Answer
Step-by-step explanation:
A=2πrh+2πr2=2·π·3·6+2·π·32≈169.646
a tank contains 200 liters of fluid in which 30 grams of salt is dissolved. Brine containing 2 grams of salt per liter is then pumped into the tank at a rate of 4 L/min. The well-mixed solution is pumped out at a slower rate of 3 L/min. Write a differential equation that models the amount of salt in the tank at any time.
Salt flows in at a rate of
(2 g/L) * (4 L/min) = 8 g/min
and out at a rate of
(B/(200 + t) g/L) * (3 L/min) = 3B/(200 + t) g/min
where B is the amount of salt in the tank at time t.
Then the net rate at which B changes is governed by the ODE,
[tex]B'=8-\dfrac{3B}{200+t}[/tex]
[tex]B'+\dfrac{3B}{200+t}=8[/tex]
Multipy both sides by [tex](200+t)^3[/tex]:
[tex](200+t)^3B'+3B(200+t)^2=8(200+t)^3[/tex]
[tex]\left(B(200+t)^3\right)'=8(200+t)^3[/tex]
Integrate both sides:
[tex]B(200+t)^3=2(200+t)^4+C[/tex]
[tex]B=2(200+t)+C(200+t)^{-3}=\dfrac{2(200+t)^4+C}{(200+t)^3}[/tex]
The tank starts with 30 g of salt, so B(0) = 30, which gives
[tex]30=2(200) + C(200)^{-3}\implies C=-2,960,000,000[/tex]
Justin plans to attend a four-year college. He has
estimated the costs per year.
I Tuition = $2,900
Justin's plan doesn't cover his costs completely. What
are his options for covering the rest of his costs? Select
all that apply.
He could try to save more money.
He could get a student loan for the extra amount he
needs.
Other educational expenses = $280
Housing and living expenses = $4,100
Justin's counselor estimates he will receive $3,500 a
year in grants. He also will be eligible for a work-study
program that pays $2,800 per year. Justin also plans to
save enough money to contribute $500 each year.
He could apply for a scholarship.
He could ask his friends to loan him money.
He could ask his family to contribute.
Answer:
a, b. c, e
Step-by-step explanation:
Hence, Justin will have to ask for 1480 from family and friends to cover cost.
What is cost?
Amount at which any product prices , that is it can be sold or bought.
How to calculate?
I Tuition = -$2,900
Other educational expenses = -$280
Housing and living expenses =- $4,100
estimates of grants= $3,500
work-study program =$2,800
savings = $500
hence cost = 3500-2900-280-4100+2800-500=-1480
∴ Justin will have to ask for 1480 from family and friends to cover cost.
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Solve the proportion. 5/7=x/35
Answer:
x = 25
Step-by-step explanation:
[tex] \frac{5}{7} = \frac{x}{35} \\ \\ x = \frac{5 \times 35}{7} \\ \\ x = 5 \times 5 \\ \\ \huge \red{ \boxed{ x = 25}}[/tex]
py+qy=-4y+8 Solve for Y
Here,
py+qy=-4y+8
or, py+qy+4y=8
or,y(p+q+4)=8
therefore,
y=8/(p+q+4)
What are the solutions of the quadratic equation 49x2 = 9? x = StartFraction 1 Over 9 EndFraction and x = StartFraction negative 1 Over 9 EndFraction x = StartFraction 3 Over 7 EndFraction and x = Start Fraction negative 3 Over 7 EndFraction x = StartFraction 3 Over 4 EndFraction and x = StartFraction negative 3 Over 4 EndFraction x = StartFraction Over 49 EndFraction and x = StartFraction negative 9 Over 49 EndFraction
The solution of the quadratic equation is x = ±3/7
How to solve quadratic equationsQuadratic equations are equations that have a leading degree of 2
Given the quadratic function
49x^2 = 9
Divide both sides by 49
49x^2/49 = 9/49
x^2 = 9/49
x = √9/49
x = ±3/7
Hence the solution of the quadratic equation is x = ±3/7
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what can 8 and 6 both go into equally
write 64 as a power with exponent 3
Answer:
4
Step-by-step explanation:
because 4x4 is 16 and 16 x four is 64
Answer:
4³
I think this is right. the problem isnt explained very well.
