Answer:
6750 - 3894 = 2856
Step-by-step explanation:
You have to make use of the arithmetic facts you know.
The least-significant asterisk must be 0, because the sum of 4 and 6 is 10.
The 10s asterisk must be 9,so that the sum 5 + 9 + 1 has a least-significant digit of 5.
The 100s asterisk must be 7, because that is the least-significant digit of the sum 8 + 8 + 1 = 17.
The 1000s asterisk must be 3, so that 2 + 3 + 1 = 6.
(The "1" in each of these sums is the carry from the sum of the digits with the next lower place value.)
So, the subtraction problem is ...
6750 - 3894 = 2856
_____
Comment on the solution method
For the most part, we worked this as an addition problem. The sum of the last two numbers must be equal to the first: 6570 = 3894 +2856. For some of us, addition facts are easier to work with than subtraction facts. The carry/borrow can be less confusing that way.
En una encuesta sobre preferencias entre los deportes Tenis (T), Surf (S) y Golf (G) se sabe que:
90 personas fueron encuestadas
15 personas prefieren Golf
10 no prefieren ninguno de estos deportes
ninguno de los que prefiere los deportes Tenis ó Surf prefieren Golf
30 prefieren sólo Surf
20 prefieren sólo Tenis
a) ¿Cuántas personas prefieren dos de estos deportes?
b) ¿Cuántos prefieren sólo uno de estos deportes?
Answer:
a) 15
b) 65
Step-by-step explanation:
Adjunto se encuentra el diagrama asociado a esta situación. Comenzamos por ubicar aquellas afirmaciones que relacionan todos los deportes. Sabemos que 10 personas no prefieren ningún deporte. Luego, ubicamos 10 fuera de los conjuntos mostrados. Sabemos que 30 personas prefieren sólo surf y 20 personas prefieren sólo Tenis. Es decir, hay 30 personas en el conjunto S que no intersectan a los otros dos. En este momento, hemos ubicado a 60 personas. Nos hacen falta 30 personas. La afirmación "15 personas prefieren Golf" significa que la suma de los números dentro del conjunto G es 15. La afirmación "ninguno de los que prefieren los deportes Tenis o Surf prefieren el golf. Es decir, que la intersección de G con T y con S son vacías. Es decir que las 15 personas que prefieren golf, lo prefieren únicamente. Esto nos deja con 15 personas por ubicar. El único lugar donde podemos ubicar a dichas 15 personas es en en la intersección de T y S.
a). ¿cuántas personas prefieren dos de estos deportes? Por el diagrama, son aquellas personas que prefieren Tenis o Surf. Es decir, 15.
b) ¿Cuánto prefieren sólo uno de estos deportes? Es la suma de aquellos que prefieren sólo un deporte. Es decir, sólo G, sólo T o sólo S. Es decir 15+20+30 = 65.
Minimize
z = 20x1 + 32x2 + 40x3,
subject to
3x1 + x2 + 6x3 ≥ 9
x1 + x2 ≥ 9
4x2 + x3 ≥ 12
x1 ≥ 0, x2 ≥ 0, x3 ≥ 0.
solve for x1, x2, x3 and z
Answer:
Step-by-step explanation:
1. constraints with "[tex]\geq[/tex]" we should subtract surplus variable S1, S2, S3 and add artificial variable A1, A2, A3
Hence Z = 20 x1 + 32x2 + 40x3 + 0S1 + 0S2 + 0S3 + MA1 + MA2 + MA3
subject to
[tex]3x_1 +x_2+6x_3-S_1+A_1=9[/tex]
[tex]x_1+x_2-S_2+A_2=9[/tex]
[tex]4x_2+x_3-S_3+A_3=12[/tex]
and [tex]x_1,x_2,x_3,S_1,S_2,S_3,A_1,A_2,A_3\geq 0[/tex]
Consider the scatterplot above. Write a sentence explaining the meaning of the value of the slope for this linear model. The is an average of per year .
Answer:
Slope: The percent that voted falls by 0.1271 units per year.
Step-by-step explanation:
The slope of a regression line represent the average rate of change in the dependent variable (y) based upon the changes in the independent variable (x).
In this case the regression equation provided is:
y = -0.1271 x + 307.53
The slope of the line is -0.1271.
The dependent variable is the percent that voted and the independent variable is the year.
The slope of -0.1271 indicates that every year, on average, the percent that voted decreases by 0.1271 units.
Or the percent that voted falls by 0.1271 units per year.
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
If your good at maths help me
Answer:
6n+1
Step-by-step explanation:
first term=13-6=7
nth term=7+(n-1)6=7+6n-6=6n+1
Answer:
aₙ= 6n +1
Step-by-step explanation:
Second term a₂= 13
Common difference d= 6
Then first term
a₁= 13 -6= 7nth term:
aₙ= a₁ + (n-1)daₙ= 7 + (n-1)*6= 7+6n -6 = 6n +1aₙ= 6n +1
Can someone plz help me solved this problem I need help ASAP plz help me! Will mark you as brainiest!
Answer:
2 is the answer
Step-by-step explanation:
area=1/2*base*height
as height = 2*base and area =4 it comes
1/2*2*base*base=4
so base *base=4
so base = 2
How would I solve this problem. A researcher wishes to estimate the mean height of women aged between 60 and 65 in the U.S. She desires a margin of error of 0.3 inches. Past studies suggest that a population standard deviation of 3.3 inches is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
Answer:
465
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
Assuming 95% confidence, CV = z = 1.96.
Standard error is:
SE = σ / √n
SE = 3.3 / √n
Given margin of error of 0.3:
0.3 = 1.96 × 3.3 / √n
n = 465
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
Autism is a serious and lifelong disability that is characterized by a severely decreased ability to engage in communication and social interaction. In 1998 citizens in a New Jersey town were concerned about the number of children diagnosed with autism, and a study was undertaken to establish the prevalence in the community. Data from the study are reported below:
Numbers of Children Diagnosed with Autistic Disorder
Age Category (y) Diagnosed with Autistic Disorder Number of Children in Population
3-5 19 3479
6-10 17 5417
Required:
a. Calculate the prevalence rate of autism for these children for the two age categories.
b. Convert the prevalence rate to a rate per 1,000
Answer:
a. Calculate the prevalence rate of autism for these children for the two age categories.
3-5: prevalence rate = 0.55%6-10: prevalence rate = 0.31%b. Convert the prevalence rate to a rate per 1,000
3-5: prevalence rate = 5.5 per thousand6-10: prevalence rate = 3.1 pér thousandStep-by-step explanation:
Generally prevalence is calculated using the following formula:
(number of people with autism / number of people measured) x 100%
age category
3-5: prevalence rate = (19/3,479) x 100% = 0.55%
6-10: prevalence rate = (17/5,417) x 100% = 0.31%
if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100
3-5: prevalence rate = (19/3,479) x 1,000 = 5.5
6-10: prevalence rate = (17/5,417) x 1,000 = 3.1
please please solve for x
Answer:
Step-by-step explanation:
Please help! Correct answer only, please! Determine the value of the following if it is possible. If it is not possible, explain. A. B. C. D.
Answer: C
Step-by-step explanation:
Multiply the number outside of the matrix to EVERY value inside that matrix.
Addition and subtraction of matrices is very simple - just add (or subtract) the values of each matrix that have the same designation.
[tex]X\left[\begin{array}{cc}a&b\\c&d\end{array}\right] +Y\left[\begin{array}{cc}e&f\\g&h\end{array}\right]=\left[\begin{array}{cc}X(a)+Y(e)&X(b)+Y(f)\\X(c)+Y(g)&X(d)+Y(h)\end{array}\right]\\\\\\\\\\-3\left[\begin{array}{cc}2&7\\8&-6\end{array}\right] +2\left[\begin{array}{cc}0&1\\4&-2\end{array}\right]\\\\\\=\left[\begin{array}{cc}-3(2)+2(0)&-3(7)+2(1)\\-3(8)+2(4)&-3(-6)+2(-2)\end{array}\right] \\\\\\=\left[\begin{array}{cc}-6&-19\\-16&14\end{array}\right][/tex]
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the standard deviation of the speeds in Excel file Q-14.xlsx.
Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:
1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;
2) Subtract each number with the Mean and square the result;
3) Add the differences and divide it by the total number of elements of the set;
4) Take the square root of the result and that is the Standard Deviation.
The calculations can be done by a calculator like Excel:
1) In each cell of a same column, write the data you want to know the deviation.
2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).
3) Press Enter. The deviation will appeared on the same cell.
