According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:
The value of the test statistic is z = 1.65.The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Before:
Average of 0.250 in 56 at bats, so:
[tex]p_B = 0.25[/tex]
[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]
After:
Average of 0.44 in 25 at bats, so:
[tex]p_A = 0.44[/tex]
[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]
Test if there was improvement:
At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:
[tex]H_0: p_A - p_B = 0[/tex]
At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:
[tex]H_1: p_A - p_B > 0[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{s}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.
0 is tested at the null hypothesis:
This means that [tex]\mu = 0[/tex]
From the samples:
[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]
[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{s}[/tex]
[tex]z = \frac{0.19 - 0}{0.1149}[/tex]
[tex]z = 1.65[/tex]
P-value of the test and decision:
The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.
Looking at the z-table, z = 1.65 has a p-value of 0.9505.
1 - 0.9505 = 0.0495.
The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.
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Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $16.51 and a 95% confidence interval of [$15.96, $17.04]. Which of the following statements is a valid interpretation of the confidence interval??
a. 95% of all taxi fares are between $14.77 and $16.23.
b. We are 95% confident that a randomly selected taxi fare will be between $14.77 and $16.23.
c. The mean amount of a taxi fare is $15.51, 95% of the time.
d. With 95% confidence, we can report that the average taxi fare between Logan Airport and downtown Boston will fall between $14.77 and $16.23.
Answer:
The answer is "Option d".
Step-by-step explanation:
Please find the correct and complete question in the attachment file.
The taxis were known to also be uniformly distributed through the Logan airport to the city of Boston, as well as a sample of seven taxi rates gives an average of $15.51 for [$14.77 and $16.23] for a 95% trust interval. Having 95 percent confidence, we could give a valid interpretation of the confidence level for the averages taxi rates among both Logan Airport and Boston Centre.
Martinez' General Store is having a 45% off sale on men's clothing. John paid $70.95 for a jacket that was on sale. What was the original price of the jacket?
Answer:
$129
Step-by-step explanation:
We can use this equation:
x - 0.45x = 70.95
0.55x = 70.95
x = $129
The tiles below represent the polynomial 2x^2 + 7x+6.
What is the factorization of 2x^2 + 7x + 6?
A. (x+3)(x + 2)
B. (2x + 2)(x+3)
C. (2x+3)(x + 2)
D. (x+3)(x+6)
Answer:
C (x+2)(2x+3)
Step-by-step explanation:
You can count in the picture that in the top part there are two x's (2x) and three ones (3). So the top would be (2x+3)
On the left side there is one x (x) and two ones (2). It would be (x+2).
So combine them together, it would be (x+2)(2x+3).
C.
Answer:
answer is (2x+3)(x+2)
I hope this will help you
Combine terms 7x3 + 2x - 5x2 + 6 + x + 9 + 3x3 + 12x2
Answer:
10x^3 + 7x^2 + 3x + 15
Step-by-step explanation:
hope this helps have good day.
Answer:
the fellow is correct
Step-by-step explanation:
I would have done it but without the symbols I can't
what is the average speed for the interval t=1 hour to t=3 hours
Step-by-step explanation:
2 hours
3+1 / 2 = 4/2 = 2 hours speed average
The area of rectangle is 105cm².If it length is 21 cm,what is its length and perimeter.
Answer:
length of other side is 5cm and the perimeter is 52
Step-by-step explanation:
The area is side x times side y.
Knowing that the area A is 105cm2 and side x is 21cm
A= x*y
105cm2= 21 y /21
Arranging for y we get
y= 105/21
y= 5 cm
The perimeter is all sides added up
P= 21+21+5+5=52cm
Answer:
length 5cm and perimeter 52 cm
Step-by-step explanation:
length=area/breadth
=105/21
=5 cm
perimeter=2(length+breadth)
=2(5+21)
=52 cm
Help me please! Parabola question
The parabola opens upward with the y- intercept being at y=7 (0,7) and the x- intercepts on x= -2,-4 / (-2,0), (-4,0). The axis of symmetry is on x=-3, and the vertex is on (-3,-1).
Fond the square root of 169 by division method
Answer:
13
Step-by-step explanation:
square root of 169 is 13
Which equation can be used to find 60 percent of 50
Answer:
x = 0.6 * 50
Step-by-step explanation:
x = 60% of 50
x = 60% * 50
x = 0.6 * 50
Answer:
60% of 50 = 60 / 100 × 50 = ⅗ × 50 = 150 / 5 = 30
________
x% of y = x / 100 × y = xy / 100
What happens to the mean of the data set shown below if the number 20 is added to the data set?
A. The mean increases by 0.75.
B. The mean does not change.
C. The mean increases by 12.
D. The mean increases by 0.25.
Answer:
This shows that the mean increases by 2.95
Step-by-step explanation:
Assume the given data is 2, 5, 6, 8
Mean = 2 +5+6+8/4
Mean = 21/4
Mean = 5.25
If number 20 is added, the data becomes 2, 5, 6, 8, 20
New mean = 2 +5+6+8+20/4
New mean = 41/5
New mean = 8.2
Taking the difference in the mean:
Difference = 8.2 - 5.25
Difference = 2.95
This shows that the mean increases by 2.95
NB: The data used was assumed since we are not given any data in question
Answer:
The answer is A
Step-by-step explanation:
A lot is in the shape of a trapezoid. The sum of the bases is 180 feet. If the area of the lot is 8100 square feet, what is the distance across the lot, i.e., the altitude of the figure?
Answer: The altitude is 90.
Step-by-step explanation: the formula to calculate a trapezoid: A = (.5)(B+b)h.
plug the values in.
8100 = (.5)(180)h
8100 = 90h
h = 8100/90
h = 90
What is the answer to this? Is it d?
Answer:
Step-by-step explanation:
yeah of course..your answer is true.. it's part d and there is no solution for that system...w and v both of them remove in solution of system and we don't have any unknown variable for solving.
9514 1404 393
Answer:
D. no solutions
Step-by-step explanation:
The first equation can be simplified to standard form:
0.5(8w +2v) = 3
4w +v = 3 . . . . . . . eliminate parentheses
__
The second equation can also be simplified to a comparable standard form:
8w = 2 -v +4w
4w +v = 2 . . . . . . add v -4w
__
Comparing these two equations, we find the variable expressions to be the same, but the constants to be different. If any set of variable values were to satisfy one of these equations, it could not satisfy the other equation. There are no solutions to the system.
16. Which symbol will make the number sentence |-12? 12 true? (1 point)
0=
O=\
O<
O >
Answer:
0>
Step-by-step explanation:
Santos flipped a coin 300 times. The coin landed heads up 125 times. Find the ratio of heads to total number of coin flips. Express a simplified ratio
Answer:
5:12
Step-by-step explanation:
125:300 simplified = 5:12
I hope this helps
Exaluate: (4/9)^1/2.
Answer:
2/3
Step-by-step explanation:
We know that (a/b) ^ (1/2) is a^ (1/2) / b^ 1/2
( 4/9) ^ 1/2
4^1/2
-----------
9 ^ 1/2
2
----
3
5. Sarah and Aarnav had a 3-layer wedding cake made for their wedding. Each layer was 6 inches in height. The lower layer had a diameter of 12 inches, while the middle layer had a radius of 5 inches. The top layer had a diameter of 8 inches.
