Test the claim about the difference between two population means mu 1μ1 and mu 2μ2 at the level of significance alphaα. assume the samples are random and independent, and the populations are normally distributed
In hypothesis testing of two population means with a 5% significance level, we compare the difference between two sample means against a null hypothesis that states no difference, using t- or z-distributions depending on whether population standard deviations are known.
Explanation:Hypothesis Testing of Two Population Means
In statistics, when we want to test the claim about the difference between two population means,
(μ1 and μ2), we use a procedure known as a hypothesis test. If we assume that the samples are random, independent, and drawn from normally distributed populations, we usually proceed with a formula involving the sample means, sample standard deviations, and sample sizes.
In a hypothesis test, the null hypothesis (H0) typically states that there is no difference between the two population means (H0: μ1 = μ2). The alternative hypothesis (Ha) suggests that there is a difference (Ha: μ1 ≠ μ2). To assess the validity of H0, we calculate a test statistic that follows a known distribution (typically a t-distribution if standard deviations are unknown and a z-distribution if they are known) under the assumption that H0 is true.
For a test at the 5 percent level of significance (α=0.05), we determine the critical value(s) from the statistical tables of the chosen distribution. If the calculated test statistic falls into the critical region determined by α, we reject the null hypothesis in favor of the alternative hypothesis. If not, we fail to reject the null hypothesis. This process is essentially a two-tailed test, given that we allow for the possibility of the sample mean being either larger or smaller than the hypothesized population mean.
The assumption of normality is critical when the sample sizes are small. For larger samples, according to the Central Limit Theorem, the sampling distribution of the mean will be approximately normal regardless of the underlying distribution of the population.
It is important to note that while we can never prove a hypothesis definitively, hypothesis testing allows us to make probabilistic statements about whether data is consistent with a given hypothesis.
The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $ 3 comma sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $ 4 will cause the sales to fall to 5000 Fun Noodles per day. a. Assume that the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold).
Using standard linear equation, y = m*x + c
where m = slope and c = constant
putting ordered pairs, (3,7000) and (4,5000) in the above equation, we get two equations
3*m + c = 7000 and 4*m + c = 5000
On solving,
m = -2000 and c = 13000
So, the required equation is
y = -2000*x + 13000
Consumer reports stated that the mean time for a chrysler concorde to go from 0 to 60 miles per hour was 8.7 seconds. (a) if you want to set up a statistical test to challenge the claim of 8.7 seconds, what would you use for the null hypothesis? μ > 8.7 μ = 8.7 μ ≠ 8.7 μ < 8.7 (b) the town of leadville, colorado, has an elevation over 10,000 feet. suppose you wanted to test the claim that the average time to accelerate from 0 to 60 miles per hour is longer in leadville (because of less oxygen). what would you use for the alternate hypothesis? μ = 8.7 μ ≠ 8.7 μ < 8.7 μ > 8.7 (c) suppose you made an engine modification and you think the average time to accelerate from 0 to 60 miles per hour is reduced. what would you use for the alternate hypothesis? μ > 8.7 μ = 8.7 μ < 8.7 μ ≠ 8.7 (d) for each of the tests in parts (b) and (c), would the p-value area be on the left, on the right, or on both sides of the mean? both; left left; both right; left left; right
Please help with this algebra question!! thanks!
write the expression (1-2i)/(2-3i) as a complex number in standard form
Answer:
8/13 - 1/13i
Step-by-step explanation:
Final answer:
To convert the expression (1-2i)/(2-3i) to standard form, multiply by the complex conjugate of the denominator (2+3i). After simplification, the standard form of the complex number is 0.8 - 0.1i.
Explanation:
To write the expression (1-2i)/(2-3i) as a complex number in standard form, we need to eliminate the imaginary unit i from the denominator. This can be achieved by multiplying both the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of a complex number 2-3i is 2+3i.
Multiplying the expression by the complex conjugate, we get:
(1-2i)(2+3i) / (2-3i)(2+3i).
Now, we can expand both the numerator and denominator:
Numerator: (1 × 2) + (1 × 3i) - (2i × 2) - (2i × 3i) = 2 + 3i - 4i - 6(i²)
Denominator: (2 × 2) + (2 × 3i) - (3i × 2) - (3i × 3i) = 4 - 6(i²)
Recall that i² = -1, so we can simplify the expression further.
Numerator: 2 + 3i - 4i + 6 = 8 - i
Denominator: 4 + 6 = 10
Therefore, our complex number in the standard form is:
(8 - i) / 10 = 0.8 - 0.1i.
Please help me with this question
Which situation is most likely to have a constant rate of change? A. Length of a bead necklace compared with the number of identical beads B. Distance a school bus travels compared with the number of stops C. Number of trees in a park compared with the area of the park D. Number of runs scored in a baseball game compared with the number of innings
Answer:
A. Length of a bead necklace compared with the number of identical beads
Step-by-step explanation:
Using identical beads in a necklace means that the length of the necklace will depend on the total number of identical beads in the necklace.
For each bead added, the length of the necklace will increase a given, constant, amount. This is a constant rate of change.
Answer: A. Length of a bead necklace compared with the number of identical beads
Step-by-step explanation:
A. Length of bead necklace increases simultaneously compared with the increases in number of identical beads . This is a proportional relationship .
So, There is constant rate of change which is equals to the length of each bead.
B. Distance a school bus travels compared with the number of stops .
There is no constant rate of change between the quantities .[The time when bus stops matter]
C.Number of trees in a park compared with the area of the park.
There can be free space ,so there is not proportional relationship .
D.Number of runs scored in a baseball game compared with the number of innings
Not proportional relationship.
I need help on this
Wyatt uses 3.15 cups of flour in a recipe that makes 9 shortcakes. Cora uses 2.4 cups of flour in a recipe that makes 8 shortcakes. How much more flower per shortcake is needed for Cora’s recipe?
number of per month__number of moviegoers
more than 7____________96
5-7_______________ ___180
2-4__________________219
less than 2____________205
total _________________700
Use the frequency table. Find the probability that a person goes to the movies at least 2 times a month. Round to the nearest thousandth.
A. 0.138
B. 0.707
C. 0.137
D. 0.394
sorry for the poor graph up top,,,,:/
Answer:
B. 0.707
Step-by-step explanation:
The frequency table is given by,
Number of months Number of movie goers
More than 7 96
5 - 7 180
2 - 4 219
Less than 2 205
Total 700
Since, Probability of an event is the ratio of favorable events to the total number of events.
As, the number of people going to movies atleast 2 times a month = 96 + 180 + 219 = 495
The probability that a person goes to the movies atleast 2 times a month = [tex]\frac{495}{700}=0.707[/tex].
Thus, option B is correct.To obtain the graph of y=(x- 8)2 shift the graph of y= x2
Answer:
You would shift this to the right 8 places
Step-by-step explanation:
How many different ways can you choose 5 books from a shelf containing 12 books? Type a numerical answer in the space provided. Do not type spaces in your answer.
A coin is tossed then a number 1-10 is chosen at random what is the probability of getting heads then a number less than 4
The probability of getting heads then a number less than 4 is, 0.15
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
The formula of the probability of an event A is:
[tex]P(A)=\frac{n(A)}{n(S)}[/tex] , where [tex]n(A)[/tex] is the number of favorable outcomes and [tex]n(S)[/tex] is the total number of events in the sample space.
For given situation,
Let, event A: getting heads on a coin toss
and event B: choosing a number less than four from 1-10
For event A, [tex]n(A)=1[/tex] and [tex]n(S)=2[/tex] (either head or tail)
So, [tex]P(A)=\frac{1}{2}[/tex]
Similarly, for event B:
choosing a number less than four = {1, 2, 3}
So, [tex]n(B)=3[/tex] and [tex]n(S)=10[/tex]
⇒ [tex]P(B)=\frac{3}{10}[/tex]
The probability of getting heads and choosing a number less than 4 is:
⇒ [tex]\frac{1}{2}[/tex] × [tex]\frac{3}{10}[/tex]
[tex]=\frac{3}{20}[/tex]
[tex]=0.15[/tex]
Hence, the probability of getting heads then a number less than 4 is 0.15
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Plot and connect the points A(2,3), B(2,-5), C(-4,-3), and find the area of the triangle it forms.
The area of the triangle is 24 square unit.
What is Area?Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the area that its perimeter encloses. The quantity of unit squares that cover a closed figure's surface is its area.
If we plot the points A(2,3), B(2,-5), C(-4,-3) on the graph we get a triangle which can be divided into two right Triangles.
So, Area of Triangle 1
= 1/2 x base x height
= 1/2 x 6 x 6
= 18 sq units
Now, area of Triangle 2
= 1/2 x base x height
= 1/2 x 6 x 2
= 6 sq units
Thus ,the Area of required triangle
= 18 + 6
= 24 sq units
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Which expression is equivalent to ^4√16x^11y^8/81x^7y^6 ? Assume x > 0 and y = 0
The equivalent expression to the 4th root of 16x^11y^8/81x^7y^6 is (2x/3)^4, assuming x > 0 and y = 0. The expression simplifies to x because the y terms become 0 and the exponents on x reduce to 1 when the fourth root is taken into account.
Explanation:The question asks for an expression equivalent to 4th root of the fraction 16x^11y^8/81x^7y^6 assuming that x > 0 and y = 0. First, we need to deal with the fourth root and exponents separately. To find the fourth root of a number, you can raise that number to the 0.25 power. This rule simplifies finding roots, as a full calculation is not always needed with modern calculators that have a y* button or equivalent.
The fourth root of 16 is 2 because (2^4) = 16. We can address the exponents of x and y by subtracting the exponents in the denominator from those in the numerator for each variable: x^(11-7) = x^4 and y^(8-6) = y^2. Now, considering y = 0, any term with y to any power will be 0, so we can omit y terms. For x, we have x^4.
Regarding the numbers, we have (2/3)^4 because the fourth root of 81 is 3, and this is in the denominator. Finally, because y = 0, our expression reduces to just concerning x, which is (2x)^4/(3)^4, or (2x/3)^4. This simplifies to x raised to the power of 1 because (2/3)^4 * x^4 with x^4 raised to the 1/4th power cancels out the fourth power.
To simplify the given expression, we can find the fourth roots of the numbers inside the radical and then simplify the variables using exponent rules.
Explanation:To simplify the expression ^4√16x^11y^8/81x^7y^6, we can first simplify the numbers inside the radical by finding their fourth roots. The fourth root of 16 is 2, and the fourth root of 81 is 3. So, the expression becomes 2x^(11/4)y^2 / 3x^(7/4)y^6.
Next, we can simplify the variables inside the expression by subtracting the exponents. So, x^(11/4) / x^(7/4) simplifies to x^((11/4)-(7/4)) = x^(4/4) = x^1 = x, and y^2 / y^6 simplifies to y^(2-6) = y^(-4).
Combining the simplified numbers and variables, the expression becomes 2x * y^(-4) / 3 = (2x)/(3y^4).
The formula for centripetal acceleration, a, is given below, where v is the velocity of the object and r is the object's distance from the center of the circular path. Solve the formula for the velocity. the formula is a= v^2/ r
Answer:
The required formula is [tex]v=\sqrt{ar}[/tex].
Step-by-step explanation:
The given formula is
[tex]a=\frac{v^2}{r}[/tex]
where, v is the velocity of the object and r is the object's distance from the center of the circular path.
Multiply both sides by r, to solve the formula for the velocity.
[tex]ar=v^2[/tex]
Taking square root both the sides.
[tex]\sqrt{ar}=v[/tex]
Therefore the required formula is [tex]v=\sqrt{ar}[/tex].
For the given data, (a) find the test statistic, (b) find the standardized test statistic, (c) determine the p-value, and (d) decide whether you should reject or fail to reject the null hypothesis. the samples are random and independent. claim: mu 1μ1less than
solve the system of equations below by graphing them please
Median number for 100 110 120 125 140 150 160
PLZ HELP NNOOOOOOOWW!! 15 points!!
What is the midpoints of the line segment with endpoints (-3,7) and (9,-2)?
Unit Activity: Advanced Functions
n May, Bradley bought 48 Styrofoam balls and decorated them as toy figurines. In June, he sold 19 figurines. In May, Lupe bought 44 Styrofoam balls to decorate, and in June, she sold 21 figurines. Which matrix represents all of their May purchases and their June sales?
Answer: The matrix would be
[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]
Step-by-step explanation:
Since we have given that
Number of Styrofoam balls bought by Bradley in May = 48
Number of figurines sold by Bradley in June = 19
Number of Styrofoam balls bought by Lupe in May = 44
Number of figurines sold by Lupe in June = 21
So, it will be written as
Purchases Sales
May 48 19
June 44 21
So, the matrix would be
[tex]\left[\begin{array}{ccc}48&19\\\\44&21\end{array}\right][/tex]
Question:
Martha has a piece of cloth. She used 1/5 of the cloth to make a pillow case and another 5/9 of the cloth to make a tablecloth.
A. What fraction of the cloth was used total for the pillow case
and the tablecloth?
B. What fraction of the cloth was left over?
C. Does Martha have enough cloth left over to make another pillow case.
Write an equation and solve. Round to the nearest hundredth where necessary. What percent of 24 is 30?
Answer:
80%
Step-by-step explanation:
24/30=.80
.80=80%
Hope this helps :)
To solve what percent of 24 is 30, set up the equation 30/24 times 100 = p, which results in 125%. Therefore, 30 is 125% of 24.
To find what percent of 24 is 30, we need to set up a proportion where 30 is the part, 24 is the whole, and we are solving for the percentage (we'll call this p). The equation for percent is (part/whole) times 100 = percent. So in this case, the equation becomes (30/24) tmes 100 = p.
Next, we'll divide 30 by 24 to get a decimal, then multiply by 100 to convert it to a percent. The calculation looks like this: (30 / 24) times 100 which gives us 125%. This means that 30 is 125% of 24.
Always remember to round to the nearest hundredth if necessary, but in this case, 125% is already to the nearest whole percent.
Matt has a box that is 15 inches long and 5 inches wide. The volume of the box is 225 cubic inches. What is the height of the box?
The mean time it takes to walk to the bus stop is 8 minutes (with a standard deviation of 2 minutes) and the mean time it takes for the bus to get to school is 20 minutes (with a standard deviation of 4 minutes). the distributions are normal.
a. how long will it take (in minutes), on average, to get to school?
b. what is the standard deviation of the trip to school?
c. what is the probability that it will take longer than 30 minutes to get to school? due to a miscalculation, you realize it actually takes an average of 10 minutes to walk to the bus stop.
d. how long will it take (in minutes), on average, to get to school?
e. what is the standard deviation of the trip to school? f. what is the probability that it will take longer than 30 minutes to get to school
A water sprinkler sprays water over a distance of 25 feet and rotates through an angle of 130 degrees. find the area of the lawn sprinkled
The area of the lawn that the sprinkler covers is approximately 708.25 square feet. This was calculated using the formula for the area of a sector of a circle, converting the rotation angle to radians, and then substituting the given values into the formula.
