Answer:
a)
The null hypothesis is [tex]H_0: p = 0.91[/tex].
The alternate hypothesis is [tex]H_1: p < 0.91[/tex].
The decision rule is: accept the null hypothesis for [tex]z > -1.645[/tex], reject the null hypothesis for [tex]z < -1.645[/tex].
Since [tex]z = -1.79 < -1.645[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
b)
The p-value for this test is 0.0367. Since this p-value is less than the significance level of [tex]\alpha = 0.05[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
Step-by-step explanation:
Question a:
Perform the appropriate hypothesis test to determine whether this is significant evidence that the percentage of athletes who graduate is less than for the student population at large:
At the null hypothesis, we test if the proportion is the same as the student population, of 91%. Thus:
[tex]H_0: p = 0.91[/tex]
At the alternate hypothesis, we test that the proportion for athletes is less than 91%, that is:
[tex]H_1: p < 0.91[/tex]
The test statistic is:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
Test if the proportion is less at the 0.05 level:
The critical value is z with a p-value of 0.05, that is, z = -1.645. Thus, the decision rule is: accept the null hypothesis for [tex]z > -1.645[/tex], reject the null hypothesis for [tex]z < -1.645[/tex].
0.91 is tested at the null hypothesis:
This means that [tex]\mu = 0.91, \sigma = \sqrt{0.91*0.09}[/tex]
A sports reporter contacted 152 athletes randomly sampled from that same university and time period and found that 132 of them had graduated within 6 years.
This means that [tex]n = 152, X = \frac{132}{152} = 0.8684[/tex]
Value of the test statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.8684 - 0.91}{\frac{\sqrt{0.91*0.09}}{\sqrt{152}}}[/tex]
[tex]z = -1.79[/tex]
Since [tex]z = -1.79 < -1.645[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
(b) (3 points) Calculate the P-value for this test. Explain how this P-value can be use to test the hypotheses in part (a).
The p-value of the test is the probability of finding a sample proportion of 0.8684 or below. This is the p-value of z = -1.79.
Looking a the z-table, z = -1.79 has a p-value of 0.0367.
The p-value for this test is 0.0367. Since this p-value is less than the significance level of [tex]\alpha = 0.05[/tex], we reject the null hypothesis and accept the alternate hypothesis that that percentage of athletes who graduate is less than for the student population at large.
brainlest for answered
Answer:
Hello! answer: 4/5
Step-by-step explanation:
20 ÷ 5 = 4 25 ÷ 5 = 5 that is 4/5 therefore 4/5 is the answer because we cannot reduce any further HOPE THAT HELPS!
Answer:
[tex]\frac{20}{25} =\frac{4}{5}[/tex]
What additional piece of information
would prove ALMK = ANMK by
Side-Angle-Side?
Answer:
MK bisects <LKN
Step-by-step explanation:
We can already say two sets of sides are equal; LK = NK because it is given and MK = MK because of reflexive property. In order to use Side-Angle-Side, we need to prove the angles between the sides are congruent. This means <LKM and <NKM. The only option that would help is with the is the lat option, MK bisects <LKN because, then we could say <LKM and NKM are congruent because MK would be an angle bisector. This is exactly what we want, so the answer is MK bisects <LKN.
The top rail of a boat is 4 ft out of the water. If the water rises 3 ft, how far out of
the water is the top rail of the boat?
Answer:
the correct answer is 1ft
Step-by-step explanation:
4ft-3ft
=1ft
la
You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
Answer: 3¼ hours
Step-by-step explanation:
Number of hours used in baking = 2¾ hours
Number of hours used in cleaning up the kitchen = ½ hour
Therefore, the time used in the kitchen will be the addition of the time used in baking plus the time used in cleaning the kitchen which will be:
= 2¾ + ½
= 2 3/4 + 2/4
= 2 5/4
= 2 + 1¼
= 3¼ hours
Therefore, 3¼ hours was used in the kitchen.
find the measure of each angle indicated
a. 33
b. 36
c. 31
d. 136
Answer:
31
Step-by-step explanation:
Let the missing angle be x.
Sum of angles in a triangle is supplementary,
x + 20 + 129 = 180
x + 149 = 180
x = 180 - 149
x = 31
Answer:
31
Step-by-step explanation:
A triangle is 180 degrees.
129 + 20 = 149
180 - 49 = 33
Y-intercept = -4
• Slope = -1
2
y
10
9
8
2
6
5
4
3
2
-10
-9
-8
-7
-6
-5
- 4
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
-1
2
-3
-4
-5
-6
-7
-8
-9
-10
Answer:
First point: -4 on y axis.
Second point: (2, -5)
Step-by-step explanation:
When graphing, we always set the equation as y=mx+b where m = slope and b = y intercept
y = mx + b
y = [tex]-\frac{1}{2}x-4[/tex]
Then we plot by starting with the y intercept going four units down, one unit below and two units to the right.