The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.
A bucket that has a mass of 30 kg when filled with sand needs to be lifted to the top of a 30 meter tall building. You have a rope that has a mass of 0.3 kg/m that must be secured to the bucket. It takes 1 meter of rope to secure the bucket. Once the bucket reaches the top of the building it only has mass 15 kg because there was a hole in the bottom and sand was leaking out at a constant rate while it was being lifted to the top of the building. Find the work done lifting the bucket (sand and rope) to the top of the building.
Answer:
765 J
Step-by-step explanation:
We are given;
Mass of bucket = 30 kg
Mass of rope = 0.3 kg/m
height of building= 30 meter
Now,
work done lifting the bucket (sand and rope) to the building = work done in lifting the rope + work done in lifting the sand
Or W = W1 + W2
Work done in lifting the rope is given as,
W1 = Force x displacement
W1 = (30,0)∫(0.2x .dx)
Integrating, we have;
W1 = [0.2x²/2] at boundary of 30 and 0
W1 = 0.1(30²)
W1 = 90 J
work done in lifting the sand is given as;
W2 = (30,0)∫(F .dx)
F = mx + c
Where, c = 30 - 15 = 15
m = (30 - 15)/(30 - 0)
m = 15/30 = 0.5
So,
F = 0.5x + 15
Thus,
W2 = (30,0)∫(0.5x + 15 .dx)
Integrating, we have;
W2 = (0.5x²/2) + 15x at boundary of 30 and 0
So,
W2 = (0.5 × 30²)/2) + 15(30)
W2 = 225 + 450
W2 = 675 J
Therefore,
work done lifting the bucket (sand and rope) to the top of the building,
W = 90 + 675
W = 765 J
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
4x2 - 14x + 6
x3 - 7x2 + 12x
What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common
factors.
Answer:
Answer is given below.
Step-by-step explanation:
let us solve the numerator first
=4x²-14x+6
=2(2x²)+2(-7x)+2(3)
= GCF of the terms of the numerator is 2.
denominator
x³-7x²+12x
x(x²)+x(-7x)+x(12)
GCF of the terms of the denominator is x.
factorise the numerator
4x²-14x+6
4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no.s are added they should give -14)
(4x²-2x) + (-12x+6)
2x(2x-1) -6(2x-1)
(2x-6)(2x-1)
factors are
(2x-6), (2x-1)
denominator
this can also be done by splitting the middle term
x³-7x²+12x
x³-3x²-4x²+12x
(x³-3x²) + (-4x²+12x)
x²(x-3) -4x(x-3)
(x²-4x)(x-3)
factors are
(x²-4x), (x-3)
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
Simplify the expression. (-3 + 6i)(-3 + 5i)
Answer:
11i-6
Step-by-step explanation:
Answer:
11i-6
Step-by-step explanation:
(-3+6i)(-3+5i)
combine like terms (-3)+(-3)=-6
6i+5i=11i
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
A box contains 16 transistors, 4 of which are defective. if 4 are selected at random, find the probability that
a. all are defective.
b. none are defective.
Answer:
(a)0.0005
(b)0.2720
Step-by-step explanation:
Total Number of Transistors = 16
To find the probability that 4 selected at random are defective (or non-defective), we find the probability of the 1st, 2nd, 3rd, and 4th defective (or non-defective) items in that order, Note that the selection is without replacement.
(a)Probability that all are defective
Number of Defective Transistors =4
P(all are defective) [tex]=\dfrac{4}{16} \times \dfrac{3}{15} \times \dfrac{2}{14} \times \dfrac{1}{13}[/tex]
=0.0005
(b)Probability that none are defective
Number of Non-Defective Transistors =16-4=12
P(none are defective) [tex]=\dfrac{12}{16} \times \dfrac{11}{15} \times \dfrac{10}{14} \times \dfrac{9}{13}[/tex]
=0.2720
Write a sine function that has a midline of 2, an amplitude of 4 and a period of 11.
Answer:
y = 4 sin(2π/11 x) + 2
Step-by-step explanation:
y = A sin(2π/T x + B) + C
where A is the amplitude,
T is the period,
B is the phase shift,
and C is the midline.