a) Calculate the total volume of cake to the nearest cubic inch. (3 marks)
b) The baker who made the cake needed to calculate the total surface area of the outside of the cake to the nearest square inch to find out how much icing to buy. The baker will not be icing the bottom of any of the layers of cake. However, the baker will ice the top and sides of each layer separately and then stack the three layers of cake. Calculate the surface area of the cake that the baker plans to ice to the nearest square inch. (3 marks)
c) The baker bought the buttercream icing from Crave Cupcakes. Using your surface area calculation from part b, calculate how many containers of icing the baker needs to buy in order to ice Sarah and Aarnav’s cake. Each container of icing contains 16 ounces of icing. If it takes 56 ounces of icing to cover 678 square inches of cake, calculate the total cost for the icing before tax if each 16-ounce (2 cup) container of icing costs $10. (3 marks)
Answer:
Total volume of cake = 1452 cubic inches
Step-by-step explanation:
Each layer of the cake has a cylindrical shape, so that:
volume of a cylinder = [tex]\pi[/tex][tex]r^{2}[/tex]h
Where r is the radius and h represents the height.
i. For the lower layer;
h = 6 inches and r = 6 inches
volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{22}{7}[/tex] x [tex](6)^{2}[/tex] x 6
= 678.86 cubic inches
ii. For the middle layer;
h = 6 inches and r = 5 inches
volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{22}{7}[/tex]x [tex](5)^{2}[/tex] x 6
= 471.43 cubic inches
iii. For the top layer;
h = 6 inches and r = 4 inches
volume = [tex]\pi[/tex][tex]r^{2}[/tex]h
= [tex]\frac{22}{7}[/tex] x [tex](4)^{2}[/tex]x 6
= 301.71 cubic inches
Total volume of cake = 678.86 + 471.43 + 301.71
= 1452 cubic inches
10% of 360 is how much more than 5% of 360
10% of 360 is 18 more than 5% of 360.
What is the percentage?The percentage is defined as ratio expressed as a fraction of 100.
What are Arithmetic operations?
Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Given data as :
10% of 360
5% of 360
Firstly, we have to determine 10% of 360,
⇒ 10% of 360
⇒ (10/100)360
⇒ (0.10)360
So, 10% of 360 is 36.
⇒ 5% of 360
⇒ (5/100)360
⇒ (0.05)360
So, 5% of 360 is 18.
Since 10% of 360 is more than 5% of 360
So, substract 18 from 36, and
⇒ 36 - 18
⇒ 18
Hence, 10% of 360 is 18 more than 5% of 360.
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Counting numbers are to be formed using only the digits 1, 3, 7,5,4,8, and 2. Determine the number of different possibilities for two-digit numbers.
Answer:
11699 numbers and 42 two-digit numbers
I need help with this
Answer:
sorry but I don't know the answer
Answer:
B. 0.30
Step-by-step explanation:
30/100 = 0.30
Taree fourts of the 64 books were math books. determine the percent of the books that were math books.
Answer: 75% - these are books on mathematics.
Step-by-step explanation:
[tex]\dfrac{3}{4} \cdot 64 = 48\\[/tex]
64 - 100%
48 - x%
[tex]\dfrac{64}{100} =\dfrac{48}{x}\\\\x=\dfrac{48 \cdot 100}{64} \\\\x=75 \%[/tex]
The length of a rectangle is 4 meters and the width is 4 meters. What is the perimeter of the rectangle? Do not include units in your answer.
9 bushes in 81 minutes , how much time taken per bush
Answer:
9
Step-by-step explanation:
9 bushes in 81 minutes.
Take 81, divide by 9, 81÷9 equals 9. 9 minutes are taken per bush.
which exponential function has an initial value of 2
Answer:
Exponential growth formula. a represents the initial value.
Step-by-step explanation:
The value of "b" will determine the growth or decay behavior of the exponential function.
An exponential function can be represented in the form:
f(x) = a * b^x
where "a" is the initial value or the value of the function when x = 0, and "b" is the base of the exponential function.
If we want an exponential function with an initial value of 2, we can set "a" equal to 2:
f(x) = 2 * b^x
The value of "b" will determine the growth or decay behavior of the exponential function. Without further information or constraints on the value of "b," we cannot determine the specific exponential function. Additional information, such as the growth/decay factor or a specific point on the function, is needed to determine the value of "b" and fully define the exponential function.
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PLEASE HURRY!!!
Which statement about these rectangles is true?
Answer:
A. The dilation is an enlargement.
Step-by-step explanation:
Well, it's showing a bigger rectangle with a "(1.5)" in parenthesis meaning it's multiplying.
Which means the rectangle is being dilated by 1.5.
Which inequality is shown in the graph?
Answer:
A.
Step-by-step explanation:
the equation of the parabola shown in the graph is y=x²-5, then the inequality is y≥x²-5 (inside the parabola).
So for this problem, I almost got it however my rounding is off causing my answers to be wrong. Can someone please help me with the two that are wrong. Thank you for your help!
Answer:
it 94x26.2 i think it right if not sorry :/
Step-by-step explanation:
can someone help me with this question
9514 1404 393
Answer:
local minima: at x=-1, x=3local minimum values: -2 and -1 (respectively)Step-by-step explanation:
A local minimum is where the curve stops going down and starts going up. It is the bottom of any U-shaped spot. Here, those are identified with dots at the coordinates (-1, -2) and (3, -1).
(a) the x-values at which f has a local minimum are -1 and 3.
(b) the local minimum values of f are -2 and -1 at those x-values.
graph a circle with General form.x^2 +y^2+8x-12y+24=0
Answer:
jhshejwjabsgsgshshsnsjs
Answer:
Step-by-step explanation:
Put the equation into center-radius form.
x² + y² + 8x - 12y + 24 = 0
x² + y² + 8x - 12y = -24
(x²+8x) + (y²-12y) = -24
(x²+8x+4²) + (y²-12y+6²) = 4²+6²-24
(x+4)² + (y-6)² = 28
Center: (-4,6)
radius: √28
Use the diagram to determine the height of the tree.
where's the diagram?
A tank contains 200 L of salt solution which contains 100 grams of salt. Pure water enters the tank ata rate of 4 L/min, but the thoroughly mixed solution leaves the tank at a rate of 2 L/min.Write andsolve an IVP to determiney, the number of grams of salt in the tank at timet.
Answer:
a. dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. y = 20000/(200 + t)
Step-by-step explanation:
a. Write an IVP to determine y, the number of grams of salt in the tank at time, t.
Let y be the mass of salt.
The net flow into the tank dy/dt = mass flow in - mass flow out
Since only water flows into the tank, the mass flow in = 0 g/min
Let m be the mass of salt in the tank at time t. Since the volume of the tank is 200 L and water flows in at a rate of 4 L/min and out at a rate of 2 L/min, the net rate of increase of the volume of the tank is rate in - rate out = 4 L/min - 2 L/min = 2L/min. So, in time, t, the volume of the water in the tank increases by 2t. So, the volume of the tank in time, t is V = 200 + 2t.
So, the concentration of salt in the tank at time t is mass/volume = m/(200 + 2t).
Since the well mixed solution leaves at a rate of 2 L/min, the mass flow out is concentration × volume flow out = y/(200 + 2t) × 2 = 2y/(200 + 2t)
The net flow into the tank dy/dt = mass flow in - mass flow out
dy/dt = 0 - 2y/(200 + 2t)
dy/dt = - 2y/(200 + 2t)
Since the initial mass of salt in the tank is 100 g, y(0) = 100 g
So, the initial value problem IVP is
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
b. Solve an IVP to determine, the number of grams of salt in the tank at time, t.
Solving the IVP, we have
dy/dt = - 2y/(200 + 2t) where y(0) = 100 g
Separating the variables, we have
dy/y = - 2dt/(200 + 2t)
Integrating both sides, we have
∫dy/y = - ∫2dt/(200 + 2t)
㏑y = - ㏑(200 + t) + ㏑C
㏑y + ㏑(200 + t) = ㏑C
㏑[y(200 + t)] = ㏑C
y(200 + t)] = C
y = C/(200 + t) since y(0) = 100, we have
100 = C/(200 + 0)
100 = C/200
C = 100 × 200
C = 20000
So, y = C/(200 + t)
y = 20000/(200 + t)