What number do the blocks represent?
Write your answer as a decimal.
7m + 3mn
when m = 3 and n = -4
Answer:
-15
Step-by-step explanation:
When m=3 and n=-4
So, put the values
7(3)+3(3)(-4)
-> -15
Answer:
-15
Step-by-step explanation:
= 7(3) + 3(3)(-4)
= 21 + 3(3×-4)
= 21 + 3(-12)
= 21 + -36
= 21-36
= -15
Need help anything would help at this point !!!? Extra points
Answer:
here,radius =2 in
now use formula pie (r)^2 where pie is 3.14
=pie *(r)^2
=3.14*(2in.)^2
=3.14*4in.^2
12.56in.^2
Step-by-step explanation:
What is coordinates of point C?
Answer:
(3,6)
Step-by-step explanation:
Using the midpoint segment formula
M(X, Y) = [(ax1+bx2/2, ay1+by2/2)]
Given (-2 -6) and (4,6) divided in the ratio 1:5
X = 1(-2) + 5(4)/1+5
X = -2+20/6
X = 18/6
X = 3
Similarly
Y = 1(-6)+ 5(6)/1+5
Y = -6+30/6
Y = 24/6
Y = 4
Hence the required coordinate of C is (3,6)
What is the ratio of 765000 to 100000
Answer:
153:20
Step-by-step explanation:
765000/100000
=153/20
ABCD is a parallelogram. Find x and the length of CD.
Answer:
3×+9=5x-5
-2×=-14
×=7...thenCD=3(7)+9=30
A video store charges $5 per game rental plus $12 to rent the game system. Write an expression for renting the game system and a number of games.
Answer:
12 + 5X = Y
Step-by-step explanation:
Given that a video store charges $ 5 per game rental plus $ 12 to rent the game system, to write an expression for renting the game system and a number of games the following logical reasoning must be performed:
5 = variable not fixed, depends on the number of games
12 = fixed variable
X = number of games
Y = total value
12 + 5X = Y
Thus, if 5 video games were rented, the equation would operate as follows:
12 + 5x5 = Y
12 + 25 = Y
37 = Y
find the area of the figure
area: units2
Answer:
Area of the figure = 25 square units
Step-by-step explanation:
Area of the given figure = Area of ΔCDE + Area of rectangle BCEI + Area of ΔABH + Area of GIF
Area of ΔCDE = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]
= [tex]\frac{1}{2}(CE)(DK)[/tex]
= [tex]\frac{1}{2}(8)(4)[/tex]
= 16 units²
Area of rectangle BCEI = Length × Width
= CE × EI
= 8 × 1
= 8 units²
Area of ΔABH = Area of ΔGIF = [tex]\frac{1}{2}(1)(1)[/tex]
= [tex]\frac{1}{2}[/tex] units²
Area of the complete figure = 16 + 8 + [tex]\frac{1}{2}[/tex] + [tex]\frac{1}{2}[/tex]
= 25 units²
Factor the following expressions completely. Show and check all work on your own paper.
5x2-50x+125
3. What is the missing term in the sequence 10, 12, 16, 24,
, 72?
A. 32
B. 40
C. 48
D. 64
4. What rule is being used in this sequence 25, 28, 26, 29, 27?
A. Add 3.
B. Add 3, subtract 2...
C. Subtract 3, add 2...
D. Multiply by 3, subtract 2...
5. What is the value of kin 6k - 19 = 23?
A. 14
B. 11
C. 7
D. 5
Answer pls. ASAP Need it now
Answer:
3. B
4. B
5. C
Step-by-step explanation:
answer plz faaast any one know the answer
Step-by-step explanation:
[tex] \binom{ \lim}{x→0} ( \frac{1}{x} - \frac{1}{ \ \: sinx} ) = \binom{ \lim}{x→0}( \frac{ \ sinx - x }{x \ sinx } ) = \binom{ \lim}{x→0}( \frac{ \ cosx - 1 }{x \ cosx + \ sinx } ) = \frac{0}{0} = 0[/tex]
J.UIV1.2.2 DUN 2 formative Jackson, Braddyn OO 10 1 Abox, shaped like a rectangular prism, is shown below. 2 in. 8 in. 10 in. What is the surface area of the box? 232 square inches 160 square inches 116 square inches O 96 square inches ?
Answer:m
Step-by-step explanation:
A tank contains 40 gallons of a solution composed of water and bleach. At the start there are 4 gallons of bleach in the tank. A second solution containing half water and half bleach is added tothe tank at the rate of 4 gallons per minute. The solution is kept throughly mixed and drains from the tank at the rate of 4 gallons per minute.
(a) How much blcach is in the tank after t minutes?
(b) Will there be at least 14 gallons of bleach in the tank after 10 minutes?
(c) How much bleach will there be in the tank after a very long time has passed?
Answer:
a) x* e∧ t/10 = 20 *e∧ t/10 + 2
b) x = 14,2 gall. In 10 min. we get 14,2 gallons of bleach in the tank
c) After a very long time we will find 20 gallons of bleach in the tank
Step-by-step explanation:
The variation of bleach in water in the tank is Δ(x)t:
Δ(x)t = [Amount of x added to the tank - Amount of x drain out of the tank]*Δt
Now the amount of x added to the tank is:
Rate of adding* the concentration
Rate of adding = 4 gallons per minute
Concentration half and half ( water + bleach) = 0,5
Rate of draining = 4 gallons per minute
Concentration of draining: Unknown but can be expressed as:
x(t)/40. According to this
Δ(x)t = [4 * 0,5 - 4 * x(t)/40]*Δt
Dividing by Δt on both sides of the equation and tacking limits we get
dx/ dt = 2 - x / 10
dx/dt + x/10 =2
Multyiplying by e∧ t/10 on both sides
e∧ t/10* [ dx/dt + x/10 ] = 2 *e∧ t/10
To solve it, integrating the first member is
x* e∧ t/10 = 20 *e∧ t/10 + C
for initial condition t = 0
4 = 20 + C
C = -16
a) x* e∧ t/10 = 20 *e∧ t/10 - 16
b) in 10 minutes
x* e∧ t/10 = 20 *e∧ t/10 - 16
x *e = 20*e - 16
x = 20 - 16/e
x = 20 - 16/2,718
x = 20 - 5,88
x = 14,2 gallons.
c) After a very long time we will find 20 gallons of bleach in the tank
How long will it take $10,000 to double at 11% simple interest? (Round to the nearest year)
Answer:
[tex]I =\frac{P*R*T}{100} = \frac{10000 * 11 * T}{100} = 1100T[/tex]
Given A =20000
[tex]Amount = Interest + Principal\\20000 = 1100T + 10000\\20000 - 10000 = 1100T\\\\T= \frac{10000}{1100} = \frac{100}{11} = 9.09 years[/tex]
T =9years
Please help and thank you
Find the value of x. Round the lengths to the nearest tenth of a unit.
Please help!
Answer:
the other angle equal 52
we can use the specail trangle 3 4 5
300 400 500
the 38 degrees angle meet 300
and the 52 degrees angle meet 400
so the answer is 300 i dont know if you understand but i hope you are
pls ask in the comments and i will try to explain because my ebgilish the baddest
The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airports. The maximum possible rating is 10. Suppose a simple random sample of business travelers is selected and each traveler is asked to provide a rating for the Miami International Airport. The ratings obtained from the sample of business travelers follow.
3 7 8 9 10 10 10 9 9 9 9 8 5
6 7 7 9 8 10 9 8 7 6 8 7 9
5 3 9 10 10 9 9 8 9 8 6 10 8
4 7 3 10 8 9 8 10 10 8 8
Develop a 95% confidence interval estimate of the population mean rating for Miami (to 2 decimals).
Answer:
The 95% confidence interval estimate of the population mean is (7.38, 8.46).
Step-by-step explanation:
Before building the confidence interval, we need to find the mean and standard deviation of the sample.
In this sample, there are 50 values.
Mean of the sample:
Sum of all values divided by the number of values.
With the help of a calculator, the mean is of 7.92.
Standard deviation:
Square root of the division of the sum of the difference squared between each value and the mean by the number of the values.
With the help of a calculator, the standard deviation is of 1.8958.
Confidence interval:
We have the confidence interval for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 50 - 1 = 49
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 49 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.01
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.01\frac{1.8958}{\sqrt{50}} = 0.54[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 7.92 - 0.54 = 7.38
The upper end of the interval is the sample mean added to M. So it is 7.92 + 0.54 = 8.46
The 95% confidence interval estimate of the population mean is (7.38, 8.46).
Which expression is equivalent to 1/3b - 7
Answer:
The answer Is 1/3(b-21)
Step-by-step explanation:
Dawn weighs 80 pounds. Olivia weighs 48 ounces more. How much does Olivia weigh?
Help ur homie out pls
I'm still doing the rest but number 1 is D
what is the answer (x + 3)2 – 5 = 0
x= -1/2 is the answer to your question. Mark as brainliest!!!!
What is the measure of angle IXA?
Answer:
is it 120
Step-by-step explanation:
it is 120 I can't really explain how I got it though
What is the rule of 72?
Answer:
Brainiest please
Step-by-step explanation:
In finance, the rule of 72, the rule of 70 and the rule of 69.3 are methods for estimating an investment's doubling time. The rule number (e.g., 72) is divided by the interest percentage per period (usually years) to obtain the approximate number of periods required for doubling. Although scientific calculators and spreadsheet programs have functions to find the accurate doubling time, the rules are useful for mental calculations and when only a basic calculator is available.
The terminal side of in standard position contains the point (20, 21) . Find the exact values of the six trigonometric functions of? Please help
Answer:
27,29
Step-by-step explanation: