Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]
And rounded up we have that n=385
Step-by-step explanation:
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
The estimated proportion for this case is [tex]\hat p=0.5[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]
And rounded up we have that n=385
Please answer this question in two minutes
Answer:
W = (18,0)
Step-by-step explanation:
I found the slope of the line from point M to point V. The slope is -3.875. I continued this slope starting with point V to find the coordinates of point W. The coordinates of point W are (18,0).
I graphed the coordinates and the line of VW on the graph below.
HELP PLEASE ITS FOR PLATO
Answer:
i think it might be A. 0.2
Step-by-step explanation:
Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis.
y= -x +4
Answer: V = [tex]\frac{64}{3}\pi[/tex]
Step-by-step explanation: A solid formed by revolving the region about the x-axis can be considered to have a thin vertical strip with thickness Δx and height y = f(x). The strip creates a circular disk with volume:
V = [tex]\pi. y^{2}.[/tex]Δx
Using the Disc Method, it is possible to calculate all the volume of these strips, giving the volume of the revolved solid:
V = [tex]\int\limits^a_b {\pi. y^{2} } \, dx[/tex]
Then, for the region generated by y = - x + 4:
V = [tex]\int\limits^4_0 {\pi.(-x+4)^{2} } \, dx[/tex]
V = [tex]\pi.\int\limits^4_0 {(x^{2}-8x+16)} \, dx[/tex]
V = [tex]\pi.(\frac{x^{3}}{3}-4x^{2}+16x )[/tex]
V = [tex]\pi.(\frac{4^{3}}{3}-4.4^{2}+16.4 - 0 )[/tex]
V = [tex]\frac{64}{3}.\pi[/tex]
The volume of the revolved region is V = [tex]\frac{64}{3}.\pi[/tex]
The evaluation of the definite integral that represents the volume of the solid is [tex]\mathbf{\dfrac{64 \pi}{3}}[/tex]
Using the Disk Method to determine the volume of a solid formed by revolving the region about the x-axis and the interval [a, b]; we have:
[tex]\mathbf{V = \int ^b_a \pi (y)^2 \ dx}[/tex]
where;
b = 4a = 0[tex]\mathbf{V = \int ^4_0 \pi \Big[-x +4 \Big]^2 \ dx}[/tex]
[tex]\mathbf{V =\pi \int ^4_0\Big[-x^2 -8x+16 \Big] \ dx}[/tex]
[tex]\mathbf{V =\pi \Big[\dfrac{x^3}{3} -4x^2+16x \Big]^4_0 \ dx}[/tex]
[tex]\mathbf{V =\pi \Big[\dfrac{4^3}{3} -4(4)^2+16(4) -0 \Big]}[/tex]
[tex]\mathbf{V =\dfrac{64 \pi}{3}}[/tex]
Therefore, we can conclude that the evaluation of the definite integral that represents the volume of the solid is [tex]\mathbf{\dfrac{64 \pi}{3}}[/tex]
Learn more about the volume of a solid here:
https://brainly.com/question/3845281
The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 23x − 132, y = 0; about the y−axis
Answer:
V = 23π/6
Step-by-step explanation:
V = 2π ∫ [a to b] (r * h) dx
y = −x² + 23x − 132
y = −(x² − 23x + 132)
y = −(x − 11) (x − 12)
Parabola intersects x-axis (line y = 0) at x = 11 and x = 12 ----> a = 11, b = 12
r = x
h = −x² + 23x − 132
V = 2π ∫ [11 to 12] x (−x² + 23x − 132) dx
V = 23π/6
John comes across a recent survey and wants to gauge the strength of the results.
Which of the following would best reflect upon the researcher.
O a margin of error of +/- 10%
O a margin of error of +/- 3%
O a margin of error of +/- 98%
O a margin of error of +/-8%
Answer:
A margin of error of +/- 3%
Step-by-step explanation:
Strenght of surveys:
The lesser the margin of error, the more precise, stronger, the confidence interval is.
The margin of error depends of the number of people surveyed. The more people are surveyed, lower the margin of error is, giving a stronger interval.
In this question:
We want the smaller margin of error, which is given by:
A margin of error of +/- 3%
What is the total surface area of a rectangular prism whose net is shown 29 in. 25in. 25.in. Venus do not delete my question you hater
Answer:
V = 18125 in^3
Step-by-step explanation:
Surface Area of Rectangular Prism:
V = 18125 in^3
Step-by-step explanation:
Surface Area of Rectangular Prism:
S = 2(lw + lh + wh)
length l = 25 in
width w = 25 in
height h = 29 in
diagonal d = 45.7274535 in
total surface area S_tot = 4150 in^2
lateral surface area S_lat = 2900 in^2
top surface area S_top = 625 in^2
bottom surface area S_bot = 625 in^2
volume V = 18125 in^3
Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the planex + 9y + 4z = 27.
Answer:
81/4
Step-by-step explanation:
From the given information; we are to use Lagrange multipliers to find the volume of the largest rectangular box
The coordinate planes and the vertex given in the plane is x + 9y + 4z = 27.
By applying Lagrange multipliers, we have;
[tex]fx = \lambda gx[/tex]
where;
[tex]f: V = xyz[/tex]
[tex]g : x + 9y + 4z = 27[/tex]
From; [tex]fx = \lambda gx[/tex]
[tex]yz = \lambda[/tex] --------- equation (1)
From; [tex]fy = \lambda gy[/tex]
[tex]xz = 9 \lambda[/tex] --------- equation (2)
From; [tex]fz = \lambda gz[/tex]
[tex]xy = 4 \lambda[/tex] --------- equation (3)
Comparing and solving equation (1),(2) and (3);
[tex]\lambda x = 9 \lambda y = 4 \lambda z[/tex]
divide through by [tex]\lambda[/tex]
x = 9 y = 4z
3x = 27
x = 27/3
x = 9
From x = 9y
9 = 9 y
y = 9/9
y = 1
From
x = 4z
9 = 4 z
z = 9/4
Thus; the Volume of the largest rectangular box = 9 × 1 × 9/4
= 81/4
1)5/6 of 3/4÷7/8×2/2
2)3/2of3/4÷8/2
Step-by-step explanation:
[tex] (\frac{5}{6} \times \frac{3}{4} ) \times \frac{8}{7} \times 1 \\ = \frac{5}{8} \times \frac{8}{7} \\ = \frac{5}{7} [/tex]
[tex]( \frac{3}{2} \times \frac{3}{4} ) \times \frac{2}{8} \\ = \frac{9}{8} \times \frac{2}{8 } \\ = \frac{9}{32} [/tex]
Help me pls pls pls pls
Answer:
A. y-intercept is 8, Slope is -4/3
Step-by-step explanation:
Simplify: 1. (x−1)+(12−7.5x) 2. b−(4−2b)+(3b−1) 3. (2p+1.9)−(7−p)
Answer:
1. -6.5x+11
2. 6b-5
3. 3p-5.1
Step-by-step explanation:
[tex]1. \\(x-1)+(12-7.5x)=\\x-1+12-7.5x=\\x-7.5x-1+12=\\-6.5x-1+12=\\-6.5x+11\\\\2.\\b-(4-2b)+(3b-1)=\\b-4+2b+3b-1=\\b+2b+3b-4-1=\\3b+3b-4-1=\\6b-4-1=\\6b-5\\\\3.\\(2p+1.9)-(7-p)=\\2p+1.9-7+p=\\2p+p+1.9-7=\\3p+1.9-7=\\3p-5.1[/tex]
You make $85,000 per year and your company matches 50 cents for every dollar you deposit into your 401k plan, up to 8% of your salary. Complete parts (a) through (c) below.
(a) If you contribute $200 every month to your 401k, what will your company contribute each month?