Explanation:The area of the lawn that the water sprinkler covers can be calculated using the formula for the area of a sector of a circle. The formula is Area = 1/2 * r2 * θ, where r is the radius (which is the distance the sprinkler can spray, 25 feet in this case) and θ is the central angle in radians. First, we must convert the given angle from degrees to radians. We know that 180 degrees equals π radians. Therefore, to convert 130 degrees to radians, we multiply by π/180, getting approximately 2.26893 radians.
Substituting these values into the formula, we get: Area = 1/2 * 252 * 2.26893 = 708.25 square feet.
So,
the sprinkler covers an area of approximately 708.25 square feet
when rotating through an angle of 130 degrees.
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Match each function formula with the corresponding transformation of the parent function y = -4 x . .
1. y = -4x - 1 ANSWERS
Translated right by 1 unit
2. y = 1 - 4x Translated down 1 unit
3. y = -4-x Reflected across the x-axis
4. y = -4x + 1 Reflected across the y-axis
5. y = 4x Translated up by 1 unit
6. y = -1 - 4x Translated left by 1 unit
Answer:
1. y = - 4(x - 1) ⇒ Translated right by 1 unit
2. y = 1 - 4x ⇒ Translated up by 1 unit
3. y = - 4(-x) ⇒ Reflected across the y-axis
4. y = - 4(x + 1) ⇒ Translated left by 1 unit
5. y = 4x ⇒ Reflected across the x-axis
6. y = -1 - 4x ⇒ Translated down by 1 unit
Step-by-step explanation:
Lets explain how to solve the problem
- If the function f(x) reflected across the x-axis, then the new
function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new
function g(x) = f(-x)
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
- If the function f(x) translated vertically up
by k units, then the new function g(x) = f(x) + k
- If the function f(x) translated vertically down
by k units, then the new function g(x) = f(x) – k
* Lets solve the problem
∵ y = - 4x is the parent function
- The function after some transformation is:
1. y = - 4(x - 1)
∵ We subtract 1 from x
∴ The function translated right by 1 unit
∴ y = - 4(x - 1) ⇒ Translated right by 1 unit
2. y = 1 - 4x
∵ We add 1 to y = - 4x
∴ The function translated up by 1 unit
∴ y = 1 - 4x ⇒ Translated up by 1 unit
3. y = -4(-x)
∵ We multiply x by (-)
∴ The function reflected across the y-axis
∴ y = - 4(-x) ⇒ Reflected across the y-axis
4. y = -4(x + 1)
∵ We add 1 to x
∴ The function translated left by 1 unit
∴ y = - 4(x - 1) ⇒ Translated left by 1 unit
5. y = 4x
∵ We multiply y = - 4x by (-)
∴ The function reflected across the x-axis
∴ y = 4x ⇒ Reflected across the x-axis
6. y = -1 - 4x
∵ We subtract 1 from y = - 4x
∴ The function translated down by 1 unit
∴ y = -1 - 4x ⇒ Translated down by 1 unit
Use any method to solve the equation. If necessary, round to the nearest hundredth.
9x2 − 21 = 0
4.58, –4.58
3, –3
0.65, –0.65
1.53, –1.53
Answer:
[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]9x^{2}-21=0[/tex]
To solve this equation, we just have to isolate the variable, because the quadratic expression has only one variable, the linear term is not present. So
[tex]9x^{2} =21\\x^{2} =\frac{21}{9}[/tex]
Now, we apply a square root, to have the variable complete isolated
[tex]\sqrt{x^{2} }=\sqrt{\frac{21}{9} } \\x=\±1.53[/tex]
Remember that all square roots have two results, one positive and one negative.
Therefore, the solutions for this equation are
[tex]x_{1}=1.53\\x_{2}=-1.53[/tex]
Two cards are drawn without replacement from a shuffled deck of 52 cards. what is the probability that the first card is a black ace and the second card is a red ace? 1265212652 16631663 1130011300 1270412704