Let a1equals=[Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column 2 3rd Row 1st Column negative 1 EndMatrix ]1 2 −1 , a2equals=[Start 3 By 1 Matrix 1st Row 1st Column negative 6 2nd Row 1st Column negative 5 3rd Row 1st Column 3 EndMatrix ]−6 −5 3 , and bequals=[Start 3 By 1 Matrix 1st Row 1st Column 3 2nd Row 1st Column negative 8 3rd Row 1st Column h EndMatrix ]3 −8 h . For what value(s) of h is b in the plane spanned by a1 and a2?
Answer:
Check attachment for solution
Step-by-step explanation:
Given that,
The mean number of miles driven per vehicle annually in the United States is 12,494 miles. Choose a randomly selected vehicle, and assume the annual mileage is normally distributed with a standard deviation of 1290 miles. Would you buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year
No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year and this can be determined by using the formula of z-score.
Given :
The mean is 12,494 miles. The standard deviation of 1290 miles.The following steps can be used in order to determine whether you have to buy a vehicle or not:
Step 1 - The formula of z-score can be used in order to determine whether you have to buy a vehicle or not.
Step 2 - The z-score formula is given below:
[tex]\rm z = \dfrac{x-\mu}{\sigma}[/tex]
Step 3 - Substitute the known terms in the above expression.
[tex]\rm z = \dfrac{6000-12494}{1290}=-5.0341[/tex]
Step 4 - Now, the p-value is given below:
[tex]\rm P(x < 6000)=P(z<-5.0341)[/tex]
Step 5 - Now, using the z table the value of P is:
P(x < 6000) = 0
No, you do not have to buy a vehicle if you had been told that it had been driven less than 6000 miles in the past year.
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2 Points
Multiply the polynomials.
(x+4)(x2 - 5x+3)
Answer:
x^3-x^2-17x+12
Step-by-step explanation:
Multiply
on how many points do the graphic cross each other
[tex]y = x \: \: y = x {}^{2} [/tex]
A)3
B)2
C)1
D)0
Find the average value of the function over the given interval. (Round your answer to three decimal places.) f(x) = −sin x, [0, π] Find all values of x in the interval for which the function equals its average value. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
Answer with Step-by-step explanation:
We are given that
[tex]f(x)=-sin x[/tex]
[tex][0,\infty][/tex]]
Average value of the function is given gy
[tex]f_{avg}=\frac{1}{b-a}\int_{a}^{b}f(x)dx=\frac{1}{\pi-0}\int_{0}^{\pi}-sinx dx[/tex]
[tex]f_{avg}=\frac{1}{\pi}[cosx]^{\pi}_{0}[/tex]
Using the formula
[tex]\int sin xdx=-cos x[/tex]
[tex]f_{avg}=\frac{1}{\pi}(cos\pi-cos0)[/tex]
[tex]f_{avg}=\frac{1}{\pi}(-1-1)=-\frac{2}{\pi}[/tex]
[tex]f(x)=f_{avg}[/tex]
[tex]-sinx=-\frac{2}{\pi}[/tex]
[tex]sinx=\frac{2}{\pi}[/tex]
[tex]x=sin^{-1}(\frac{2}{\pi})=0.69radian[/tex]
The average value of the function is [tex]-\frac{2}{\pi}[/tex].
Average value :The average value of the function is given as,
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {f(x)} \, dx[/tex]
Given function is, [tex]f(x)=-sinx[/tex]
Substitute values in above relation.
[tex]Average=\frac{1}{\pi} \int\limits^\pi_0 {-sinx} \, dx\\\\Average=\frac{1}{\pi} (cosx)^{\pi} _{0}\\\\Average=\frac{1}{\pi}(cos\pi - cos 0)\\\\Average=\frac{1}{\pi}(-1-1)\\\\Average=-\frac{2}{\pi}[/tex]
The values of x in the interval for which the function equals its average value is,
[tex]-sinx=-\frac{2}{\pi}\\ \\x=sin^{-1} (\frac{2}{\pi} )=39.56[/tex]
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Cecil solved a theoretical prediction problem, where a spinner would be spun 30 times. She correctly concluded: “The spinner will land on the red section 6 times.” What could the spinner look like? Is there more than one possible solution?
