The president of a university claimed that the entering class this year appeared to be larger than the entering class from previous years but their mean SAT score is lower than previous years. He took a sample of 20 of this year's entering students and found that their mean SAT score is 1,501 with a standard deviation of 53. The university's record indicates that the mean SAT score for entering students from previous years is 1,520. He wants to find out if his claim is supported by the evidence at a 5% level of significance. Referring to Scenario 9-9, what is the critical value
Answers
Answer:
Step-by-step explanation:
To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level
The nul hypothesis is
\(H_0; \mu \geq 1520\)
The alternative hypothesis is
\(H_0 ; \mu\leq 1520\)
The test statistic is
\(t=\frac{\bar x- \mu}{(\frac{s}{\sqrt{n} } )}\)
\(t= \frac{1501-1520}{(\frac{53}{\sqrt{20} } )} \\\\=-1.603\)
The t - test statistics is -1.603
The t - critical value is,
The small size is small and left tail test.
Look in the column headed \(\alpha = 0.05\) and the row headed in the t - distribution table by using degree of freedom is,
d.f = n - 1
= 20 - 1
= 19
The t - critical value is -1.729
The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance.
there is insignificance evidence ti indicate that the mean SAT score is less than 1520. The result is not statistically significant
Answer:
Critical value = -1.729
Step by Step explanation:
Given:
n = 20
X' = 1501
Standard deviation = 53
Mean, u = 1520
Level of significance, a = 0.05
The null and alternative hypotheses:
H0 : u = 1520
H1 : u < 1520
This is a lower tailed test.
Degrees of freedom, df = 20 - 1 = 19
For critical value:
\(t critical = - t_a, _d_f \)
From t table df = 19, one tailed
\(t critical = -t _0._0_5, _1_9 = -1.729\)
Critical value = -1.729
Decision: Reject null hypothesis H0, if test statistic Z, is less than critical value.
Test statistic Z =
\( Z = \frac{X' - u}{\sigma / \sqrt{n}} \)
\( Z = \frac{1501 - 1520}{53/ \sqrt{20}}= -1.603\)
Z = -1.603
For p-value:
From excel,
P(t< -1.603) = t.dist( -1.603, 19, 1)
= 0.06269
≈ 0.0627
P value = 0.0627
Since test statistic Z, -1.603, is greater than critical value, -1.729, we fail to reject the null hypothesis H0.
There is not enough statistical evidence to conclude that mean is less than 1520.
Related Questions
PLEASE HELP IM SO LOST
Answers
Answer: f(x) has an axis of symmetry at x = 4 and h(x) has an axis of symmetry at x = -2
Step-by-step explanation:
You can easily find the axis of symmetry by investigating around which line the functions are symmetrical about
for instance, in h(x), the graph is symmetrical on either side of x = -2, meaning that the line x = -2 cuts the parabola in 'half'
in f(x), this is a little harder to think about, but if you know how the graph will be shifted on the x-axis you can figure it out! In this case (x-4)^2 means that the graph will be shifted on the x-axis 4 units to the right (or from the origin to +4 on the X axis)
as such the line x = 4 will cut the function f(x) in 'half'
Cameron invests money in a bank account
which gathers compound interest each year.
After 4 years there is $736.80 in the account.
After 7 years there is $788.82 in the account.
Work out the annual interest rate of the bank
account.
Give your answer as a percentage to 1 d.p.
Answers
The annual interest rate of the bank account is 2.3%
Let's check the equation for each year.
Compound Interest earned amount
A = P( 1 + r/n)ⁿˣ
A = accumulated amount
P = original amount deposited
r = interest rate
n = times it compounds per year
x = years
when Amount = $736.80, x = 4 years and r% → r/100
736.80 = P(1 +[(r/100)/1] ¹×⁴
736.80 = P(1 + r/100)⁴
when Amount =$788.82 , x = 7 years and r% → r/100
788.82 = P(1 +[(r/100)/1] ¹×⁷
788.82 = P(1 + r/100)⁷
using the 1st equation:
736.80 = P(1 + r/100)⁴
P = 736.80 /[(1 + r/100)⁴]
Substitute on the Using 2nd equation
788.82 = P(1 + r/100)⁷
788.82 = 736.80 /[(1 + r/100)⁴] * (1 + r/100)⁷
788.82 = 736.80 * [(1 + r/100)⁷/(1 + r/100)⁴]
788.82 = 736.80 * (1 + r/100)³
788.82/736.80 = (1 + r/100)³
∛788.82/736.80 = ∛ (1 + r/100)³
∛788.82/736.80 = (100 + r)/100
100 ∛788.82/736.80 = 100 + r
100 ∛788.82/736.80 - 100 = r
r ≈ 2.3%
Hence, the annual interest rate of the bank account is 2.3%
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Un hombre posee 50 acciones con un valor de 30 cada una , la corporación declaró un dividendo del 6% pagadero en acciones ¿cuantas acciones poseía entonces?
