Answer:
5/8
that's mah answer tht is correct
Fifteen students from Poppy High School were accepted at Branch University. Of those students, six were offered academic scholarships and nine were not. Mrs. Bergen believes Branch University may be accepting students with lower ACT scores if they have an academic scholarship. The newly accepted student ACT scores are shown here.
Academic scholarship: 25, 24, 23, 21, 22, 20
No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27
Part A: Do these data provide convincing evidence of a difference in ACT scores between students with and without an academic scholarship? Carry out an appropriate test at the α = 0.02 significance level. (5 points)
Part B: Create and interpret a 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship. (5 points)
Answer:
See below for answers and explanations
Step-by-step explanation:
Part A:
Given:
Pooled sample size: [tex]n=15[/tex]
Sample size (with academic scholarships): [tex]n_1=6[/tex]
Sample size (no academic scholarships): [tex]n_2=9[/tex]
Population standard deviations: Unknown
Sample mean (with academic scholarships): [tex]\bar{x}=\frac{25+24+23+21+22+20}{6}=22.5[/tex]
Sample mean (no academic scholarship):[tex]\bar{x}=\frac{23+25+30+32+29+26+27+29+27}{9}=27.\bar{5}[/tex]
Sample standard deviation (with academic scholarships): [tex]s_1=1.7078[/tex]
Sample standard deviation (no academic scholarships): [tex]s_2=2.5868[/tex]
Degrees of freedom: [tex]df=n-2=15-2=13[/tex]
Significance level: [tex]\alpha =0.02[/tex]
Decide which test is most appropriate to conduct:
Therefore, we will conduct a 2-sample t-test assuming our conditions are satisfied.
List null and alternate hypotheses:
[tex]H_o:\mu_1=\mu_2[/tex] -> There's no difference in ACT scores between students with and without an academic scholarship
[tex]H_a:\mu}_1\neq\mu_2[/tex] -> There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
Determine the value of the test statistic:
We will use the formula [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }[/tex] to compute the test statistic [tex]t[/tex]. Therefore, the test statistic is [tex]t=\frac{\bar{x}_1-\bar{x}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2} } }=\frac{27.\bar{5}-22.5}{\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9} } }=4.5592[/tex]
Calculate the p-value:
Because the test is two-sided, [tex]p=2tcdf(4.5592,1e99,13)=2(0.0003)=0.0006[/tex]
Interpret p-value and conclude test:
Given our significance level is [tex]\alpha =0.02[/tex], since [tex]p<\alpha[/tex], we reject the null hypothesis and conclude that there is significant evidence that suggests that there is a difference in ACT scores between students with and without an academic scholarship (it's more likely that the alternate hypothesis is true)
Part B:
The formula for a confidence interval for the difference in 2 population means is [tex]CI=(\bar{x}_1-\bar{x}_2)\pm t^*\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}[/tex] where [tex]\bar{x}_1-\bar{x}_2[/tex] is the difference of the 2 sample means and [tex]t^*[/tex] is the critical score for the desired confidence level.
The critical score for our 98% confidence interval would be [tex]t^*=invT(0.99,13)=2.6503[/tex]
Therefore, our 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is [tex]CI=(27.\bar{5}-22)\pm 2.6503\sqrt{\frac{1.7078^2}{6}+\frac{2.5868^2}{9}}}=[2.6167,8.4944][/tex]
This means that we are 98% confident that the true difference in the ACT scores between students with and without an academic scholarship is contained within the interval [tex][2.6167,8.4944][/tex]
The evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
How to perform two sample t-test?If the sample sizes < 30, and we want to test the difference between the sample means, then we perform t-test.
Let we have:
[tex]\overline{x}_1[/tex] = mean of first sample[tex]\overline{x}_2[/tex] = mean of second sample[tex]s_1[/tex] = standard deviation of first sample[tex]s_2[/tex] = standard deviation of second sample.Then, the value of t-test statistic is obtained as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}}[/tex]
If the level of significance is [tex]\alpha[/tex], then as we have:
the degree of freedom (d.f) = [tex]n_1 + n_2 - 2[/tex], the critical value of t is found to be [tex]t_{\alpha/2}[/tex], then if we get:
[tex]|t| < t_{\alpha/2}[/tex]null hypothesis
and if we get [tex]|t| > t_{\alpha/2}[/tex] null hypothesis, and thus, accept the alternate hypothesis.
For this case, we want to test if there is
Thus, we form the hypotheses as:
Null hypothesis: There's no difference in ACT scores between students with and without an academic scholarship
or: [tex]H_0: \mu_1 = \mu_2[/tex]
Alternative hypothesis: There's a difference in ACT scores between students with and without an academic scholarship (it's two-sided)
or [tex]H_1: \mu_1 \neq \mu_2[/tex]
where we have:
[tex]\mu_1[/tex] = population mean score of ACT of students having academic scholarship[tex]\mu_2[/tex] = population mean score of ACT of students having no academic scholarshipFor this case, we evaluate the mean and standard deviation as:
Sample 1: Academic scholarship: 25, 24, 23, 21, 22, 20Sample size = [tex]n_1 = 6[/tex]
Mean = sum of all observation/ number of observations = 135/6 =22.5
Thus, standard deviation = [tex]s_1 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_1})^2}} = \sqrt{\dfrac{17.5}{6}} \approx1.71[/tex]
Sample 2: No academic scholarship: 23, 25, 30, 32, 29, 26, 27, 29, 27Sample size = [tex]n_2 = 9[/tex]
Mean = sum of all observation/ number of observations = 248/9 ≈27.56
Thus, standard deviation = [tex]s_2 = \sqrt{\dfrac{1}{n}\sum{(x_i - \overline{x_2})^2}} \approx \sqrt{\dfrac{60.22}{9}} \approx 2.59[/tex]
The t-test statistic is evaluated as:
[tex]t = \dfrac{\overline{x}_1 - \overline{x}_2}{\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}} = \dfrac{22.5 -27.56}{\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}}} \approx -4.56[/tex]
Degree of freedom = [tex]n_1 + n_2 - 2 = 6 + 9 - 2 = 13[/tex]
Level of significance = 0.02 = 2%
The critical value of t is found to be [tex]t_{0.02/2} =2.65[/tex]
Thus, we get: [tex]|t| \approx 4.56 > 2.65 =t_{\alpha/2}[/tex]
Thus, we may reject the null hypothesis.
That means, there is enough evidence of a difference in ACT scores between students with and without an academic scholarship at 0.02 level of significance.
Now, the 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is calculated as:
[tex]CI = (\overline{x}_1 - \overline{x}_2) \pm t_{\alpha/2}\sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_1}}\\\\CI = -5.06 \pm 2.65(\sqrt{\dfrac{2.92}{6} + \dfrac{6.69}{9}})\\\\CI \approx -5.06 \pm 2.65 \times 1.11\\CI \approx -5.06 \pm 2.94\\CI \approx [-5.06 - 2.94, -5.06 + 2.94] = [-7.00, -2.14][/tex]
Thus, the evaluation of sub-parts results in:
Part A: Yes, the data provides convincing evidence of a difference in A at CT scores between students with and without an academic scholarship at α = 0.02
Part B: The 98% confidence interval for the difference in the ACT scores between students with and without an academic scholarship is evaluated to be [tex]CI \approx [-7.00, -2.14][/tex]
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Hellppp pleaseee
Please be quick lol
Answer:
20(pi)
Step-by-step explanation:
• equation for the circumference of a circle= 2(pi)r
• You are given the diameter ( 20ft) but you need the radius (r) for the equation.
• divide 20 by 2 to get the radius since it is half of the diameter.
• 20/2=10 so c= 2(pi)(10)
• 2(10)=20
• plug in pi and your final answer is 20(pi)
Hey help me out please?
Answer:
I believe it is C
It's the only one that makes sense
An equation with no solutions
3x + 7 = X + 3
Answer:
X = -2
Step-by-step explanation:
Hope this helps
Assume that you want to construct a box with a square base (closed top) and a volume of 1000 cm3 . Find the dimensions of the box to minimize the surface area of the box.
Answer:
[tex]x=10\sqrt[3]{2}[/tex]
Step-by-step explanation:
The Volume of a box with a square base
x by x cm and height h cm is
V =x^2h
The amount of material used is directly proportional to the surface area, so we will minimize the amount of material by minimizing the surface area.
The surface area of the box described is
A = x ^2 +4 x h
We need
A as a function of x alone, so we'll use the fact that
V= x^2h = 1000 cm^3
This imples [tex]h=\frac{1000}{x^2}[/tex]
This makes
[tex]A= x^2 + 4x(1000/x^2)\\A= x^2+4000/x[/tex]
Differentiating A w.r.t. x
[tex]A' = 2x-4000/x^2[/tex]
Now, A'=0
[tex]x=10\sqrt[3]{2}[/tex]
Therefore, minimum value x = [tex]x=10\sqrt[3]{2}[/tex]
plz help me asap !!!
Answer:
Step-by-step explanation:
x+60=140
x=140-60
x=80 degree
Three families, a, b, & c share 480 kg of rice. B receives twice as much as a, c receives half of b. How much rice does each family get?