6 out of 30 times would be written as
6/30 which reduces to 1/5 which would mean the spinner is divided into 5 different colors.
There could be more than one solution. The spinner could be divided into 10 spaces and red could be 2 of the spaces, or any other multiple of 5s
Answer:
The spinner has 5 equal sections, with one section red.
It can have 5N equal sections, with N sections Red
Step-by-step explanation:
p(red) = 6/30 = 1/5
1/5 = 2/10
Out of 10 sections, 2 are Red
In general,
It can have 5N equal sections, with N sections Red
Dalgliesh the detective fancies himself a shrewd judge of human nature. In careful tests, it has been discovered that he is right 80 percent of the time about whether a suspect is lying or telling the truth. Dalgliesh says that Jones is lying. The polygraph expert, who is right 100 percent of the time, says that 40 percent of the subjects interviewed by Dagliesh are telling the truth. What is the probability that Jones is lying?
Answer:
The probability that Jones is lying is 6/7
Step-by-step explanation:
First we will list out 2 different cases when the outcome is a lie
1.probability that Jones tells lies is = 0.6 and probability that dalgiliesh analyses it correctly is 0.8
So the probability that dagliesh correctly analyses that he is telling lies is 0.8*0.6=0.48
2.Probability that Jones tells truth is 0.4 and if dagliesh analyses it incorrectly (which has a probability of 0.2) the outcome(as analysed by dagiliesh) is a lie
So probability that dagliesh analyses Jones truth as a lie is 0.2*.0.4=0.08
Total probability of outcome being a lie is 0.48+0.08=0.56
But we need the probability of Jones actually saying a lie which is nothing but 0.48/0.56= 6/7
The probability of that Jones is lying is [tex]\frac{6}{7}[/tex] .
Probability is defined as, divide favourable outcomes by total outcomes.
First case:
Probability that Jones tells lies is = 0.6
Probability that Dalgliesh analyses it correctly is, = 0.8
Therefore, the probability that Dalgliesh correctly analyses that Jones is telling lies is,
[tex]P=0.8*0.6=0.48[/tex]
Second case :
Probability that Jones tells truth is, = 0.4
Probability of Dalgliesh analyses it incorrectly that Jones tells truth is,
= 0.2
So, Probability that Dalgliesh analyses Jones truth as a lie is,
[tex]0.2*.0.4=0.08[/tex]
Total probability of outcome being a lie is,
[tex]0.48+0.08=0.56[/tex]
Thus, Probability of Jones telling lie is, [tex]=\frac{0.48}{0.56} =\frac{6}{7}[/tex]
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The price of a home is 240,000. The bank requires a 20% down payment and two points at the time of closing. The cost of the home is financed with a 30 year fixed rate mortgage at 7%. Find the amount of the mortgage. How much must be paid for the two points at closing?
Final answer:
The mortgage amount for the home is $192,000 after a 20% down payment on a $240,000 purchase price. The cost for two points at closing is $3,840, which is 2% of the mortgage amount.
Explanation:
The amount of the mortgage can be found by subtracting the 20% down payment from the purchase price of the home. For a home priced at $240,000, a 20% down payment is $48,000 ($240,000 × 0.20), leaving a mortgage amount of $192,000 ($240,000 - $48,000).
Next, the cost of the two points at closing is calculated based on the mortgage amount. Each point costs 1% of the mortgage amount, so two points would be 2% of $192,000, which comes to $3,840
A bag contains 3 gold marbles, 6 silver marbles, and 22 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you play this game
The expected value of this marble-drawing game is approximately -$0.032, meaning that you would expect to lose about 3.2 cents per play on average.
In order to calculate the expected value of this marble-drawing game, you need to consider the probability of drawing each color of marble and the payoff associated with each one. The probabilities are as follows: P(gold) = 3/31, P(silver) = 6/31, and P(black) = 22/31, based on the quantities provided in the bag. The payoffs are $3 for a gold marble, $2 for a silver marble, and -$1 for a black marble.
The formula for expected value, E(X), is given by:
E(X) = (P(gold) * payoff gold) + (P(silver) * payoff silver) + (P(black) * payoff black)
Substituting the given values leads to:
E(X) = (3/31 * $3) + (6/31 * $2) + (22/31 * -$1)
After calculations, we get:
E(X) = (9/31) + (12/31) - (22/31)E(X) = 21/31 - 22/31E(X) = -1/31The expected value in playing this game would be -$0.032 approximately. This means that on average, you would expect to lose about 3.2 cents per play.
What’s 0.798 as a percent
Answer:
The answer would be, 79.8%.
-Hope this helps! :D
Answer:
[tex]0.798\%[/tex]
Step-by-step explanation:
[tex]0.798 \times 100\% \\ 0.798 \times \frac{100}{100} \\ = \frac{0.798 \times 100}{100} \\ = 0.798\%[/tex]
Complete the recursive formula of the arithmetic sequence 12, 10, 8, 6, ....
6(1) = _
6(n) = b(n − 1) + _
The recursive formula for the arithmetic sequence 12, 10, 8, 6, ... is a sequence where a(1) = 12, and a(n) = a(n - 1) - 2.
Explanation:The recursive formula of an arithmetic sequence is a rule that uses each term to find the next. In this case, we start with the first term of the sequence, which is 12, and each following term decreases by 2. So, to find any term in the sequence, we take the previous term and subtract 2.
The recursive formula for the arithmetic sequence 12, 10, 8, 6, ... is:
a(1) = 12
a(n) = a(n - 1) - 2
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According to a recent census, 14.6% of all housing units in a certain country are vacant. A county supervisor wonders if her county is different from this. She randomly selects 865 housing units in her county and finds that 159 of the housing units are vacant.
Name the model and check appropriate conditions for a hypothesis test. What kind of test is this?
A. One-proportion z-test
B. Two-proportion t-test
C. Proportional t-test
D. Difference in proportions test
Answer:
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:
Null hypothesis:[tex]p=0.146[/tex]
Alternative hypothesis:[tex]p \neq 0.146[/tex]
A. One-proportion z-test
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And the conditions required are:
1) The data comes from a random sampling
2) Independence condition between observations
3) np>10 and n(1-p)>10
4) The sample size is 10 times lower than the population size.
Step-by-step explanation:
Data given and notation
n=865 represent the random sample taken
X=159 represent the housing units that are vacant
[tex]\hat p=\frac{159}{865}=0.184[/tex] estimated proportion of vacant units
[tex]p_o=0.146[/tex] is the value that we want to test
[tex]\alpha[/tex] represent the significance level
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Solution to the problem
We need to conduct a hypothesis in order to test the claim that the true proportion is equal to 14.6% or not. So we need to use a one proportion z test and the system of hypothesis are:
Null hypothesis:[tex]p=0.146[/tex]
Alternative hypothesis:[tex]p \neq 0.146[/tex]
A. One-proportion z-test
When we conduct a proportion test we need to use the z statisitc, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And the conditions required are:
1) The data comes from a random sampling
2) Independence condition between observations
3) np>10 and n(1-p)>10
4) The sample size is 10 times lower than the population size.
Findthe
y -intercept
oftheparabola
y = x2 − 2x .
Answer:
Step-by-step explanation:
kupa
645665465
Answer:
y=x(x-2)
Step-by-step explanation:
(19.28) To estimate the mean score μ of those who took the Medical College Admission Test on your campus, you will obtain the scores of an SRS of students. From published information you know that the scores are approximately Normal with standard deviation about 6.6. You want your sample mean x¯¯¯ to estimate μ with an error of no more than 1.4 point in either direction.
What standard deviation (±0.0001) must x¯ have so that 99.7% of all samples give an x¯ within 1.4 point of μ?
Answer:
standard deviation = ±0.4667
Step-by-step explanation:
In Normal distribution, approximately 68% of all the data lie within 1 standard deviation from the mean, approximately 95% of all the data lie within 2 standard deviations from the mean and approximately 99.7% of all the data lie within 3 standard deviations from the mean.