Answers
el hombre tenía 50 acciones.
La pregunta es, ¿cuántas acciones poseía el hombre si declararon un dividendo del 6% pagadero en acciones y tenía 50 acciones con un valor de $30 cada una?Para calcular cuántas acciones tenía el hombre,
se puede utilizar la siguiente fórmula:Dividendos = Número de acciones * Precio por acción * Tasa de dividendosDe esta fórmula,
podemos despejar el número de acciones. Así, tenemos:Número de acciones = Dividendos / (Precio por acción * Tasa de dividendos)De los datos del problema, se sabe que el hombre tenía 50 acciones con un valor de $30 cada una.
Además, la corporación declaró un dividendo del 6% pagadero en acciones. Por lo tanto, la tasa de dividendos es del 6%.Para resolver el problema, primero debemos calcular el valor del dividendo que se pagará en acciones.
Para ello, se debe multiplicar el valor de las acciones del hombre por la tasa de dividendos.
Así, tenemos:Valor del dividendo = 50 acciones * $30 * 0.06 = $90El valor del dividendo es de $90. Ahora, podemos sustituir este valor en la fórmula para calcular el número de acciones que tenía el hombre.
Así, tenemos:Número de acciones = $90 / ($30 * 0.06) = 50 accionesPor lo tanto,
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The lengths of pregnancies in a small rural village are normally distributed with a mean of 269 days and a standard deviation of 17 days.
In what range would you expect to find the middle 98% of most pregnancies?
Between
299.34
Incorrect229.3 and
303.4
Incorrect308.7.
If you were to draw samples of size 58 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Between
264
Correct and
274.1
Correct.
Enter your answers as numbers. Your answers should be accurate to 1 decimal places.
Answers
You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.
To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.
For the given data:
Mean (μ) = 269 days
Standard deviation (σ) = 17 days
To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.
To find the z-score for the 1% percentile (lower bound):
z1 = Φ^(-1)(0.01)
Similarly, to find the z-score for the 99% percentile (upper bound):
z2 = Φ^(-1)(0.99)
Now, we can calculate the z-scores:
z1 = Φ^(-1)(0.01) ≈ -2.33
z2 = Φ^(-1)(0.99) ≈ 2.33
To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:
lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days
upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days
Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.
Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:
Mean of sample means (μ') = μ = 269 days
Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229
To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').
Now, calculate the z-scores:
z1 = Φ^(-1)(0.01) ≈ -2.33
z2 = Φ^(-1)(0.99) ≈ 2.33
Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:
lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days
upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days
Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.
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Factor completely.
5x² + 25x + 20 =
Answers
Answer: 5(x + 1)(x + 4)
Step-by-step explanation Tell me if it is wrong
Pls help me solve whole page
Answers
Find the slope of a line perpendicular to the line whose equation is x + 6y = -24.
Fully simplify your answer.
Answers
Answer:
\(m_{perpendicular}\) = 6
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
x + 6y = - 24 ( subtract x from both sides )
6y = - x - 24 ( divide through by 6 )
y = - \(\frac{1}{6}\) x - 4 ← in slope- intercept form
with slope m = - \(\frac{1}{6}\)
given a line with slope m then the slope of a line perpendicular to it is
\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{-\frac{1}{6} }\) = 6
A line passes through the point (1,5) and has a slope of 7
Answers
Therefore, the equation of the line passing through the point (1,5) with a slope of 7 is y = 7x - 2.