The company will contribute $
(Type an integer or a decimal rounded to two decimal places as needed.)
(b) If you contribute $830 every month to your 401k, what will your company contribute each month?
The company will contribute $
(Type an integer or a decimal rounded to two decimal places as needed.)
(c) What is the maximum amount of money the company will contribute to your 401k each year?
The maximum amount that the company will contribute each year is $
(Type an integer or a decimal rounded to two decimal places as needed.)
Answer:
a) 100 $
b) 566,66 $
c) 566,66 $
Step-by-step explanation:
Mak 85,000 $ /per year, means 85000/12 per month that is 7083,33
8% of 7083,33 is 566,66 $ . Then
a) 200 < 566,33 then my company will contribute with 0,5*200 = 100 $
b) If I contribute with 830 $ ( 830 > 566,66 ) then my company will contribute with 566,66 $ the biggest amount
c) 566,66 s the maximm amount of money
In the multiplication sentence below, which numbers are the factors? Check
all that apply.
7x3 = 21
Answer:
The factors are 7 and 3
Step-by-step explanation:
The factors of a multiplication sentence are the numbers that are being multiplied for the product (or answer).
Help me please thank you
Answer:
104 degrees
Step-by-step explanation:
The angle of the whole set of lines is 140 degrees. In addition, the partial angle of it is also given--which is 36 degrees. In order to solve for the remaining part, Subtract 36 degrees from 140 degrees to get 104 degrees.
Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various college on campus. A survey of 338 college of business (COBA) student yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoint s of the desired confidence interval.
Variable N Lo 95% CI Means Up 95%CI SD
Parking time 388 9.1944 10.466 11.738 11.885
Explain what the phrase "95% confident" means when working with a 95 % confidence interval.
Answer:
The phrase "95% confident" means that there is a 95% confidence that the true mean parking time of students from within the various college on campus is included in the interval (9.1944, 11.738).
Step-by-step explanation:
The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.
Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.
From the provided data the 95% confidence interval for the population mean parking time of students from within the various college on campus is:
CI = (9.1944, 11.738)
This 95% confidence interval implies that the true mean parking time of students from within the various college on campus is included in the interval (9.1944, 11.738) with a specific probability or confidence of 95%.
Thus, the phrase "95% confident" means that there is a 95% confidence that the true mean parking time of students from within the various college on campus is included in the interval (9.1944, 11.738).
Express $0.\overline{1}+0.\overline{01}+0.\overline{0001}$ as a common fraction.
Answer:
[tex]\dfrac{1213}{9999}[/tex]
Step-by-step explanation:
We are required to express [tex]0.\overline{1}+0.\overline{01}+0.\overline{0001}[/tex] as a common fraction.
The bar on top of the decimal part indicates the decimal number is a repeating decimal.
Therefore:
[tex]0.\overline{1}=\dfrac{1}{10-1}= \dfrac{1}{9}\\\\0.\overline{01}=\dfrac{1}{100-1}= \dfrac{1}{99}\\\\0.\overline{0001}=\dfrac{1}{10000-1}= \dfrac{1}{9999}\\\\\\$Therefore$:\\0.\overline{1}+0.\overline{01}+0.\overline{0001} \\=\dfrac{1}{9}+\dfrac{1}{99}+\dfrac{1}{9999}\\\\=\dfrac{1213}{9999}[/tex]
Which phrases can be used to represent the inequality 6.5 x + 1.5 less-than-or-equal-to 21? Select two options. The product of 6.5 and the sum of a number and 1.5 is no more than 21. The sum of 1.5 and the product of 6.5 and a number is no greater than 21. The product of 6.5 and a number, when increased by 1.5, is below 21. The product of 6.5 and a number, when increased by 1.5, is at most 21. The sum of 1.5 and the product of 6.5 and a number is at least 21.
Answer:
The option with “at most” and “no more than”
Step-by-step explanation:
These two phrases mean “greater than or equal to”
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
What is inequality ?In which mathematical expression both sides are not equal, i.e. one side is greater or less or greater equal or less equal than other side, is called inequality.