Answer:
Family a got 120kg, b got 240 kg and c got 120 kg
Step-by-step explanation:
Given that 480kg of rice is shared by families a, b, c. let these alphabets represent the amount received by each family.
a + b + c = 480
Given that B receives twice as much as a, c receives half of b then,
b = 2a and
c = 1/2 b = b/2
from b = 2a,
a = b/2
substituting into the first equation
b/2 + b + b/2 = 480
b + b = 480
2b = 480
b = 480/2
= 240 kg
a = c = b/2
hence a = c = 240/2 = 120kg
Increase £140 by 5%.
Thank you so much
Answer:
£140 increased by 5% is £147.00
Answer:
it should be 147.00 , I'm so sorry if I'm wrong!
What percent of 8 is 6? pls give a detailed explanation thanks
Answer:
x/100 x 8 = 6
8x/100 = 6
x100 x100
8x = 600
Divide by 8 on both sides:
X = 75
Consider a percent out of 100. 'Of' meaning multiplication. 'is' meaning equal to that number.
(unknown number/percent)x/100 x 8(of 8) = 6(is 6)
Which symbol correctly compares the two angles?
45° pi/3
Answer:
a pi = 3.14
Step-by-step explanation:
The symbol which compares the two angles is "< ".
What is an angle?
Angles around a point define the sum of angles that can be arranged together so that they construct a full arch. Angles around a point add to 360 °.
π/3 =180/3 = 60 degree
π/3 > 45 degree
45 degree < π/3
Therefore, the correct answer is option A. <.
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1. Gwen deposits $7,000 in a savings account with an annual interest rate of 2.5%. What function
represents the value of her account after x years? What will her balance be after 9 years?
Answer:
Results are below.
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $7,000
Interest rate (i)= 2.5%
To calculate the future value after x years, we need to use the following formula:
FV= PV*(1 + i)^x
Now, for 9 years:
x= 9
FV= 7,000*(1.025^9)
FV=$8,742.04
Returns on stock X are listed below: Period 1 2 3 4 5 6 7 Stock X 6% 5% -2% 10% 3% 8% -4% What is the mean of the data?
Answer:
The mean of the data is of 3.7143%.
Step-by-step explanation:
Mean of the data:
Sum of all returns divided by the number of returns.
Returns:
6% 5% -2% 10% 3% 8% -4%
7 returns.
Sum: 6 + 5 - 2 + 10 + 3 + 8 - 4 = 26%
Mean: 26%/7 = 3.7143%
The mean of the data is of 3.7143%.
A point is on a circle if the distance from the center of the circle to the point is equal to the
area.
circumference.
radius.
diameter
Answer:
radius
Step-by-step explanation:
Answer:
Radius
Step-by-step explanation:
Center of the circle to a point on a circle would be the radius, seeing how as diameter is one edge of the circle to the other edge,of the circle, crossing the middle of the circle
please help ASAP! 7th grade
Since their were no numbers to the questions i had to write it by the problem
Circle with 9 feet question
C=2(pi)r or C=(pi)d
Circular table question
A=(pi)r^2
Interest question
I=Prt
Volume of a rectangular prism
V=Bh
Triangular pyramid
V=1/3Bh
pls help i need help
Answer:
Put x's on the numbers on the line that are above the line
Step-by-step explanation:
I BELIVE IN YOU
35 POINTS!!!!
Every morning, Jorge runs a circular path that has a radius of 42 ft. How far does Jorge run if he does one lap around the track? Round your answer to the nearest foot. Use π=3.14.
A. 264 ft
B. 66 ft
C. 5,539 ft
D. 132 ft
y = 3x2 – 2x +3
Please help
Answer:
[tex]y = {3x}^{2} - 2x + 3 \\ y = ( \frac{1}{3} + i) {}^{2} [/tex]
What is the value of 11g - 9k + 3 when g = 9 and k = 11?
Neatly show your work.
Answer:
3
Step-by-step explanation:
11g - 9k + 3
Let g = 9 and k =11
11 * 9 - 9*11 +3
Multiply
99 - 99 +3
Add
3
Answer:
3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
Identify
11g - 9k + 3
g = 9
k = 11
Step 2: Evaluate
Substitute in variables: 11(9) - 9(11) + 3Multiply: 99 - 99 + 3Subtract: 3What's the mean of {4,7,10}
Answer:
mean = (4 + 7 + 10 ) / 3
= 21 / 3
= 7
Step-by-step explanation:
Answer:
Average of 4,7 and 10:
Add all together 4+7+10=21
Then 21 divided by number of scores so 3.
21 divided by 3=7
So the mean is 7
Can someone please help me?
p-8=3 can some one help me
Answer:
p=3+8=11
Step-by-step explanation:
Answer:
p = 11
Step-by-step explanation:
add 8 to both sides of the equation, so p = 3 + 8
p = 11
Find the area of the shaded region.
Answer:
12.86 sq ft
Step-by-step explanation:
Find area of square and subtract out area of semi-circle; the diameter of the semi-circle equals the side of the square, which is 4 so radius is 2
A(square) = 4 x 4 = 16
A(semi-circle) = πr²/2
= 4π/2 or 2π
Area of Shaded Region = 16-3.14 which is 12.86
1,367.5897 to the nearest whole
Answer:
1368
hope this helps
have a good day :)
Step-by-step explanation:
Can someone help me with this thank you
Answer:
30 sq cm
Step-by-step explanation:
The area of a parallelogram is the base times the height. We can see that the base is 10 cm, and 3 cm would be the height because it is perpendicular to the base. We get the equation:
Area = 10 cm x 3 cm
Area = 30 sq cm
A 25.5 foot ladder rests against the side of a house at a point 24.1 feet above the ground. The foot of the ladder is x feet from the house. Find the value of x to one decimal place.
Answer:
8.3
Step-by-step explanation:
Use the pythagorean theorem: a2 + b2 = c2 a2 would be 24.1 and c2 would be 25.5. square them then subtract a2 from b2. then find the square root of your answer which is 8.3
Match the vocabulary word with the correct definition.
1. compound event
2. independent event
3. dependent event
- the occurrence of one event affects
the probability of the occurrence of another event
- the occurrence of one event does
not affect the probability of the occurrence of another event
- two or more events considered
independent event-the occurrence of one event does not affect the probability of the occurrence of another event
compound event-two or more events considered
dependent event-the occurrence of one event affects the probability of the occurrence of another event
a) Compound Event refers to the combination of two or more events considered.
b) Independent Event occurs when one event does not affect the probability of the occurrence of another event.
c) Dependent Event describes a situation where the occurrence of one event affects the probability of the occurrence of another event
a) Compound Event: This refers to the combination of two or more events considered together. It involves analyzing the probability of multiple events occurring in a specific situation or experiment. For example, when rolling a pair of dice, the compound event might be the probability of getting a sum greater than 9.
b) Independent Event: This occurs when the outcome or occurrence of one event has no impact on the probability of the outcome or occurrence of another event. In other words, the events are unrelated and do not influence each other. For example, flipping a coin and rolling a die are independent events since the outcome of the coin flip does not affect the outcome of the die roll.
c) Dependent Event: This describes a situation where the occurrence of one event does affect the probability of the occurrence of another event. In dependent events, the outcome or happening of the first event has an impact on the likelihood of the second event. For instance, drawing cards from a deck without replacement is a dependent event since the probability of drawing a certain card changes after each card is drawn.
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Please I need help.
Find each length or area to the nearest tenth.
ZY:_____
XZ:_____
Area of XYZ:_____
Answer:
XZ = 26.7
ZY = 11.7
Area = 140.4 sq inches
Step-by-step explanation:
m∠Z = 180-(26+90) = 64°
to get XZ you can use the law of sines:
sin 90°/XZ = sin 64°/24
1/XZ = sin(64°)
cross-multiply to get:
XZ·sin(64°) = 24
XZ = 24/sin(64°)
XZ = 26.7
to get ZY you can use the law of sines again:
sin 64°/24 = sin 26°/ZY
cross-multiply to get:
ZY·sin(64°) = 24·sin(26°)
ZY = 24·sin(26°) ÷ sin(64°)
ZY = 11.7
Area = 1/2(11.7)(24)
= 12(11.7)
= 140.4 sq inches
Find the value of x that makes m∥n. PLEASEE HELP
Answer:
Step-by-step explanation:
143=5x+13(being corresponding angles)
143-13=5x
130/5=x
26=x
=======================================================
Explanation:
The angles shown are corresponding angles. Notice how they are in the northeast corner of their respective four-corner configuration.
If m is parallel to n, then the corresponding angles are congruent, and we can say...
5x+13 = 143
5x = 143-13 .... subtract 13 from both sides
5x = 130
x = 130/5 .... divide both sides by 5
x = 26
So taking this logic in reverse: if x = 26, then that leads to 5x+13 equal to 143, making the corresponding angles congruent. Therefore, it would lead to lines m and n being parallel.
Which of the following is the graph of (x + 3)2 + (y - 1)2 = 9? A B с 2. 2 2 2 4 -2 4 2 -2 2 2 4 2.
The third one is the correct graph for the equation
hope it helps !!
The equation [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex] is the equation of a circle. Graph B shows the given equation.
What is a graph?A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.
The standard equation of the circle is;
[tex]\left(x-h\right)^{2}+\left(y-k\right)^{2}=r^{2}[/tex]
Where,
(h,k) are the coordinates of points on the x and y-axis.
r is the radius
The equation [tex]\left(x-3\right)^{2}+\left(y-1\right)^{2}=3^{2}[/tex] is the equation of a circle.
Hence, graph B shows the given equation.
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3
Find the missing angle.
20
180°
A
100°
B
50°
80°
D 70°