Find the accumulated amount of an initial investment after certain number of periods if the interest is compounded every period. Strategy for solution: Obtain a general formula for future value (F) of an initial investment after one, two, and three compounding periods. Thus, the general formula for the accumulated amount, or future value F, at the end of the n th period is F=P(1+i) n
Questions to answer: 1. How does the future value change with time? 2. How does the future value change when interest rate increases? 3. Imagine you want to purchase a car in 5 years. Think of the car that you would like to buy. What would be the estimated price of the car that you would like in 5 years? This is your future value. Research what is the interest rate at your bank? How often the accumulated amount is compounded (e.g. monthly, quarterly, semiannually, etc.)? How much do you need to deposit now to have enough for your purchase in 5 years according to the loan you can acquire from your bank? 4. Excel has a built-in function that can calculate present value automatically. Redo number 4 using Excel.
Answers
1) interest rate increases
2) compounded interest rate will be higher
3) Present Value (P) = Future Value (F) / (1+i)n
4)PV()
1. The future value changes with time as the interest rate increases. The future value is calculated by multiplying the initial investment with a compounded interest rate for a certain number of periods. The compounded interest rate is determined by the frequency of compounding (e.g. monthly, quarterly, etc.), and is expressed as (1+i)n where ‘i’ is the interest rate and ‘n’ is the number of compounding periods.
2. When the interest rate increases, the future value will also increase as the compounded interest rate will be higher.
3. The estimated price of the car that you would like in 5 years is the future value. You will need to research the interest rate at your bank and the frequency of compounding. To calculate how much you need to deposit now, you can use the formula: Present Value (P) = Future Value (F) / (1+i)n.
4. To redo number 4 using Excel, you can use the built-in function PV() to calculate present value automatically. The syntax for the PV() function is PV(rate, nper, pmt, [fv], [type]). The rate is the interest rate, nper is the number of compounding periods, pmt is the payment made each period, fv is the future value, and type is the number 0 or 1 and indicates when payments are due.
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Related Questions
Find the value of x and XY if Y is between X and Z. You may need to draw a picture. XY = 5x, YZ = x, and XZ = 24 x=1 XY =
Answers
Answer:
x = 4
XY = 20
Step-by-step explanation:
X____Y____Z
XZ= XY+YZ
24 = 5x + x
6x = 24
x= 24/6
x =4
XY = 5x = 5(4) = 20
I hope I helped you^_^
do this correctly for 20 points and brainliest! Please help
Answers
Answer:
Step-by-step explanation:
It is shaded on the top side because y is greater than or equal to 2x
I just need level two and three solved please
Answers
Answer:
intercepts: (0, 5/2) or (-5, 0)arbitrary point: (7, 6)Step-by-step explanation:
You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).
InterceptsWriting the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -2 = 1/2(x -(-1)) . . . . . using given slope and point
2y -4 = x +1 . . . . . . . . . . multiply by 2
x -2y = -5 . . . . . . . . . . . . add -1 -2y
Setting x=0 tells us the y-intercept is ...
0 -2y = -5
y = -5/-2 = 5/2
So, the y-intercept is (0, 5/2).
Setting y=0 tells us the x-intercept is ...
x -2(0) = -5
x = -5
So, the x-intercept is (-5, 0).
Arbitrary pointIt will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...
x -2y = -5
x = -5 +2y = -5 +2(6) = 7
Another point on the line is (7, 6).
__
Additional comment
If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.
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Please help i will do anything!! Pleasee
Answers
Answer:
i will say the first one is yes and then is the third one
Step-by-step explanation:
Marty’s bike ride is represented by the graph shown on the right.
What is Marty’s average speed? Explain how you arrived at this answer.
Marty’s average speed: ________________
Answers
Answer:
10 m/h
Step-by-step explanation:
By finding the slope of the line you find how fast he is traveling
Count the points if ykyk
My sthool day starts at 8:25 A.M.
and ends at 1:43 P.M. How much time
did I spend of school?
Answers
Answer:
5 hours and 18 minutes. (318 minutes)
Step-by-step explanation:
1. Add 35 minutes to 8:25 to get it to 9:00.
2. Add 3 hours (180 min.) to 9:00 to get to 12:00.
3. Add 1 hour and 43 minutes (103 min.) to get to 1:43 PM.
35 + 180 + 103 = 318 min. = 5 hours and 18 minutes
Answer:
5 hours and 18 minutes 8 25 plus 35 is 60 , an hour, 4 hours till 1 plus another hour when you add 35 plus the 43 in 1:43 which is 78. 78-18 is 60
so the remaining is 18 minutes so 5 hours and 18 minutes
On its municipal website, the city of Tulsa states that the rate it charges per 5 CCF of residential water is $21.62. How do the residential water rates of other U.S. public utilities compare to Tulsa's rate? The data shown below ($) contains the rate per 5 CCF of residential water for 42 randomly selected U.S. cities.10.38 9.08 11.7 6.4 12.32 14.43 15.4610.02 14.4 16.08 17.5 19.08 17.88 12.7516.7 17.25 15.54 14.7 18.81 17.89 14.818.32 15.95 26.75 22.22 22.66 20.88 23.3518.95 23.6 19.16 23.65 27.7 26.95 27.0426.89 24.58 37.76 26.41 38.91 29.36 41.55(a)Formulate hypotheses that can be used to determine whether the population mean rate per 5 CCF of residential water charged by U.S. public utilities differs from the $21.62 rate charged by Tulsa. (Enter != for ≠ as needed.)H0:Ha:(b)What is the test statistic for your hypothesis test in part (a)? (Round your answer to three decimal places.)What is the p-value for your hypothesis test in part (a)? (Round your answer to four decimal places.)(c)At α = 0.05, can your null hypothesis be rejected? What is your conclusion?Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.(d)Repeat the preceding hypothesis test using the critical value approach.State the null and alternative hypotheses. (Enter != for ≠ as needed.)H0:Ha:Find the value of the test statistic. (Round your answer to three decimal places.)State the critical values for the rejection rule. Useα = 0.05.(Round your answers to three decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistic≤test statistic≥State your conclusion.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Do not reject H0. The mean rate per 5 CCF of residential water throughout the United States does not differ significantly from the rate per 5 CCF of residential water in Tulsa.Reject H0. The mean rate per 5 CCF of residential water throughout the United States differs significantly from the rate per 5 CCF of residential water in Tulsa.
Answers
The null hypothesis for the data will be 21.62 and the alternate hypothesis is 2.02 for the p-value for the data is 0.2253 .
The charge at which anything happens is referred to as the velocity at which it happens.
The required details for mean rate :
(a) H0: µ = 21.62
Ha: µ ≠ 21.62
(b) t = -1.231
p-value = 0.2253
(c) Stop rejecting H0 right now. No longer significantly different from the domestic water tariff in Tulsa, the suggested household water charge per five CCF for the entire USA.
(d) H0: µ = 21.62
Ha: µ ≠ 21.62
t = -1.231
check statistic ≥ 2.020
Don't dismiss H0 any longer. The suggested five CCF residential water charge for the entirety of the USA is no longer significantly different from the five CCF residential water tariff in Tulsa.
The P-value is higher at 0.05, the level of significance. The impact in this instance is negligible. The attempt to reject the null hypothesis failed.
The conclusion is that there is insufficient statistical support to determine whether other American cities have a different mortality rate than Tulsa.
The crucial values for t at this level of significance are t=2.019.
Given that the statistic t = -1.15 is inside the acceptance range in this case, the null hypothesis is not disproved.
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.2. Determine whether the feasible set for each of the following systems of constraints is convex, and if not, indicate points x^1 and x² that violate definition. a) (x1)² + (x2)² > 9
x1 + x2 ,10
x1, x2 > 0
Answers
The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.
To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.
a) (x1)² + (x2)² > 9
This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.
b) x1 + x2 ≤ 10
This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.
c) x1, x2 > 0
This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.
Now, let's analyze the intersection of these constraints:
Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).
To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.
If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).
Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.
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In the diagram below, DE is parallel to AB. If AB is twice the length of DC,
AC = 28, and DE = 13, find the length of DC. Figures are not necessarily drawn
to scale. State your answer in simplest radical form, if necessary ty
Answers
Answer:
\(\sqrt{182}\)
Step-by-step explanation:
A car uses 3t gallons of gasoline to travel 5 miles.
a) How many gallons of gasoline are needed to travel 8 miles? Give your answer in terms of t.
24t/5 (fraction)
b) The car uses 9t gallons of gasoline to travel from Town X to Town Y. How many miles apart are the two towns?
please answer “b” i know a for certain
Answers
Answer: a) \(\frac{24}{5}t gallons\) are needed to travel 8 miles
b) Town X and town Y are 15 miles apart.
Step-by-step explanation:
Given : Gasoline used to travel 5 miles = 3t gallons
a) To find: Gasoline used to travel 8 miles = ?
Using unitary method:
If Gasoline used to travel 5 miles = 3t gallons
Thus Gasoline used to travel 8 miles = \(\frac{3t}{5}\times 8=\frac{24}{5}t gallons\)
\(\frac{24}{5}t gallons\) are needed to travel 8 miles
b) when 3t gallons of gasoline are used , distance covered = 5 miles
Thus when 9t gallons of gasoline are used , distance covered = \(\frac{5}{3t}\times 9t=15 miles\)
Thus town X and town Y are 15 miles apart.
I need some help on this fast.
Answers
Answer: -2
Step-by-step explanation:
Second post answer first one too for full 95 points and 2 brainiest
Answer as many as possible all is appreciated and expected thank you!!!!!
Question 1(Multiple Choice Worth 2 points)
(Statistical Measurements MC)
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 3
3 1, 1, 5
4 1, 3, 4
5 0, 8
6 2
Key: 4|1 means 4.1
What is the mean, and what does it tell you in terms of the problem?
4.59 feet; The value means that a typical throw of the ball results in 4.59 feet.
4.1 feet; The value means the furthest the ball went.
3.825 feet; The value means that a typical throw of the ball results in 3.825 feet.
3.1 feet; The value means this measurement had the most occurrences.
Question 2(Multiple Choice Worth 2 points)
(Statistical Measurements LC)
The table displays data collected, in meters, from a track meet.
one third 2 4 1
7 two thirds four fifths five halves
What is the median of the data collected?
1
1.5
2
2.5
Question 3(Multiple Choice Worth 2 points)
(Statistical Measurements LC)
Which of the following is a statistical question that can result in numerical data?
How many letters are in your first name?
How many hours do you practice your musical instrument each week?
How many books do the students in your class read each month?
Who is your favorite cartoon character?
Question 4(Multiple Choice Worth 2 points)
(Statistical Measurements MC)
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has one dot, the value of 4.5 has two dots, the value of 5 has two dots, the value of 6 has one dot, the value of 6.5 has two dots, the value of 7 has one dot, and the value of 8 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5, and it means that the data varies by a value of 4.5.
The range is 3.5, and it means that it is the value that occurs the most.
The range is 4.0, and it means that the data varies by a value of 4.0.
The range is 4.0, and it means that it is the value that is the smallest.
Question 5(Multiple Choice Worth 2 points)
(Statistical Measurements LC)
A student earned the scores in the data set in one course.
{88, 72, 68, 78, 94}
What is the mean of the scores?
26
68
78
80
Question 6 (Essay Worth 4 points)
(Statistical Measurements HC)
The stem-and-leaf plot displays the amount of time, in minutes, that 10 students spent practicing their musical instrument one day.
1 5
2 0, 2, 5
3 2, 4
4 5
5 3, 6
6 0
Key: 2|0 means 20
Part A: Calculate the mean and median for the data given. (2 points)
Part B: A student would like to show their teacher that they have practiced long enough for the day. Which measure of center should the student give to their teacher? Explain your answer. (2 points)
Answers
Question 1:
3.825 feet; The value means that a typical throw of the ball results in 3.825 feet.
Question 2:
2.5
What are the responses to other questions?Question 3:
How many hours do you practice your musical instrument each week?
Question 4:
The range is 4.5, and it means that the data varies by a value of 4.5.
Question 5:
80
Question 6:
Part A: Mean: (5 + 20 + 22 + 25 + 32 + 34 + 45 + 53 + 56 + 60)/10 = 35 minutes. Median: 32 minutes.
Part B: The student should give the median to their teacher because it represents the middle value and is not affected by outliers.
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N
What is the solution to the equation 36 – 5x = 5 – 6(x - 4) ?
68bpoints
Answers
Step-by-step explanation:
36-5x=5-6(x-4)36-5x=5-6x+24
-5x+6x=24+5-36
x=29-36
x=-7
Answer:
x = -7
Explanation:
36 − 5x = 5 − 6(x − 4)
[ Simplify both sides of the equation ]
36 − 5x = 5 − 6(x − 4)
36 + −5x = 5 + (−6)(x) + (−6)(−4) [ Distribute ]
36 + −5x = 5 + −6x + 24
−5x + 36 = (−6x) + (5 + 24) [ Combine Like Terms ]
−5x + 36 = −6x + 29
−5x + 36 = −6x + 29
[ Step 2: Add 6x to both sides ]
−5x + 36 + 6x = −6x + 29 + 6x
x + 36 = 29
[ Step 3: Subtract 36 from both sides ]
x + 36 − 36 = 29 − 36
x = −7
Kristina received $125 for her birthday. Her parents offered to pay her 3.5% simple interest per year if sh
Answers
Answer:
Uhh...
Step-by-step explanation:
You didn't finish your question, so I'll calculate the next three years.
After 1: 129.37
After 2: 133.90
After 3: 138.58
if n is a positive integer, how many integers from 0 through 2n must you pick in order to be sure of getting at least one that is odd? how many integers must be picked in order to be sure of getting at least one that is even?
Answers
To guarantee to select at least one odd integer, pick one from {1,3,5,...,2n-1}. To guarantee at least one even integer, pick two from {0,2,4,...,2n}.
To be sure of getting at least one odd integer, you need to pick just one integer from the set {1,3,5,...,2n-1}. Any integer in this set is odd, so selecting just one integer guarantees that you will get an odd integer.
On the other hand, to be sure of getting at least one even integer, you need to pick two integers from the set {0,2,4,...,2n}. If you pick only one integer from this set, it could be an odd integer, which means you didn't get an even integer. But if you pick two integers, at least one of them must be even. This is because if you pick two odd integers, their sum will be even, and if you pick an even integer and an odd integer, their sum will be odd.
In summary, to be sure of getting at least one odd integer, you need to pick one integer from {1,3,5,...,2n-1}, and to be sure of getting at least one even integer, you need to pick two integers from {0,2,4,...,2n}.
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If a town with a population of 5,000 doubles in size every 11 years, what will the population be 44 years from now?
Answers
Solve 4+3(x-2)=2x-4.
Answers
Answer:
x=-2
Step-by-step explanation:
isolate the variable and the numbers
Answer:
-2
Step-by-step explanation:
4+3(x-2)=2x-4
distibute 3 to (x-2)
4+3x-6=2x-4
simplify
3x-2=2x-4
add -4 (becomes +4) to -2
3x+2=2x
subtract 3x
2=-x
divide the negative
-2=x
A . What is the slope in the line of the graph ?
Answers
Answer:
0.2x+3
Step-by-step explanation:
Find the equation of the circle of radius 5 units and concentric with the circles x2 + y2 - 6x + 4y + 12 = 0.
Answers
Step-by-step explanation:
x² + y² - 6x + 4y + 12 = 0
(x - 3)² + (y + 2)² = 1
Hence the equation of the concentric circle is (x - 3)² + (y + 2)² = 25.
What is the answer to
26 x 438 ≈
Answers
Answer:
11388
Step-by-step explanation:
Answer:
The answer to this question is 11,388
Negative Exponents
If Xand a are counting numbers, is *** less than or greater than 1?
Answers
Answer:
Well I think its less then
Step-by-step explanation:
Which of the following tools is used to capture data packets over time(continuously or overnight)?PuTTYTraffic AnalyzerWiresharkNetWitness Investigator
Answers
Wireshark is the tool used to capture data packets over time, either continuously or overnight.
Wireshark is a powerful network protocol analyzer that allows you to capture and examine data packets flowing through a network. It provides a comprehensive set of features for capturing, analyzing, and interpreting network traffic.
With Wireshark, you can capture packets from various network interfaces and save them to a capture file for later analysis. It supports capturing packets in real-time, allowing you to monitor network activity as it happens.
Wireshark offers detailed packet-level inspection, allowing you to examine packet headers, payloads, protocols, and other relevant information.