Example : 4x+5>3x-2
What are the required phrases ?The given inequality is [tex]6.5x+1.5\leq 21[/tex]
Firstly, The sum of 1.5 and the product of 6.5 and a number (say x) is 6.5x+1.5, which is no greater than 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Again, The product of 6.5 and a number (say x) is 6.5x, when increased by 1.5, it will be 6.5x+1.5 which is at most 21, i.e. [tex]6.5x+1.5\leq 21[/tex]
Hence, the correct options are,
1. The sum of 1.5 and the product of 6.5 and a number is no greater than 21.
2. The product of 6.5 and a number, when increased by 1.5, is at most 21.
Learn more about inequality here :
https://brainly.com/question/11613554
#SPJ2
A sample of n = 168 students was asked, "Do you believe in love at first sight?" The choices below show confidence intervals, in scrambled order, for 90%, 95%, 98%, and 99% confidence levels for the population proportion who would answer yes. Which choice gives the 99% confidence interval? Group of answer choices
Group of answer choices:
A) 0.56 to 0.68
B) 0.52 to 0.72
C) 0.53 to 0.71
D) 0.55 to 0.69
Answer:
Option B) 0.52 to 0.72
Step-by-step explanation:
This is a very trivial exercise. A very good point that is required to solve this question is that the wider the Confidence level, the wider the Confidence Interval.
Let us consider the options one after the other for the width of interval:
Option A) 0.56 to 0.68
Width of Interval = 0.68 - 0.56 = 0.12
Option B) 0.52 to 0.72
Width of Interval = 0.72 - 0.52 = 0.20
Option C) 0.53 to 0.71
Width of Interval = 0.71 - 0.53 = 0.18
Option D) 0.55 to 0.69
Width of Interval = 0.69 - 0.55 = 0.14
Assigning the confidence level based on the width of the confidence intervals:
Option A) 0.56 to 0.68 = 90%
Option D) 0.55 to 0.69 = 95%
Option C) 0.53 to 0.71 = 98%
Option B) 0.52 to 0.72 = 99%
In the parallelogram below, solve for x and y. (Give your answer as a decimal, when necessary)
Answer: x = 15, y = 12.5
Step-by-step explanation:
The sum of the three angle measures of a triangle equals 180ᴼ
Since these triangles are vertical, the measures are congruent.
45 + 60 = 105
180 - 105 = 75
So now we know that 5x = 75ᴼ and 6y = 75ᴼ.
To find x, divide 75 by 5
75 / 5 = 15
x = 15
To find y, divide 75 by 6
75 / 6 = 12.5
y = 12.5
to prove triangleABC is isosceles, which of the following statements can be used in the proof?
&
given circleR, how is it known that QS = YT?
(idk the answers i guessed)
Answer:
Step-by-step explanation:
In an isosceles triangle, the base angles are equal. This also means that the length of two sides of the triangle are equal. Looking at triangle ABC, to prove that it is an isosceles triangle, then
Angle CAB = angle CBA
For the second question, to determine how it is known that QS is equivalent to YT, we would recall that the diameter of a circle passes through the center and from one side of the circle to the other side. Assuming R is the center of the circle, then QS and YT are the diameters of the circle and also the diagonals of the rectangle. Thus, the correct option is
The diameters act as diagonals
The vector matrix[ 27 ]is dilated by a factor of 1.5 and then reflected across the X axis if the resulting matrix is a B then a equals an VE
Correct question:
The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???
Answer:
a = 3
b = 10.5
Step-by-step explanation:
Given:
Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]
Dilation factor = 1.5
Since the vector matrix is dilated by 1.5, we have:
[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]
= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]
Here, we are told the vector is reflected on the x axis.