The equation of a line in the point-slope form is given by the following equation:
y-y_1 = m(x-x_1)
where m is the slope of the line and (x1, y1) is any point on the line.
Therefore, we can write the equation of the line passing through the point (1,5) with a slope of 7 as follows:
y-5 = 7(x-1)
Expanding the right-hand side of the equation gives:
y-5 = 7x-7
Adding 5 to both sides of the equation gives:
y = 7x-2
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3 · {(300 - 70 ÷ 5) - [3 · 23 - (8 - 2 · 3)]}
Answers
Answer:
(657)
Step-by-step explanation:
Simplify the following:
3 (300 - 70/5 - (3×23 - (8 - 2×3)))
The gcd of -70 and 5 is 5, so (-70)/5 = (5 (-14))/(5×1) = 5/5×-14 = -14:
3 (300 + -14 - (3×23 - (8 - 2×3)))
-2×3 = -6:
3 (300 - 14 - (3×23 - (-6 + 8)))
8 - 6 = 2:
3 (300 - 14 - (3×23 - 2))
3×23 = 69:
3 (300 - 14 - (69 - 2))
| 6 | 9
- | | 2
| 6 | 7:
3 (300 - 14 - 67)
300 - 14 - 67 = 300 - (14 + 67):
3 ((300 - (14 + 67)))
| 1 |
| 6 | 7
+ | 1 | 4
| 8 | 1:
3 (300 - 81)
| | 9 |
| 2 | | 10
| | |
- | | 8 | 1
| 2 | 1 | 9:
3 (219)
3 (219) = (3×219):
(3×219)
3×219 = 657:
Answer: (657)
if p(e and f)=.392, p(e/f)=.56 and p(f/e)=.7, then p(e)=
Answers
On solving the provided question, we can say that Probability(A and B) = P(A)P(B|A) and P(E or F) = P(E) + P(F) - P(E and F)
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
Probability(A and B) = P(A)P(B|A).
P(A and B) = P(B and A), this may also be written as P(A and B) = P(B)P(A|B).
Using the general multiplication rule, we have
P(E and F) = P(E)P(F|E)
.392 = P(E)(.7)
P(E) = .56
P(E and F) = P(F)P(E|F)
.392 = P(F)(.56), so
P(F) = .7
P(E or F) = P(E) + P(F) - P(E and F)
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Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches greater than the box he originally planned to build?
Answers
Answer:
The new volume is 3n^2+2n inches greater.
Step-by-step explanation:
Volume of a cube = s^3 where s is side of cube
Original volume = n^3
Volume of a Rectangular Prism = LBH
New Volume = (n+1)(n+2)(n)= n^3+3n^2+2n
DIfference = New- original = 3n^2+2n
Find the range of the relation
Answers
Answer:
1st {-6, -3, 0, 3, 6}
Step-by-step explanation:
range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}
Use the following scenario to answer the question below:
You are deciding between two cars with different engines and want the bigger
of the two. One engine displaces 350 cubic inches. The other displaces 5,500
cubic centimeters. How many significant figures do the values in this problem
involve?
A. 4
B. 3
C. 2
D. 1
Answers
How much 72-octane gas and 84-octane gas should be blended to make 12 gallons of 78-octane gas?
The amount of 72 octane gas is enter your response here gallons.
The amount of 84 octane gas is enter your response here gallons.
Answers
Answer:
6 gallons 72-octane
6 gallons 84-octane
Step-by-step explanation:
(84 + 72)/2 = 78
The average octane in 72-octane and 84-octane is 78-octane.
Therefore, you need equal amounts of each.
Answer:
6 gallons 72-octane
6 gallons 84-octane
Solve for elimination
1.−2x−5y=−19
2.3x+2y=−10
Answers
#40: how many hours did the repair work take?
Answers
Answer:
6 hours
Step-by-step explanation:
$311 - $125 = $186
$186/$31 = 6 hours
WHAT I KNOW
CAN YOU DO THIS? LET'S HAVE A GUESSING GAME ON POLYGONS.
__________1. I AM A POLYGON WITH FOUR EQUAL SIDES AND 4 RIGHT CORNERS. WHAT AM I?
__________2.I HAVE THREE SIDES AND THREE ANGLES. WHAT AM I?
__________3. I HAVE TWO PAIRS OF PARALLEL SIDES AND FOUR RIGHT ANGLES. WHAT SHAPE AM I?
__________4. I AM A POLYGON WITH 4 SIDES AND ONE PAIR OF WHICH IS PARALLEL. WHAT AM I?
__________5. I HAVE TWO OF OPPOSITE SIDES WHICH ARE PARALLEL. WHAT AM I?
PLS ANSWER
Answers
Answer:
1. Square
A square has 4 side of equal lengths, and all right angles.
2. Triangle
A triangle has 3 sides and 3 angles. It could either be an isosceles, equilateral or obtuse triangle.
3. Rectangle
A rectangle has 4 sides. 2 are parallel and the other 2 are parallel. All angles are 90 degrees.
4. Trapezoid
This shape has 4 sides. Only 1 pair of sides is parallel. The other 2 sides are not parallel
5. Parallelogram
It has 4 sides, and both pair of opposite sides are parallel.
Which of the following is the most likely the next step in the series?
Answers
Answer: C is the correct answer!I don't feel like explaining. sorry.Please let me know if I am wrong.
2x + y = 7
x + y = 1
Answers
The solution to the system of equations is x = 6 and y = -5, which is the same as we obtained using the elimination method.
What is the system of equations?A system of equations is a collection of one or more equations that are considered together. The system can consist of linear or nonlinear equations and may have one or more variables. The solution to a system of equations is the set of values that satisfy all of the equations in the system simultaneously. The given system of equations is:
2x + y = 7 ---(1)
x + y = 1 ---(2)
To solve this system, we can use the method of elimination or substitution.
Method 1: Elimination
In this method, we eliminate one of the variables by adding or subtracting the two equations. To do this, we need to multiply one or both equations by a suitable constant so that the coefficients of one of the variables become equal in magnitude but opposite in sign.
Let's multiply equation (2) by -2, so that the coefficient of y in both equations becomes equal in magnitude but opposite in sign:
-2(x + y) = -2(1) --
Multiplying equation
(2) by -2-2x - 2y = -2
Now we can add the two equations (1) and (-2x - 2y = -2) to eliminate y:
2x + y = 7(-2x - 2y = -2)0x - y = 5
We now have a new equation in which y is isolated.
To solve for y, we can multiply both sides by -1:
-1(-y) = -1(5)y = -5
Now that we know y = -5, we can substitute this value into equation (2) to find x:x + y = 1x + (-5) = 1x = 6
Therefore, the solution to the system of equations is (x,y) = (6,-5).
Method 2: Substitution
In this method, we solve one of the equations for one variable in terms of the other variable and substitute this expression into the other equation to get an equation with only one variable.
From equation (2), we can solve for y in terms of x:y = 1 - x
We can then substitute this expression for y into equation (1):2x + y = 72x + (1 - x) = 7 --Substituting y = 1 - xx + 1 = 7x = 6
Now that we know x = 6, we can substitute this value into equation (2) to find y:x + y = 16 + y = 1 --Substituting x = 6y = -5
Therefore, the solution to the system of equations is (x,y) = (6,-5), which is the same as we obtained using the elimination method.
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identify the time being asked 12 hours and 24 hours 1 quarter after 0:00h 2 quarter to 14:00h 3 half past 13:00h 4 5 to 23:00h
Answers
One quarter after 0:00h is 0:15h (12:15 AM) in the 12-hour format and 00:15h in the 24-hour format.
Two quarters to 14:00h is 13:30h (1:30 PM) in both the 12-hour and 24-hour formats.
Half past 13:00h is 13:30h (1:30 PM) in both the 12-hour and 24-hour formats.
Five minutes to 23:00h is 22:55h (10:55 PM) in both the 12-hour and 24-hour formats.
Let's identify the time being asked in both the 12-hour and 24-hour formats for each scenario:
One quarter after 0:00h:
In the 12-hour format, 0:00h is midnight or 12:00 AM.
One quarter after 0:00h would be 0:15h (or 12:15 AM).
In the 24-hour format, 0:00h remains the same as 00:00h.
One quarter after 0:00h would be 00:15h.
Two quarters to 14:00h:
In the 12-hour format, 14:00h is 2:00 PM.
Two quarters to 14:00h would be 13:30h (or 1:30 PM).
In the 24-hour format, 14:00h remains the same as 14:00h.
Two quarters to 14:00h would be 13:30h.
Half past 13:00h:
In the 12-hour format, 13:00h is 1:00 PM.
Half past 13:00h would be 13:30h (or 1:30 PM).
In the 24-hour format, 13:00h remains the same as 13:00h.
Half past 13:00h would be 13:30h.
Five minutes to 23:00h:
In the 12-hour format, 23:00h is 11:00 PM.
Five minutes to 23:00h would be 22:55h (or 10:55 PM).
In the 24-hour format, 23:00h remains the same as 23:00h. Five minutes to 23:00h would be 22:55h.
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y=3^n is an example of an exponential function.
True
False
Answers
Answer:
True
Step-by-step explanation:
A function of form y = a^n is an exponential function as long as a>0.
The lines given by the equations y = 2x and y= 2x + 1 are
A. Parallel
B. Perpendicular
C. Neither Perpendicular nor parallel
Answers
Jayden wants to lay sod on his front yard and on half of his back yard. His front yard has a length of 50 feet and a width of 80 feet. His back yard has a length of 20 feet and a width of 30 feet. How many square feet of sod does Jayden need to purchase? OA. 4,300 square feet OB. 4,600 square feet OC. 2,600 square feet OD. 4,150 square feet
Answers
Answer:
4,300 square feet
Step-by-step explanation:
First, calculate the area of Jayden's front yard.
50 feet × 80 feet = 4,000 square feet
Next, find the area of half of Jayden's back yard.
1/2(20 feet × 30 feet) = 300 square feet
Last, add the two areas together.
4,000 feet + 300 feet = 4,300 square feet
So, Jayden needs to purchase 4,300 square feet of sod
WILL MARK BRAINLYIST
Answers
A car shop has 12 mechanics, of whom 8 can work on transmissions and 7 can work on brakes. a) What is the minimum number who can do both? b) What is the maximum number who can do both? c) What is the minimum number who can do neither? d) What is the maximum number who can do neither?
Answers
Answer:both a and b are correct
Step-by-step explanation:
y = 3x + 3 using a
{-2, 1, 2}
Answers
Answer:
y = 3x + 3 using a
{-2, 1, 2}
Step-by-step explanation:
Given the functions a(x) = 3x - 12 and b(x) = x-9, solve a[b(x)].
Oa[b(x)] = 3x²-21
O a[b(x)] = 3x² - 39
Oa[b(x)] = 3x - 21
Oa[b(x)] = 3x - 39
Answers
Answer:
Step-by-step explanation:
hello :
a(x) = 3x - 12 and b(x) = x-9, so
a[b(x)]=a(x-9) =3(x-9)-12
a[b(x)]=3x-9-12
a[b(x)]=3x+21
Two hikers are 77 miles apart and walking toward each other. They meet in 10 hours. Find the rate of each hiker if one hiker walks 5.5 mph faster than the other.
Answers
The rate of the slower hiker is 1.1 mph and the rate of the faster hiker is 6.6 mph
Explanation
One hiker walks 5.5 mph faster than the other.
Suppose, the speed of the slower hiker is (x) mph.
So, the speed of the faster hiker will be:
(x+5.5)mph
Both hikers are walking toward each other and meet in 10 hours.
We know that, Distance = speed * time
So, the distance walked by the slower hiker in 10 hours = 10x miles and the distance walked by the faster hiker in 10 hours = 10(x + 5.5) miles.
Given that, they were 77 miles apart in the beginning. So the equation will be ...
10x + 10(x + 5.5) = 77
10x + 10x + 55 = 77
20x = 77 - 55 = 22
x = 22/20 = 1.1
Thus, the rate of the slower hiker is 1.1 mph and the rate of the faster hiker is (1.1 + 5.5) mph = 6.6 mph
HELPPP PLEASEEEEEEEE
Answers
What is 5x6 + (5x5-5) to the 2nd power
Answers
Answer: 2500
Step-by-step explanation: If you calculate out 5x6 that equals 30 and 5x5-5 equals 20, when you do 30+20 that equals 50 and 50 to the 2nd power is 50x50 and that would equal 2500