To use the standard deviation formula in a significance test, the sample must be random and the population standard deviation should typically be unknown, while approximation with a normal distribution requires a sufficiently large sample size and the success-failure condition for proportions. Choosing the correct distribution depends on whether the standard deviation is known and the sample size.
Explanation:Conditions for Using the Standard Deviation Formula and Approximating with a Normal Distribution
For conducting a significance test using the standard deviation formula, certain conditions must be met:
The sample must be randomly selected.If surveying a proportion, we use \( \hat{p} \) for samples and \( p \) for populations.If calculating a sample standard deviation, the population standard deviation should be unknown.The sample size should be sufficiently large if the population distribution is not normal (usually n > 30).To approximate the sample distribution with a normal distribution, particularly when conducting hypothesis testing:
The sample size must be large enough (typically n > 30).The sample should be randomly selected and should represent the population.For proportions, the sample should meet the success-failure condition where \( np \geq 10 \) and \( n(1-p) \geq 10 \).The conditions for a hypothesis test often include:
Stating the null and alternative hypotheses.Deciding on a significance level (e.g., \( \alpha = 0.05 \)).Knowing whether population parameters are known, which determines the choice of test statistic.Finding the p-value and comparing it with the significance level to make a decision.Examples of Hypothesis Testing with Different Conditions
If you know the population standard deviation, you might use the z-distribution for hypothesis testing.If the population standard deviation is unknown but the sample size is large, the t-distribution might be the appropriate choice.The F-statistic is used when comparing two variances, such as two standard deviations of test scores.When determining the number of significant figures in a number, zeroes to the left of the decimal point are never counted.
a. True
b. False?
Two ants race across a table 61 cm long. one travels at 5.13 cm/s and the other at 3.99999 cm/s. when the first one crosses the finish line, how far behind is the second one? answer in units of cm
He scatter plot shows the number of pages scanned (y) in different number of hours (x) by a scanning machine: which function best represents the data shown in the scatter plot
can someone help me, i am very confused, i need to find the volume of the figure put i dont know how
please help me and write steps
If Polly walks across the street to buy a cracker and the people who sell them only have one left and there's a long line out the door... will Polly get a cracker? I'm so confused :/ thanks so much for the help!
In the triangle below, determine the measure of side a.
Use basic identities to simplify the expression.
cos θ - cos θ sin2θ
The solution for the expression will be cos Ф - cos Ф.sin² Ф = cos³ Ф.
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate to a triangle's side length and angle.
The given trigonometric expression will be solved as below,
cos Ф - cos Ф.sin² Ф
We know that, sin² Ф = 1 - cos² Ф
E = cos Ф - cos Ф( 1-cos² Ф)
E = cos Ф - cos Ф - cos³ Ф
E = cos³ Ф
Therefore, the expression is cos Ф - cos Ф.sin² Ф = cos³ Ф.
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Assume that a researcher randomly selects 14 newborn babies and counts the number of girlsâ selected, x. the probabilities corresponding to the 14 possible values of x are summarized in the given table. find the probability of selecting 9 or more girls.
To find the probability of selecting 9 or more girls out of 14 newborn babies, sum the probabilities for selecting 9 to 14 girls from the given table.
Explanation:To find the probability of selecting 9 or more girls out of 14 babies, we need to calculate the sum of the probabilities of selecting 9, 10, 11, 12, 13, and 14 girls. Refer to the given table that summarizes the probabilities for each value of x. Add the probabilities for these values to get the probability of selecting 9 or more girls.
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Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4)? a 180 (dagree) rotation about the origin a 90 (dagree) counterclockwise rotation about the origin and a translation down 4 units a 90 (dagree) clockwise rotation about the origin and a reflection over the y-axis a reflection over the y-axis and then a 90(dagree) clockwise rotation about the origin
The triangle ABC is mapped to A'B'C' through a 180-degree rotation about the origin, as all the points' x and y coordinates have changed signs, consistent with this transformation.
To determine which transformations can map the original triangle ABC to the new triangle A'B'C', we must closely examine the coordinates given and analyze the possible transformations.
Looking at the coordinates:
A(2, 2) to A'(-2, -2) suggests a reflection over the origin, which can be considered as a 180-degree rotation around the origin.
B(4, 1) to B'(-1, -4) also suggests a similar transformation, as the x and y values are negated and swapped in position.
C(4, 5) to C'(-5, -4) follows the same pattern.
All these transformations indicate that the original triangle has been rotated 180 degrees about the origin. This can also be observed by noting that the x and y coordinates have simply changed their signs, an effect of 180-degree rotation about the origin. This satisfies the claim of the classical geometry theorem which states that such transformations can be expressed as either a translation or a rotation. In this case, it's purely a rotation as there's no translation component.
The range of the function f(x) = x + 5 is {7, 9}. What is the function’s domain?
{2, 4}
{-2, -4}
{12, 14}
{-12, -14}
{0, 5}
which choice is equal to the repeating decimal below? 0.6
a) 0.666
b) 6/10
c) 0.66666666
The rule T1, -4 RO, 180°(x, y) is applied to rectangle KLMN. Which rectangle shows the final image??
Answer:
Figure 3.
Step-by-step explanation:
We perform the rotation first. A 180° rotation about the origin maps every point
(x, y)→(-x, -y). This means it negates both the x- and y-coordinates.
The pre-image points are:
K(3, -4); L(3, -1); M(5, -1); N(5, -4). Performing the rotation and negating the coordinates will give us:
K'(-3, 4); L'(-3, 1); M'(-5, 1); N'(-5, 4).
Now we perform the translation. The translation rule is <1, -4>; this means we add 1 to each x-coordinate and subtract 4 from each y-coordinate. This maps to our new points:
K''(-2, 0); L''(-2, -3); M''(-4, -3); N''(-4, 0)
These are the points of figure 3.
URGENT
A committee of 3 people is to be randomly selected from a group of 5 women and 8 men. What is the probability that the committee will consist only of women?
A.
5/143
B.
7/143
C.
28/143
D.
30/143
Answer:
[tex]A. \frac{5}{143}[/tex]
Step-by-step explanation:
Given,
Number of women = 5,
Number of men = 8,
Total persons = 5 + 8 = 13,
∵ Ways of selecting any 3 persons = [tex]^{13}C_3[/tex]
Also, the ways of selecting 3 women = [tex]^5C_3[/tex]
Hence, the probability of selecting 3 women
[tex]=\frac{\text{Ways of selecting any 3 women}}{\text{ Ways of selecting any 3 persons}}[/tex]
[tex]=\frac{^5C_3}{^{13}C_3}[/tex]
[tex]=\frac{\frac{5!}{2!3!}}{\frac{13!}{3!10!}}[/tex]
[tex]=\frac{10}{\frac{13\times 12\times 11}{6}}[/tex]
[tex]=\frac{60}{13\times 12\times 11}[/tex]
[tex]=\frac{5}{143}[/tex]
Hence, OPTION A is correct.
I Need Help ASAP! This is Due in 30 Minutes!
I don't Understand it at all and I need Help
Create a factorable polynomial with a GCF of 7. Rewrite that polynomial in two other equivalent forms. Explain how each form was created.
What is the factorization?
-3x^3+15x^2+42x
A. 3(x+7)(x+2)
B. 3(x^2)(x+2)
C. -3x(x+7)(x-2)
D. -3x(x-7)(x+2)
Quadrilateral abcd has side lengths of ab = 13w 5, bc = 5z 2, cd = 13w 5, and ad = 3z + 5. find the value of z for which quadrilateral abcd is a parallelogram.
To find 'z', utilise the properties of a parallelogram where opposite sides are equal. Setting these sides equal to each other and solving for 'z' provides the answer, 'z' = 3.5.
Explanation:In this problem, you're given a quadrilateral ABCD for which you are supposed to find the value of 'z' when the quadrilateral is a parallelogram. In a parallelogram, the opposite sides are equal. Therefore, we can set AB = CD and BC = AD, and then solve for 'z'. From AB = CD (13w + 5 = 13w + 5), no information is required as their lengths are already equal. From BC = AD (5z - 2 = 3z + 5), solving for 'z' would give us 'z' = 7/2 or 3.5.
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Quintin set a goal to do 15 push-ups each day. By how much would he exceed his goal if he did 17 push-ups in a day?
2
7
19
32
17-15 =2
he would exceed by 2 a day
(1 point) solve the separable differential equation y′(x)=2y(x)+18−−−−−−−−−√, y′(x)=2y(x)+18, and find the particular solution satisfying the initial condition y(5)=9.
Find the degree of the monomial. 6y2w8
ten less than twice a number is the same as 7 times the number. find the number
H-79= -83 Solve the equation ?
Choose the best definition for the following term:substitution
What is the end point and mid point
Answer:
end point is (-5/3 , 3)
mid-point: (5/6, 3/2)
Step-by-step explanation:
Read the following statement: All real numbers have a reciprocal. Which of the following choices is a counterexample to the statement?
1/4
0
1
-7
Answer: Second option is correct.
Step-by-step explanation:
Since we have given that
All real numbers have a reciprocal.
But we know that 0 has no inverse, means there is no reciprocal exists for 0.
Because,
[tex]\dfrac{1}{0}=\infty[/tex]
So, 0 is a counter example to the statement.
Hence, Second option is correct.
A cylinder has a height of 2 meters and a diameter that is 5 times the measure of the height. Using 3.14 for pi, which of the following can be used to calculate the volume?
(3.14)(2m)2(10m)
(3.14)(2m)2(5m)
(3.14)(10m)2(2m)
(3.14)(5m)2(2m)
Which of the following is a rational number?
Paul bought 9 total shirts for a total length f $72. Tee shirts cost $10 and long sleeve shirts cost $7. How many of each type shirt did he buy
How long does it take a plane, traveling at a speed of 110 m/s, to fly once around a circle whose radius is 2850 m?
Answer:
It takes to the plane [tex]162.792[/tex] seconds to fly once around a circle whose radius is 2850 m at a speed of [tex](110)\frac{m}{s}[/tex]
Step-by-step explanation:
The first step in this exercise is to find the total distance that the plane will fly.
This distance is equal to the perimeter of a circle whose radius is 2850 m.
Given a circle of radius R, the perimeter ''P'' can be calculated as :
[tex]P=\pi .d=\pi .2.R[/tex]
Where ''d'' is the diameter of the circle that is equal to 2.R
The distance that the plane will fly in the exercise is :
[tex]P=\pi .2.R=\pi .2.(2850m)=17907.078m[/tex]
Now, the speed is equal to distance divided by time.
[tex]speed=\frac{distance}{time}[/tex]
We have the speed of the plane and the distance (that is the perimeter ''P'' of the circle). We only need to replace this values in the equation and find the time variable.
[tex](110)\frac{m}{s}=\frac{(17907.078)m}{t}[/tex]
[tex]t=\frac{(17907.078)m}{(110)\frac{m}{s}}=(162.792)s[/tex]
[tex]t=(162.792)s[/tex]
We find that the time is [tex]162.792[/tex] seconds.
A line contains points (−2,−2) and (1,4). Find the distance between the line and the point (6,−1).
What is the solution of the equation e^xe^2x = 4? Round your answer to the nearest hundredth.