Therefore,
a = 3
b = 10.5
Answer:
a = 3
b = -10.5
Step-by-step explanation:
got a 100% on PLATO
suppose a triangle has two sides of length 32 and 35, and that the angle between these two sides is 120. Which equation should you solve to find the length of the third side of the triangle
Answer:
x² = 32² +35² -2·32·35·cos(120°)
Step-by-step explanation:
The equation of choice is the one that makes use of the law of cosines. If x represents the unknown side, then you would want to solve ...
x² = 32² +35² -2·32·35·cos(120°)
_____
The solution is ...
x² = 3369
x = √3369 ≈ 58.043
_____
Comment on the question
Usually, when the question asks, "Which ...", there will be a selection of answer choices. Those will give a clue as to what variables are used, how far the equation is simplified, and whether the equation is for x² or for x. That information is not provided here, so we have shown the equation we would use to solve the problem.
Answer:
The guy above me is right.
Step-by-step explanation:
I took the test.
Please help I’m struggling:(
Jose's taxi charges $5 plus $0.30 per mile for fare in a city. Kathy's taxi charges $8
plus $0.20 per mile for fare in the city. At what distance would the charges for the
two taxis be the same?
Answer:
30 miles
Step-by-step explanation:
Jose's charges are ...
j = 5 + 0.30m . . . . . for m miles
Kathy's charges are ...
k = 8 +0.20m . . . . . for m miles
The charges are the same when ...
j = k
5 +0.30m = 8 + 0.20m
0.30m = 3 + 0.20m . . . . subtract 5
0.10m = 3 . . . . . . . . . . . . subtract 0.20m
m = 30 . . . . . . . . . . . . . . . multiply by 10
The charges will be the same for a distance of 30 miles.
What is the Circumference of Aand B?
Answer:
4
Step-by-step explanation:
C1= 2π*8= 16π
C2= 2π*2= 4π
C1/C2= 16π/4π= 4
Answer:
4
Step-by-step explanation:
The circumference is pi*d.
pi*16/pi*4
Cancel pi.
16/4
= 4
Which fraction listed is between 4/7 and 6/7
Answer:
5/7
Step-by-step explanation:
4/7 < x < 6/7
Let x be the middle value of 4/7 and 6/7.
(4/7 + 6/7)/2
(10/7)/2
10/14 = 5/7
4/7 < 5/7 < 6/7
Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally. Define the following in terms of the study. Give examples where appropriate.
The sample:
a. The sample is all of the people taking skiing or snowboarding lessons.
b. The sample is all of the children taking skiing or snowboarding lessons.
c. The sample is a group of the people taking skiing or snowboarding lessons.
d. The sample is a group of the children taking skiing or snowboarding lessons.
Answer:
Option D
Step-by-step explanation:
A sample can be described as a small part or potion that is intended to describe what the whole population is like.
In this study, the sample is a group of the children taking skiing or snowboarding lessons: this group is taken out of the whole population of children taking skiing or snowboarding lessons.
Look at the three-dimensional figure.
The volume of the prism is the amount of space the figure.
120 cubes fit inside the prism, so the figure has a volume of square units.
Answer:
inside, 120
Step-by-step explanation:
Answer:
1. Inside
2. 120
did on edge
Four swimmers, Daniela, Camille, Brennan, and Amy, compete on a relay team. For the first race of the year, Daniela begins the relay. The other three swimmers can swim in any order. The sample space, S, for the event is shown below. S = {CBA, CAB, BAC, BCA, ACB, ABC} After the first race, it is determined that Camille is a strong finisher and should be the final swimmer in the race.
Answer:
A = {CBA, CAB, BCA, ACB}
Step-by-step explanation:
Answer: A. {CBA, CAB, BCA, ACB}
Step-by-step explanation: Id appreciate it if anyone else could explain why that is the answer. (?)
Find the amount in an account where $500 is invested at 2.5% compounded continuously for period of 10 years
Hi
500 *1.025^10 ≈ 640.04
Suppose that E(θˆ1) = E(θˆ2) = θ, V(θˆ 1) = σ2 1 , and V(θˆ2) = σ2 2 . Consider the estimator θˆ 3 = aθˆ 1 + (1 − a)θˆ 2. a Show that θˆ 3 is an unbiased estimator for θ. b If θˆ1 and θˆ2 are independent, how should the constant a be chosen in order to minimize the variance of θˆ3?
Answer:
Step-by-step explanation:
Given that:
[tex]E( \hat \theta _1) = \theta \ \ \ \ E( \hat \theta _2) = \theta \ \ \ \ V( \hat \theta _1) = \sigma_1^2 \ \ \ \ V(\hat \theta_2) = \sigma_2^2[/tex]
If we are to consider the estimator [tex]\hat \theta _3 = a \hat \theta_1 + (1-a) \hat \theta_2[/tex]
a. Then, for [tex]\hat \theta_3[/tex] to be an unbiased estimator ; Then:
[tex]E ( \hat \theta_3) = E ( a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]
[tex]E ( \hat \theta_3) = aE ( \theta_1) + (1-a) E ( \hat \theta_2)[/tex]
[tex]E ( \hat \theta_3) = a \theta + (1-a) \theta = \theta[/tex]
b) If [tex]\hat \theta _1 \ \ and \ \ \hat \theta_2[/tex] are independent
[tex]V(\hat \theta _3) = V (a \hat \theta_1+ (1-a) \hat \theta_2)[/tex]
[tex]V(\hat \theta _3) = a ^2 V ( \hat \theta_1) + (1-a)^2 V ( \hat \theta_2)[/tex]
Thus; in order to minimize the variance of [tex]\hat \theta_3[/tex] ; then constant a can be determined as :
[tex]V( \hat \theta_3) = a^2 \sigma_1^2 + (1-a)^2 \sigma^2_2[/tex]
Using differentiation:
[tex]\dfrac{d}{da}(V \ \hat \theta_3) = 0 \implies 2a \ \sigma_1^2 + 2(1-a)(-1) \sigma_2^2 = 0[/tex]
⇒
[tex]a (\sigma_1^2 + \sigma_2^2) = \sigma^2_2[/tex]
[tex]\hat a = \dfrac{\sigma^2_2}{\sigma^2_1+\sigma^2_2}[/tex]
This implies that
[tex]\dfrac{d}{da}(V \ \hat \theta_3)|_{a = \hat a} = 2 \ \sigma_1^2 + 2 \ \sigma_2^2 > 0[/tex]
So, [tex]V( \hat \theta_3)[/tex] is minimum when [tex]\hat a = \dfrac{\sigma_2^2}{\sigma_1^2+\sigma_2^2}[/tex]
As such; [tex]a = \dfrac{1}{2}[/tex] if [tex]\sigma_1^2 \ \ = \ \ \sigma_2^2[/tex]
According to creditcard , the mean outstanding credit card debt of college undergraduate was $3173 in 2010. A researcher believes that this amount has decreased since then.
Required:
a. Determine the null and alternative hypotheses.
b. Explain what it would mean to make a Type I and Type Il error.
Answer:
a. The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]
b. A Type I error is made when a true null hypothesis is rejected. In this case, it would happen if it is concluded that the actual mean outstanding credit card debt of college undergraduate is significantly less than $3173, when in fact it does not.
A Type II error is made when a false null hypothesis is failed to be rejected. In this case, the actual mean outstanding credit card debt of college undergraduate is in fact less than $3173, but the test concludes there is no enough evidence to claim that.
Step-by-step explanation:
We have a prior study of the mean outstanding credit card debt of college undergraduate that states that it was $3173 in 2010.
A researcher believes that this amount has decreased since then.
Then, he has to perform a hypothesis test where the null hypothesis states that the mean is still $3173 and an alternative hypothesis that states that the actual credit card debt is significantly smaller than $3173.
The null and alternative hypothesis can be written as:
[tex]H_0: \mu=3173\\\\H_a:\mu< 3173[/tex]