Therefore, for a confidence interval of 99.7% the standard deviation of the x¯ must be 3 standard deviations from the mean,
3σ = ±1.4
σ = ±1.4/3
σ = ±0.4667
Therefore, 0.4667 is the standard deviation that x¯ must have so that 99.7% of all samples give an x¯ within 1.4 point of μ.
I don’t really understand how to do this!!! Help plz
Answer:
4
Step-by-step explanation:
It works with the second one
A survey was conducted to find out how much time people have to spend commuting to work. The sample means for two samples are 71 and 72 minutes, with p-values of 0.03 and 0.06, respectively. The population mean is μμ. Choose the possible pair of the null and alternative hypotheses.A : H0:μ=80H0:μ=80, Ha:μ<80Ha:μ<80B : H0:μ=60H0:μ=60, Ha:μ>60Ha:μ>60C : H0:μ=71H0:μ=71, Ha:μ>71Ha:μ>71D : H0:μ=72H0:μ=72, Ha:μ<72Ha:μ<72E : None of the above
Answer:
E: None of the above
Step-by-step explanation:
Hello!
The objective is to find out how much time it takes people to commute to work.
Two samples where taken and two hypothesis tests where made:
One:
Sample mean 71 min; p-value: 0.03
Two:
Sample mean 72 min; p-value: 0.06
You have to choose from the options, a possible pair of hypotheses used for these two tests.
The parameter of the study is the population mean μ.
In the statistic hypotheses, the parameters are given either a known population value or a suspected value. So all options including sample values are wrong.
As said before the objective of the survey is to "determine how much time people spend commuting to work" in other words, whether or not the population mean is equal to a certain value.
H₀: μ = μ₀
H₁: μ = μ₀
Where μ₀ represents the theoretical value of the population mean. As you can say the hypotheses pair is two-tailed, not one-tailed.
Then the correct answer is E: None of the above
I hope this helps!
3 A prism is completely filled with 96 cubes that have edge length of 1 2 cm. What is the volume of the prism? Enter your answer in the box. cm³
The volume of a cube is found using the formula v = s^3, where s is the length of a side.
The volume of a cube with a side of 1/2cm is
V = 1/2^3 = 1/8 cubic cm.
Now multiply the volume of one cube by total cubes:
1/8 x 96 = 12 cubic cm
The prism has a volume of 12 cubic cm.
Answer:
it is 12 if u still need it
Step-by-step explanation:
In a class of 7 students, there are 5 students who forget their lunch. If the teacher chooses 2 students, what will the probability that neither of them forget their lunch?
Answer:
4711
Step-by-step explanation:
Answer by rothauserc(4711) (Show Source):
You can put this solution on YOUR website!
the probability that the first student picked has a lunch is 6/9 or 2/3
the probability that the second student picked has a lunch is 5/8
Plz help asap!!!!!!!!!!!!!!!!!!!!
Answer:
C) ⅙
Step-by-step explanation:
Starting with A:
April, August
2/12
1/6
Which BEST describes the shape of the distribution?
B. Skewed Right
Answer: Skewed left. (If there is an answer choice for it)
Step-by-step explanation: The data on the Y-Axis is higher on the left side of the graph than the right side of the graph. If it was higher on the right side of the graph, then it would be skewed right. Hope this helps!
Pam’s annual gross pay is $48,000. If she is paid biweekly, what is her gross pay on each pay check?
Answer:
$2000
Step-by-step explanation:
biweekly is defined as every 2 weeks
assume each month has 4 weeks
there are 12 months in a year and she is paid 2x per month so there are 24 weeks she is paid
48000/24 can be used to find the biweekly pay which is 2000
Pam's gross pay per biweekly paycheck is calculated by dividing her annual salary ($48,000) by the number of pay periods in a year (26). This results in an approximate gross pay of $1,846.15 per biweekly paycheck.
Explanation:The student's question pertains to calculating her gross pay per paycheck given her annual salary. To carry out this process, you need to understand that there are typically 52 weeks in a year and that being paid biweekly results in 26 pay periods (52 weeks divided by 2). Hence, you divide Pam’s annual gross pay amount of $48,000 by the 26 pay periods to get her gross pay, per paycheck.
Steps:
Identify the number of pay periods in a year, which in this case is 26 because she is paid biweekly (every two weeks).Divide the annual salary by the number of pay periods.The result is the gross pay per paycheck.So, $48,000 / 26 = $1,846.15
This means Pam's biweekly paycheck would be roughly $1,846.15, before taxes and other deductions.
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If d ran 12 meters in 6 second and c ran 15 meters in 5 seconds who ran faster or was it the same
Answer:
12/6 = 2 miles per second for d
15/5 = 3 miles per second for c
c runs faster because runs 3 miles every second while d only runs 2 miles per second
Step-by-step explanation:
According to researchers, a coin flip may not have a 50% chance of landing heads and a 50% chance of landing tails. In fact, they believe that a coin is more likely to land the same way it started. So if it starts out heads up, it is more likely to land heads up. Suppose someone tests this hypoth- esis with 1,000 flips of a coin where it starts out heads up each time. a. Describe what the symbol a stands for in this context. b. State your null and alternative hypotheses. c. Suppose 52% of the sample of 1,000 flips landed heads facing up. Verify the validity conditions that allow us to use a theory-based test. d. A theory-based test reports a standardized statistic of 1.26. Interpret what this means. e. A theory-based test reports a p-value of 0.1030. State your conclusion in terms of strength of evidence and what that means in the context of the study.
Answer:
a) π = np
π represents the number of heads that turn up in 1000 tosses of the coin.
b) The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
The validity conditions are met because we have 1000 tosses with 520 heads and 480 tails, indicating that we have more than 20 sample size in this sample.
The sample proportion (0.52) and the standard error of the sample proportion (0.0158) show that the distribution approximates a normal distribution and isn't skewed. So, the theory based test for this study is valid.
d) Check Explanation
e) The p-value obtained is greater than the significance level at which the test might have been performed, hence, we fail to reject the null hypothesis and conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
The researchers' claim then has to be wrong.
Step-by-step explanation:
a) If p corresponds to the proportion of 1000 tosses that turn up heads,
π = np
where n = number of tosses.
b) For hypothesis testing, the first thing to define is the null and alternative hypothesis.
The null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the directions of the test.
While, the alternative hypothesis usually confirms the the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the directions of the test.
For this question where we want to verify that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head. That is, the proportion of heads in multiple tosses is more than 0.5 given that the first toss was a head.
The null hypothesis would be that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
That is, the coin is likely to turn up heads less than or equal to 50% of the time, when it is tossed multiple times, starting with a first toss that gives a head.
The alternative hypothesis is that there is significant evidence to conclude that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Mathematically,
The null hypothesis is given as
The null hypothesis is represented as
H₀: p ≤ 0.50
The alternative hypothesis is given as
Hₐ: p > 0.50
c) The conditions that need to be satisfied before a theory based test is used include:
The validity conditions that must be met to be able to perform a theory-based test to test the hypothesis is having a sample size of 20 in each group and the distribution should not be strongly skewed.
d) The standardized statistic shows how far away from the standard proportion (the proportion that the population proportion is being compared with) the sample proportion is in terms of the standard error of the sample proportion.
It is given mathematically as,
t or z = (x - μ)/σₓ
x = p = sample proportion of the number of heads obtained in the multiple tosses starting with a first result of a head turning up = 0.52
μ = p₀ = 0.50 (the standard being tested against.
σₓ = standard error of the sample proportion, given as σₓ = √[p(1-p)/n]
n = sample size = 100
σₓ = 0.0158
The standardized statistic is also used to obtain the p-value that indicates how significant the results of the theory based test is.
e) The interpretation of p-values is that
When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.
So, for this question, like all other hypothesis testing, the significance level is usually at 0.05. On rare occasions, 0.01 and 0.10 are often used.
Whichever of the 3 is used,
p-value = 0.1030
0.1030 > 0.05, 0.01 or 0.10
Hence,
p-value > significance level
This means that we fail to reject the null hypothesis & conclude that there is no significant evidence that the coin is likely to turn up heads more times when tossed multiple times, starting with a first toss that gives a head.
Hope this Helps!!!