Furthermore, Wireshark supports numerous protocols and provides protocol-specific decoders to interpret and analyze different network protocols. It also offers advanced features like packet coloring, statistical analysis, packet comparison, and the ability to export captured data for further analysis or sharing with others.
Overall, Wireshark is widely used by network administrators, security professionals, and developers to diagnose network issues, troubleshoot problems, analyze network performance, and investigate security incidents by capturing and analyzing data packets over time.
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Consider the figure to the right.
T
Given: CT PM, CT 1 PM
Prove: CA - MA
А,
P4
M
Shown below are the statements and reasons for the proof.
They are not in correct order.
Statements
Reasons
1.
ACAT AMAP
AAS
II.
LCAT ZPAM
Vertical Angles Theorem
III.
CT & PM, CT || PM
Given
IV.
CAMA
CPCTC
V.
LCTA E LMPA
Alternate Interior Angles Theorem.
Which of these is the most logical order for the statements and reasons?
(А.
I, II, III, IV, V
Answers
Answer:B
Step-by-step explanation:
Just did it on math nation
The most logical order for the statement and reasons III, II, V, I, IV. Therefore, option B is the correct answer.
CP=PM, CT||PM (Given)
∠CAT=∠PAM (vertical angles theorem)
∠CTA=∠MPA (Alternate interior angles theorem)
ΔCAT≅ΔMAP (AAS)
CA=MA (CPCTC)
The most logical order for the statement and reasons III, II, V, I, IV. Therefore, option B is the correct answer.
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Can somebody plz answer this correctly!!! tell me which I should circle?
(Grade5math)
(WILL MARK AS BRAINLIESTTT)
:DDDDD
Answers
Answer:
13. 5/8
14. 16/24
15. 15/35
Answers:
13. 5/8
\(\frac{5}{8} \neq \frac{2}{3}\)
14. 16/24
\(\frac{16}{24} \neq \frac{3}{4}\)
15. 15/35
\(\frac{15}{35} \neq \frac{2}{7}\)
In a school the ratio of boys to girls is 2.3. If there are 300 girls in the school, then
how many boys are there?
(A) 50
(B) 120
(C) 100
(D) 150
(E) 200
Answers
Answer:
e is the answer i think.
Step-by-step explanation:
Answer:
E. 200 boys
Step-by-step explanation:
there are 2 boys for every 3 girls
so if we multiply the amount of girls by 100 to get 300 girls
then we need to multiply the amount of boys by 100 too because what you do to one side you have to do to the other
2*100= 200
200 boys for 300 girls can be simplified to the ratio 2:3 by dividing by 100 so we know our answer is correct
hope this helps babe <3
How do I solve 5x - 4x^2
Answers
Answer:
If you are asking,
5x - 4x^2=0
x(5-4x)=0
Either,
x=0
or,
5-4x=0
x=5/4
If factor,
5x - 4x^2
x(5-4x)
If difference,
5x - 4x^2
The same as they are not like terms.
. You are to give your pediatric client 1000mg of Cefazolin in 50mLs of IV fluid and run it over 30 min. At what rate will you set the delivery rate on the pump? 2. You are to give your pediatric client 20mg of Fam otidine in 10 mL of IV fluid and run it over 15 min. At what rate will you set the delivery rate on the pump?
Answers
The delivery rate for Famotidine should be set at 2/3 mL/min.
To determine the delivery rate for each scenario, we can use the formula:
Delivery rate = Volume / Time
1. Cefazolin:
Given:
- Dose: 1000 mg
- IV fluid volume: 50 mL
- Infusion time: 30 minutes
Using the formula, the delivery rate for Cefazolin will be:
Delivery rate = 50 mL / 30 min
Simplifying:
Delivery rate = 5/3 mL/min
So, the delivery rate for Cefazolin should be set at 5/3 mL/min.
2. Famotidine:
Given:
- Dose: 20 mg
- IV fluid volume: 10 mL
- Infusion time: 15 minutes
Using the formula, the delivery rate for Famotidine will be:
Delivery rate = 10 mL / 15 min
Simplifying:
Delivery rate = 2/3 mL/min
So, the delivery rate for Famotidine should be set at 2/3 mL/min.
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what is the area of this figure
Answers
Answer:
174.5m
Step-by-step explanation:
So we have to break the shapes down to triangle, rectangle and the small rectangle
Area of rectangle=WxL
Area of triangle= (BxH)÷2
triangle=
(23x11)÷2
=253÷2
=126.5m
rectangle=
9x19
=28m
square#2(the small one)=
5x4
=20m
All:
20+28+126.5
=174.5m
The p-value for a two-sided test of the null hypothesis H0: μ = 10 is 0.06.
(a) Would a 95% confidence interval for μ include the value 10?
a. No. A p-value of 0.06 indicates that the results observed are statistically significant at the 5% level, so the 95% confidence interval will not include 10.
b. No. A p-value of 0.06 indicates that the results observed are not statistically significant at the 5% level, so the 95% confidence interval will not include 10.
c. Yes. A p-value of 0.06 indicates that the results observed are statistically significant at the 5% level, so the 95% confidence interval will include 10.
d. Yes. A p-value of 0.06 indicates that the results observed are not statistically significant at the 5% level, so the 95% confidence interval will include 10.
(b) Would a 90% confidence interval for μ include the value 10?
a. No. A p-value of 0.06 indicates that the results observed are statistically significant at the 10% level, so the 90% confidence interval will not include 10.
b. No. A p-value of 0.06 indicates that the results observed are not statistically significant at the 10% level, so the 90% confidence interval will not include 10.
c. Yes. A p-value of 0.06 indicates that the results observed are statistically significant at the 10% level, so the 90% confidence interval will include 10.
d. Yes. A p-value of 0.06 indicates that the results observed are not statistically significant at the 10% level, so the 90% confidence interval will include 10
Answers
A) No. A p-value of 0.06 indicates that the results observed are not statistically significant at the 5% level.
B) Yes. A 90% confidence interval is narrower than a 95% confidence interval, meaning that it is more likely to exclude the true population mean.
(a) No. A p-value of 0.06 indicates that the results observed are not statistically significant at the 5% level, so the 95% confidence interval will include 10. This means that if we were to repeat the experiment many times and calculate a 95% confidence interval for each experiment, about 95% of those intervals would include the true population mean of 10.
(b) Yes. A 90% confidence interval is narrower than a 95% confidence interval, meaning that it is more likely to exclude the true population mean. However, since the p-value of 0.06 is not statistically significant at the 10% level, there is still a chance that the true population mean is 10 and falls within the 90% confidence interval. Therefore, the 90% confidence interval may include the value 10. However, it is important to note that we cannot say with 90% certainty that the true population mean falls within the confidence interval, as we could with a 95% confidence interval.
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g puppy prediction puppies have been used to predict the winning basketball teams for the ncaa tournament. the current record for prediction is 347 wins out of 652 picks. is it reasonable to say that the puppies can predict a win the majority of the time? choose the correct null and alternative hypothesis.
Answers
It is reasonable to say that the puppies can predict the winning basketball teams for the NCAA tournament the majority of the time.
Based on the given information, we need to choose the correct null and alternative hypothesis that determines if it is reasonable to say that puppies can predict the winning basketball teams for the NCAA tournament the majority of the time.
Null Hypothesis (H0): It is not reasonable to say that the puppies can predict the winning teams of the NCAA tournament the majority of the time. Alternative Hypothesis (Ha): It is reasonable to say that the puppies can predict the winning teams of the NCAA tournament the majority of the time.
To determine whether it is reasonable to say that puppies can predict a win the majority of the time, we need to perform the hypothesis test using the given data. Here, p = 347/652 = 0.5317 = 53.17%, which is the proportion of correct predictions. The sample size is 652, which is greater than 30, so we can use a normal distribution for the hypothesis test.
Let’s assume a significance level of α = 0.05. Therefore, the critical z-value for a two-tailed test is:
zα/2 = ±1.96.Z = (p - P) / √ (P (1 - P) / n)
Where, p = proportion of correct predictions = 0.5317 (from given data)
P = proportion of correct predictions assumed under null hypothesis = 0.5 (no significant difference)
n = sample size = 652Z = (0.5317 - 0.5) / √ [(0.5 × 0.5) / 652]= 2.23 (approx)
The calculated value of z is 2.23 which is greater than the critical value 1.96 at a 5% level of significance. Thus, we can reject the null hypothesis.
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