x^3 \div \dfrac{\pi x^2}{4}\\=\pi x^3 \times \dfrac{4}{\pi x^2}\\h=4x$ units[/tex]
Therefore:
The area of the cylinder’s base is [tex]\dfrac{1}{4}\pi x^2[/tex] square units. The height of the cylinder is 4x units.
What is the exact value of tan4pi/3?
Answer:
√ 3Step-by-step explanation:
The exact value of tan 4π/3 is √3.
What is Trigonometry?Trigonometry is a discipline of mathematics dealing with specific angle functions and their application to calculations. In trigonometry, there are six functions of an angle that are often utilised. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their names and acronyms (csc).
We have to find the exact value of tan4pi/3.
tan 4π/3
= tan (π + π/3)
= tan (π/3)
= √3.
So, the value is √3.
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if you’re probability surveys in math 30 please help it’s simple but i don’t remember how to do it!!
Answer:
4 C, 5 C
Step-by-step explanation:
4) Sum of all candies = 14
Total number of cherry candies = 5
probability of not getting a cherry candy = 14-5 / 14 = 9/14
5) Number of supporters for Lyshon = 14
Total number of supporters = 100
Probability that a student chosen at random will vote vote for lyshon =
14/100 = 7/50
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages? Use the empirical rule.Enter your answer as a percent rounded to two decimal places if necessary.
Answer:
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 185
Standard deviation = 26
The normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.
What is the probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages?
133 = 185 - 2*26
So 133 is two standard deviations below the mean.
By the Empirical Rule, of the 50% of the measures below the mean, 95% are within 2 standard deviations of the mean, that is, above 133 and below 185. The other 5% is below 133
p = 0.05*0.5 = 0.025
2.5% probability that a randomly selected book has fewer than 133 pages if the mean is 185 pages and the standard deviation is 26 pages
Find the required annual interest rate to the nearest tenth of a percent for $1100 to grow to $1900 if interest is compounded quarterly for 10yr. The required annual interest rate is _%?
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1100
A = 1900
n = 4 because it was compounded 3 times in a year and n = 12/3 = 4
t = 10 years
Therefore,.
1900 = 1100(1 + r/4)^4 × 10
1900/1100 = (1+ r/4)^40
1.73 = (1+ r/4)^40
Taking log to base 10 of both sides, it becomes
Log 1.73 = 40log(1 + 0.25r)
0.238 = 40log(1 + 0.25r)
Log(1 + 0.25r) = 0.238/40 = 0.00595
Take exponent of both sides, it becomes
10^log(1 + 0.25r) = 10^0.00595
1 + 0.25r = 1.0138
0.25r = 1.0138 - 1 = 0.0138
r = 0.0138/0.25
r = 0.0552
The The required annual interest rate is
0.0552 × 100 = 5.5%
An electrician charges $40 per visit, and $20 per hour of work. On a particular day, he made 3 visits and calculated that his average earnings were $50 per hour. Use this information to complete the statement. He worked hours that day.
Answer:
4 hours
Step-by-step explanation:
For three visits, the electrician earned $40 × 3 = $120 in "per-visit" charges. For working x hours, he earned 20x in "per-hour" charges. The total of these came to 50x:
120 +20x = 50x
120 = 30x . . . . . . . . subtract 20x
4 = x . . . . . . . . . . . . . divide by 30
The electrician worked 4 hours that day.
This rule applies: rational•___
= rational.
Answer:
rational
Step-by-step explanation:
it's rational because a rational number * a irrational number is always irrational. a rational number times a rational number = a rational number. here are examples:
case 1 irrational times rational:
root two * 4 = 5.65685424949
case 2 rational times rational
8 * 5 = 40
what is the solution set of the inequality 5x-9<21
Answer:
x < 6
Step-by-step explanation:
5x < 21 +9
5x < 30
x < 30/5
x < 6
so the value of x is 5,4,3,2,1, 0, -1, ....
Answer: x<6
Step-by-step explanation:
For this problem, we approach it as if it had an equal sign instead of an inequality.
5x-9<21 [add 9 on both sides]
5x<30 [divide 5 on both sides]
x<6
SIMPLIFY THE EXPRESSION -4 X 4 X 4 X 4 X4 X 4 X 4 X4
Answer:
-4 · [tex]4^{7}[/tex]
Step-by-step explanation:
Please answer this correctly
Answer:
8000 cubic centimeters
Step-by-step explanation:
The surface area of a cube is 6 times the square of the side length. If we call the side length of the cube s:
[tex]6s^2=2400 \\\\s^2=400 \\\\s=20[/tex]
Since the volume of a cube is the side length cubed, the volume of this is [tex]20^3=8000\text{ cm}^3[/tex].
Hope this helps!
If f(x) = + 8, what is f(x) when x = 10?
Answer:
We know that x = 10. But, we don't know what f is. In order to find f, we would divide. To divide we would use this formula: 8 ÷ 10. This equals 0.8 or 8 tenths. Now, we know what our f value is. It's 0.8! To double check, use a calculator and type in: 10*0.8 and see if the answer is 8. (Please mark brainliest! :D)
Work out 12+8÷(9-5) 0.018÷0.06 Express as single fraction 5/7÷2/5
Step-by-step explanation:
I don't know if the first set of numbers is all in one set, but I'll do my best to give you an answer.
Really all you need to do is use PEMDAS for the first question.
(Parentheses, exponents, multiply, divide, add, subtract. In that order)
[tex]1 2 + 8 \div (9 - 5) \\ 12 + 8 \div 4 \\ 12 + 2 \\ 14[/tex]
Then to simplify that fraction next to it, notice that 0.018 is 3x 0.06.
that's a 3:1 ratio, so it ends up simplifying to this:
[tex] \frac{3}{1} [/tex]
Lastly, to solve the division of that fraction. If you divide by a fraction, you multiply whatever it's dividing by its inverse.
So...
[tex] \frac{5}{7} \div \frac{2}{5} \\ \frac{5}{7} \times \frac{5}{2} \\ \frac{25}{14} [/tex]
f(x)=x^2-2x+3x; f(x)=-6x
Answer:
(-3,18) and (-1,6)
Step-by-step explanation:
[tex]x^2-2x+3=-6x\\<=> x^2+4x+3 = 0\\<=> (x+2)^2 -4+3=0\\<=> (x+2)^2-1^2 = 0\\<=> (x+2+1)(x+2-1) = 0\\<=> (x+1)(x+3) = 0\\<=> x+1 = 0 \ or \ x+3 = 0\\<=> x = -1 \ or \ x=-3[/tex]
so the solutions are
(-3,-6*-3=18) that we can write (-3,18)
and
(-1,-6*-1=6) that we can write (-1,6)
According to a recent census, 16% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which has a random sample of 437 county residents, and found that 44 of those surveyed are of Hispanic origin.Randomization condition:Choose the correct statement.Select one:a. The 437 county residents were a voluntary response sample of all county residents.b. The 437 county residents is a systematic response sample of all county residents.c. The 437 county residents were a random sample of all county residents.
Answer:
Option C is correct.
The 437 county residents were a random sample of all county residents.
a) If p is the proportion of Hispanics in the county,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.35
b) The model of the test is two-tailled, one-proportion test. And it satisfies all of the required conditions for an hypothesis test.
c) The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
Test statistic = -4.09
p-value = 0.000043
d) We can conclude that the proportion of the county that are Hispanics is different from the proportion of the country that are Hispanics.
Step-by-step explanation:
According to the question, it was clearly stated that the 437 county residents are a random sample of the residents in the county, hence, it is evident that option C is the right statement.
a) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question, the county supervisor wants to check if proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. (0.16).
Hence, the null hypothesis is that there isn't enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics. That is, there is no significant difference between the proportion of the county that are Hispanics and the proportion of the whole nation that are Hispanics. (0.16).
The alternative hypothesis will now be that enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics (0.16).
Mathematically,
The null hypothesis is represented as
H₀: p = 0.16
The alternative hypothesis is represented as
Hₐ: p ≠ 0.16
b) To do this test, we will use the z-distribution because although, no information on the population standard deviation is known, the sample size is large enough.
Hence, the model of this test is two-tailled, one-proportion test.
And the major conditions for an hypothesis test is that
- The sample must be a random sample extracted from the population, with each variable in the sample independent from one another. This is already clearly given in the question.
- The sample must be a normal distribution sample or approximate a normal distribution.
The conditions to check this is that
np ≥ 10
and
np(1-p) ≥ 10
p = sample proportion = (44/437) = 0.101
np = 437×0.101 = 44 ≥ 10
np(1-p) = 437×0.101×(1-0.101) = 39.7 ≥ 10
The two conditions are satisfied, hence, we can conclude that this distribution at least approximates a normal distribution.
c) So, we compute the t-test statistic
z = (x - μ)/σₓ
x = sample proportion = 0.101
μ = p₀ = The proportion we are comparing against = 0.16
σₓ = standard error = √[p(1-p)/n]
where n = Sample size = 437
σₓ = √[0.101×0.899/437] = 0.0144145066 = 0.0144
z = (0.101 - 0.16) ÷ 0.0144
z = -4.093 = -4.09
checking the tables for the p-value of this z-statistic
Degree of freedom = df = n - 1 = 437 - 1 = 436
Significance level = 0.05 (when the significance level isn't stated, 0.05 is used)
The hypothesis test uses a two-tailed condition because we're testing in both directions (greater than or less than).
p-value (for z = -4.09, at 0.05 significance level, df = 436, with a two tailed condition) = 0.000043
The sketch of the region of acceptance is presented in the attached image to this answer. (z < -4.09 and z > 4.09).
d) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, significance level = 0.05
p-value = 0.000043
0.000043 < 0.05
Hence,
p-value < significance level
This means that we reject the null hypothesis, accept the alternative hypothesis & say that there is enough evidence to conclude that the proportion of the county that are Hispanics is different from the proportion of the whole nation that are Hispanics.
Hope this Helps!!!
PLEASE HELP !! ASAPPP
Instructions: State what additional information is required in order to know that the triangles are congruent for the given reason. Given: AAS
The curved arcs indicate which angles are congruent with one another. The single arcs on angles R and I mean these two angles are congruent. The double arcs on angles Q and H are the other pair of congruent angles.
So far we have taken care of the two "A"s in "AAS". What we're missing is the "S", which refers to the side. This side cannot be between the two angles, otherwise we'd be talking about ASA instead of AAS.
There are two possible answers here
the first possible answer is QP = HGthe second possible answer is RP = IGif either one of those congruences are true, then we have enough to use AAS
Some books use SAA in place of AAS, and they're the same thing.
What is the volume of the container below? 2 rectangular prisms. A rectangular prism has a length of 14 inches, width of 6 inches, and height of 16 inches. A rectangular prism has a length of 10 inches, width of 6 inches, and height of 4 inches. 576 inches cubed 1,080 inches cubed 1,584 inches cubed 1,920 inches cubed
PLEASE ANSWER FAST ITS MY CUMULATIVE EXAM
Answer:
The volume of the container is 1584 inch³.
Step-by-step explanation:
The volume of a rectangular prism is:
[tex]\text{Volume}=\text{l}\times\text{w}\times\tect{h}[/tex]
It is provided that the container is made up of two rectangular prisms.
The dimensions are as follows:
Prism 1: length of 14 inches, width of 6 inches, and height of 16 inches.Prism 2: length of 10 inches, width of 6 inches, and height of 4 inches.Compute the volume of the rectangular prism 1 as follows:
[tex]\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex][tex]\text{V}_{1}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex]
[tex]=14\times 6\times 16\\=1344[/tex]
Compute the volume of the rectangular prism 2 as follows:
[tex]\text{V_{1}}=\text{l}_{1}\times\text{w}_{1}\times\text{h}_{1}[/tex][tex]\text{V}_{2}=\text{l}_{2}\times\text{w}_{2}\times\text{h}_{2}[/tex]
[tex]=10\times 6\times 4\\=240[/tex]
Then the volume of the container will be:
[tex]\text{Volume of container}=\text{V}_{1}+\text{V}_{2}[/tex]
[tex]=1344+240\\=1584[/tex]
Thus, the volume of the container is 1584 inch³.
Answer:
Step-by-step explanation:
What is the volume of the container below?
2 rectangular prisms. A rectangular prism has a length of 14 inches, width of 6 inches, and height of 16 inches. A rectangular prism has a length of 10 inches, width of 6 inches, and height of 4 inches.
576 inches cubed
1,080 inches cubed
1,584 inches cubed
1,920 inches cubed
How do you solve -3/5(x)=6
Answer:
-10
Step-by-step explanation:
[tex]-\dfrac{3}{5}x=6 \\\\\\x=\dfrac{6}{-\dfrac{3}{5}} \\\\\\x=6\times -\dfrac{5}{3} \\\\\\x=-10[/tex]
Hope this helps!
Answer:
x = -10
Step-by-step explanation:
So first and easily we have to multiply to --> -3/5x = 6
After that you just do the regular formula -->
Factor divided by the x
6 / (-3/5) = -10
-10
Hope this helps