A = 4, T = 11, and C = 2. We'll assume B = 0.
y = 4 sin(2π/11 x) + 2
The sine function with the desired characteristics is given by:
[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]
The standard sine function is given by:
[tex]y = A\sin{Bx} + C[/tex]
The amplitude is 2A.The period is [tex]\frac{2\pi}{B}[/tex].The midline is C.In this problem:
Midline of 2, thus [tex]C = 2[/tex].Amplitude of 4, thus [tex]2A = 4 \rightarrow A = 2[/tex].Period of 11, thus [tex]\frac{2\pi}{B} = 11 \rightarrow B = \frac{2\pi}{11}[/tex]Then, the equation for the sine function is:
[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]
A similar problem is given at https://brainly.com/question/18055768
Complete the following subtraction exercises.
10 – 2 =
14 – 6 =
15 – 9 =
17 – 8 =
13 – 5 =
11 – 8 =
20 – 8 =
16 – 7 =
12 – 9 =
21 – 9 =
11 – 6 =
5 – 5 =
4 – 0 =
16 – 8 =
10 – 5 =
18 – 7 =
13 – 8 =
12 – 4 =
Answer:
Below
Step-by-step explanation:
8,8,6,9,8,3,12,9,3,12,5,0,4,8,5,11,5,8. Answers are in order from the first to the last
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit.
Answer:
A.
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula:
where a is coefficient of the term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
complete the square:
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Answer: d (8, 4); The vertex represents the maximum profit.
Explanation: i got it right on the test
18x-5x=13+20 what is the answer
Answer:
3.3
Step-by-step explanation:
18x-5x=13+20
13x=33
x=2.5
In an aquarium, there are 4 large fish and 16 small fish. Half of the small fish are blue. One fish is selected at random. Find the probability that it is a small, blue fish. Write your answer as a fraction in simplest form.
Answer:
2/5
Step-by-step explanation:
There are 20 fish, 8 of which are small and blue. Therefore, the probability of randomly selecting a small blue fish is 8/20 = 2/5.
A student is getting ready to take an important oral examination and is concerned about the possibility of having an "on" day or an "off" day. He figures that if he has an on day, then each of his examiners will pass him, independently of one another, with probability 0.8, whereas if he has an off day, this probability will be reduced to 0.4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on day, should he request an examination with 3 examiners or with 5 examiners?
Answer:
The students should request an examination with 5 examiners.
Step-by-step explanation:
Let X denote the event that the student has an “on” day, and let Y denote the
denote the event that he passes the examination. Then,
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.
It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,
[tex]P(X)=2\cdot P(X^{c})[/tex]
Then,
[tex]P(X)+P(X^{c})=1[/tex]
⇒
[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]
Then,
[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]
Compute the probability that the students passes if request an examination with 3 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]
[tex]=0.715[/tex]
The probability that the students passes if request an examination with 3 examiners is 0.715.
Compute the probability that the students passes if request an examination with 5 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]
[tex]=0.734[/tex]
The probability that the students passes if request an examination with 5 examiners is 0.734.
As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.
Your local school board wants to determine the proportion of people who plan on voting for the school levy in the upcoming election. They conduct a random phone poll, where they contact 150 individuals and ask them whether or not they plan on voting for the levy. Of these 150 respondents, 78 people say they plan on voting for the levy. The school board wants to determine whether or not the data supports the idea that more than 50% of people plan on voting for the levy. Conduct a hypothesis test at the 0.10 significance level to test this claim.
Answer:
There is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy
Step-by-step explanation:
Sample size, n = 150
Number of people that plan on voting for the levy, X = 78
Proportion of people that plan on voting for the levy:
[tex]\bar{p} = X/n\\\bar{p} = 78/150\\\bar{p} = 0.52[/tex]
The study is to determine whether or not the data supports the idea that more than 50%(0.5) of people plan on voting for the levy
The null and alternative hypotheses are:
[tex]H_0: p \leq 0.5\\H_a: p > 0.5[/tex]
Calculate the test statistics:
[tex]t_s = \frac{\bar{p} - p}{\sqrt{\frac{p(1-p)}{n} } } \\t_s = \frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{150} } } \\t_s = 0.49[/tex]
For a test statistic [tex]t_s = 0.49[/tex], the p-value = 0.3121
The significance value, [tex]\alpha = 0.10[/tex]
Since the p-value(0.3121) is greater than α(0.10), the null hypothesis [tex]H_0[/tex] will be accepted.
This means that there is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy