Answer:
its A, C, E on edg
Step-by-step explanation:
Answer:
a c e
Step-by-step explanation:
answer part two please
Answer:
a.) 8x + 6y
b.) 4x + 2y
Step-by-step explanation:
Simply add like terms together (x with x and y with y).
please very soon I offer the crown !!! + 10 points urgently !!!
A residential complex has left for the recreation area a circular-shaped extension of 40 m radius. In this space, a basketball court 30 m long by 15 m wide will be built. Also, a trapezoid-shaped park will be left in the sand, 6 m with a larger base, 4 m with a lower base and 3.5 m in height. What is the area left in the circular zone, after building the basketball court and the sand park? NOTE: remember the value of π = 3.14
Answer:
Step-by-step explanation:
Area of the circular zone = [tex]\pi[/tex]r^2
= 3.14 × 40^2 = 3.14 × 1600 = 5024 m^2
Area of the basketball court = l × b
= 30 × 15 = 450 m^2
Area of the trapezium shaped park = ( 6 + 4 ) 3.5 / 2
= 35/2 = 17.5 m^2
∴ Area left in the circular zone = Area of the circular zone - ( Area of the basketball court + Area of the trapezium shaped park )
= 5024 - ( 450 + 17.5 )
= 5024 - 467.5
= 4556.5 m^2
hope this helps
plz mark it as brainliest!!!!!!!
A direct variation function contains the points (-9, -3) and (-12,4). Which equation represents the function?
Answer:
[tex]y = -\frac{7x}{3} - 24[/tex]
Step-by-step explanation:
We can model this function using the equation of a line:
[tex]y = ax + b[/tex]
Where a is the slope of the line and b is the y-intercept.
To find the values of a and b, we can use the two points given:
(-9, -3):
[tex]-3 = a * (-9) + b[/tex]
[tex]-9a + b = -3[/tex]
(-12, 4):
[tex]4 = a * (-12) + b[/tex]
[tex]-12a + b = 4[/tex]
If we subtract the second equation from the first one, we have:
[tex]-12a + b - (-9a + b) = 4 - (-3)[/tex]
[tex]-12a + 9a = 4 + 3[/tex]
[tex]-3a = 7[/tex]
[tex]a = -7/3[/tex]
Then, finding the value of b, we have:
[tex]-12a + b = 4[/tex]
[tex]28 + b = 4[/tex]
[tex]b = -24[/tex]
So the equation is:
[tex]y = -\frac{7x}{3} - 24[/tex]
Need help please guysssssss
Answer:
C
Step-by-step explanation:
3x+2-x>8
2x+2>8
2x>8-2
2x>6
x>3
Answer:
C
Step-by-step explanation:
Sekkrit help!!!!! If (x+1) is the factor of polynomial p(x) = ax²+x+1, then find a.
Answer:
The value of a is 0.
Step-by-step explanation:
Given that (x+1) is a factor to a function, it means that when x = -1 is substitute into the function, you will get a 0 value. So you have to substitute the value of x into the function and make it 0, to find a :
[tex]p(x) = a {x}^{2} + x + 1[/tex]
[tex]let \: p( - 1) = 0 \\ let \: x = -1[/tex]
[tex]p( - 1) = a {( - 1)}^{2} + ( - 1) + 1[/tex]
[tex]0 = a - 1 + 1[/tex]
[tex]a = 0[/tex]
Answer:
a=0Solution,
To find a,
We should know that,
Factor of polynomial gives root of polynomial like:x-a if a factor of p(X) then p(a)=0 at X=a
So,
X+1=0
X=0-1
X=-1
put x=-1 into p(X) it gives zero.
[tex]p( - 1) = 0 \\ a {( - 1)}^{2} + ( - 1) + 1 = 0 \\ a(1) - 1 + 1 = 0 \\ a = 0[/tex]
hope this helps....
Good luck on your assignment....
PLEASE ANSWER!!!!!!!! Which system of equations does this graph represent? Linear graph and parabola. They intersect at 2, negative 1 and negative 3, 4 (1 point)
A. y = x2 − 5 y = −x + 1
B. y = x2 − 5 y = −x − 1
C. y = x2 + 5 y = −x + 1
D. y = x2 + 5 y = −x − 1
Answer:
Option (A)
Step-by-step explanation:
For equation of the line,
Let the equation is, y = mx + b
Slope 'm' of the line passing through two points (-3, 4) and (2, -1),
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{4+1}{-3-2}[/tex]
= -1
y-intercept of this line, b = 1
Now we substitute these values in the equation,
y = -x + 1
Let the equation of the parabola is,
y = a(x - h)² + k
Here, (h, k) is the vertex of the parabola,
Since vertex of the given parabola is (0, -5),
then the equation will be,
y = a(x - 0)²- 5
y = ax² - 5
Since a point (2, -1) lies on this parabola,
-1 = a(2)² - 5
5 - 1 = 4a
a = 1
Equation of the parabola will be,
y = x² - 5
Therefore, Option (A) will be the answer.
Scores on a recent national statistics exam were normally distributed with a mean of 82.2 and a standard deviation of 5.If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
Answer:
The lowest score eligible for an award is 92.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question:
[tex]\mu = 82.2, \sigma = 5[/tex]
If the top 2.5% of test scores receive merit awards, what is the lowest score eligible for an award
The lowest score is the 100 - 2.5 = 97.5th percentile, which is X when Z has a pvalue of 0.975. So X when Z = 1.96. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 82.2}{5}[/tex]
[tex]X - 82.2 = 5*1.96[/tex]
[tex]X = 92[/tex]
The lowest score eligible for an award is 92.
What position did Theodore Roosevelt hold before he became president?
Answer:
He served as Assistant Secretary of the Navy under President William McKinley
hope i helped
-lvr
The following are the ages (years) of 5 people in a room: 12, 20, 22, 22, 23 A person enters the room. The mean age of the 6 people is now 23. What is the age of the person who entered the room?
Answer:
39
Step-by-step explanation:
12+20+22+22+23=99
new mean=23
23*6=138
138-99=39
18 + 5k / 3
I need help asap please cuz my mom asked me to solve this in 2min
#aisanmoms #SOS
Answer:
Nothing can be further done to this equation. It has been simplified all the way.
A special deck of cards has ten cards. Four are green, three are blue, and three are red. When a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
a. List the sample space.
b. Let A be the event that a blue card is picked first, followed by landing a head on the coin toss. Find P(A).
c. Let B be the event that a red or green is picked, followed by landing a head on the coin toss. Are the events A and B mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.
d. Let C be the event that a red or blue is picked, followed by landing a head on the coin toss. Are the events A and C mutually exclusive? Explain your answer in one to three complete sentences, including numerical justification.
Answer:
(a) S = {GH, GT, BH, BT, RH and RT}
(b) The value of P (A) is 0.15.
(c) A and B mutually exclusive.
(d) A and C are not mutually exclusive.
Step-by-step explanation:
There are 10 cards in a special deck of cards: 4 are green (G), 3 are blue (B), and 3 are red (R).
Also when a card is picked, its color of it is recorded. An experiment consists of first picking a card and then tossing a coin.
(a)
The sample space is:
S = {GH, GT, BH, BT, RH and RT}
(b)
A = a blue card is picked first, followed by landing a head on the coin toss
Compute the probability of event A as follows:
[tex]P(A)=P(B)\times P(H)[/tex]
[tex]=\frac{3}{10}\times\frac{1}{2}\\\\=\frac{3}{20}\\\\=0.15[/tex]
Thus, the value of P (A) is 0.15.
(c)
B = a red or green is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and B.
So, consider the events,
A as a blue card is picked first
B as a red or green is picked
There is no intersection point for the two events.
Thus, events A and B mutually exclusive.
(d)
C = a red or blue is picked, followed by landing a head on the coin toss.
The result of the coin toss is same for both events A and C.
So, consider the events,
A as a blue card is picked first
C as a red or blue is picked
There is an intersection point for the two events.
Thus, events A and C are not mutually exclusive.
Part(a): The sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b): The required probability is [tex]P(A)=0.15[/tex]
Part(c): The events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d): The events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Samples Space:A sample space is a collection of a set of possible outcomes of a random experiment. The sample space is represented using the symbol, “S”.
Part(a):
A special deck contains ten cards with colors red, green, and blue when the card is picked its color gets recorded, and after that coin will get tossed.
Then the sample space can be written as shown below:
[tex]S=\{GH,GT,BH,BT,RH,RT\}[/tex]
Part(b):
If A is the event that a blue card is picked first followed by landing ahead on the coin toss then the outcome it contains is 3 blue cards and 1 head.
Therefore the [tex]P(A)[/tex] is calculated below:
[tex]P(A):P(B)\timesP(H)\\=\frac{3}{10}\times\frac{1}{2}\\ =0.15[/tex]
Part(c):
Mutually exclusive events contain a probability [tex]P( A\ AND\ B ) = 0[/tex] that means there is no common outcome between them.
Here, it can be noticed that events A and B cannot happen at the same time. That means, the researcher cannot pick the same cards together. Either it could be red or green.
Hence, events A and B are mutually exclusive because of [tex]P( A\ AND\ B ) = 0[/tex] are equal to zero.
Part(d):
Mutually exclusive events contain a probability [tex]P( A\ AND\ C ) = 0[/tex] which means there is no common outcome between them.
Here, it can be noticed that events A and C can happen at the same time because event C can contain all outcomes of event A.
Hence, events A and C are not mutually exclusive because [tex]P( A\ AND\ C ) = 0[/tex] are not equal to zero.
Learn more about the topic samples space:
https://brainly.com/question/10684603
(Geometry) PLEASE HELP ASAP
Answer:
CD=72x=7please see the attached picture for full solution
Hope it helps
Good luck on your assignment
A random sample of 110 lightning flashes in a certain region resulted in a sample average radar echo duration of 0.81 second and a sample standard deviation of 0.34 second. This sample data is used as a pilot study, and now the investigator would like to design a new study to construct a 99% confidence interval with width 0.1. What is the necessary sample size
Answer:
[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]
So the answer for this case would be n=308 rounded up to the nearest integer
Step-by-step explanation:
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.1/2 =0.05 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for 99% of confidence interval now can be founded using the normal distribution since the sample size is large enough to assume the estimation of the standard deviation as the population deviation. The critical value for this case is [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:
[tex]n=(\frac{2.58(0.34)}{0.05})^2 =307.79 \approx 308[/tex]
So the answer for this case would be n=308 rounded up to the nearest integer
Which expression is equivalent to negative 4 times 4 times 4 times 4 times 4 times 4 times 4 times 4?
Answer:
-4*4^7
Step-by-step explanation:
Answer:
-65536
Step-by-step explanation:
I do not think I understand the question but -4*4*4*4*4*4*4*4=-65536
I think there may be missing information like if the question is multiple choice.
Hope that helps
Find the scale ratio for the map described below.
1 mm (map)equals500 m (actual)
The scale ratio is 1 to
nothing.
Answer:
The answer is nothing duh
Step-by-step explanation:
A baseball player swings and hits a pop fly straight up in the air to the catcher. The height of the baseball in meters t seconds after it is hit is given by the quadratic function h(t)= -4.9t^2 + 9.8t + 1. How long does it take for the baseball to reach its maximum height? What is the maximum height obtained by the baseball?
Answer:
Step-by-step explanation:
max can be found by the formula:
t=-b/2a
t=-9.8/2*(-4.9)
t=-9.8/-9.8
t=1
1 sec
to find maximum height obtained we find the vertex:
plug in 1 for t and simply solve:
h(t)= -4.9t^2 + 9.8t + 1
h(t)= -4.9*1^2 + 9.8*1 + 1
h(t)= -4.9*1 + 9.8 + 1
h(t)= -4.9 + 10.8
h(t)= 5.9
height is 5.9
A man starts walking from home and walks 3 miles at north of west, then 5 miles at west of south, then 4 miles at north of east. If he walked straight home, how far would he have to the walk, and in what direction
Answer:
Step-by-step explanation:
We shall find the solution of this problem with the help of vector notation of i , j , which show east and north direction .
The first displacement can be represented by the following
D₁ = - 3 cos 45 i + 3 sin45 j = - 3 / √2 i + 3 / √2 j
The second displacement can be represented by the following
D₂ = - 5 cos 45 i - 5 sin45 j = - 5 /√2 i - 5 /√2 j
The third displacement can be represented by the following
D₃ = 4 cos 45 i + 4 sin45 j = 4 /√2 i + 4 /√2 j
Total displacement D =
D₁ +D₂ + D₃
= i ( -3 -5 + 4 ) / √2 + j ( 3 - 5 + 4 ) / √2 j
= - 4 / √2 i + 2 / √2 j
D = - 2.8288 i + 1.414 j
Magnitude of D
= √ ( 2.8288² + 1.414² )
= 3.16 miles
For direction we calculate angle with X axis
Tanθ = 1.414 / 2.8288
θ = 26 °
As x is negative and Y is positive ,
the direction will be north of west .
Find the future value (FV) of the annuity due. (Round your answer to the nearest cent.) $180 monthly payment, 6.25% interest, 11 years
Answer:
The future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
Consider the provided information:
It is provided that monthly payment is $175, interest is 7% and time is 11 years.
The formula for the future value of the annuity due is:
Now, substitute P = 175, r = 0.07 and t = 11 in above formula.
Hence, the future value of the annuity due to the nearest cent is $2956.
Step-by-step explanation:
An urn contains 25 red marbles, 27 blue marbles, and 36 yellow marbles. One marble is to be chosen from the urn without looking. What is the probability of choosing a red marble?
Answer:
25/88
Step-by-step explanation:
25 red marbles, 27 blue marbles, and 36 yellow marbles. = 88 marbles
P(red) = number of red/total
= 25/88
Answer:
Dear user,
Answer to your query is provided below
Probability of choosing a red marble is 0.28 or (25/88)
Step-by-step explanation:
Total number of marbles = 88
Number of red marbles = 25
Probability = 25/88
the number 312 lies between the perfect cubes what are they
Answer:
216-343
Step-by-step explanation:
the number 312 lies between 125 and 330
How many parallel and perpendicular lines, are there in a trapezium?
Answer:
US
0 parallel linesoptionally, one or two (opposite) angles may be 90°World
2 parallel linesoptionally, one line perpendicular to the two parallel linesStep-by-step explanation:
It depends on where you are. A "trapezium" outside the US is the same as a "trapezoid" in the US, and vice versa.
A trapezium (World; trapezoid in the US) is characterized by exactly one pair of parallel lines. One of the lines that are not parallel may be perpendicular to the parallel lines, but that will only be true for the specific case of a "right" trapezium.
__
A trapezium (US; trapezoid in the World) is characterized by no parallel lines. It may have one angle or opposite angles that are right angles (one or two sets of perpendicular lines), but neither diagonal may bisect the other.
In the US, "trapezium" is rarely used. The term "quadrilateral" is generally applied to a 4-sided figure with no sides parallel.
An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 30% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)
(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?
(b) If six reservations are made, what is the expected number of available places when the limousine departs?
Answer:
(a) The probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b) The expected number of available places when the limousine departs is 0.338.
Step-by-step explanation:
Let the random variable Y represent the number of passenger reserving the trip shows up.
The probability of the random variable Y is, p = 0.70.
The success in this case an be defined as the number of passengers who show up for the trip.
The random variable Y follows a Binomial distribution with probability of success as 0.70.
(a)
It is provided that n = 6 reservations are made.
Compute the probability that at least one individual with a reservation cannot be accommodated on the trip as follows:
P (At least one individual cannot be accommodated) = P (X = 5) + P (X = 6)
[tex]={6 \choose 5}\ (0.70)^{5}\ (1-0.70)^{6-5}+{6 \choose 6}\ (0.70)^{6}\ (1-0.70)^{6-6}\\\\=0.302526+0.117649\\\\=0.420175\\\\\approx 0.4202[/tex]
Thus, the probability that at least one individual with a reservation cannot be accommodated on the trip is 0.4202.
(b)
The formula to compute the expected value is:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]P (X=0)={6 \choose 0}\ (0.70)^{0}\ (1-0.70)^{6-0}=0.000729\\\\P (X=1)={6 \choose 1}\ (0.70)^{1}\ (1-0.70)^{6-1}=0.010206\\\\P (X=2)={6 \choose 2}\ (0.70)^{2}\ (1-0.70)^{6-2}=0.059535\\\\P (X=3)={6 \choose 3}\ (0.70)^{3}\ (1-0.70)^{6-3}=0.18522\\\\P (X=4)={6 \choose 4}\ (0.70)^{4}\ (1-0.70)^{6-4}=0.324135[/tex]
Compute the expected number of available places when the limousine departs as follows:
[tex]E(Y) = \sum X\cdot P(X)[/tex]
[tex]=(4\cdot 0.000729)+(3\cdot 0.010206)+(2\cdot 0.059535)+(1\cdot 0.18522)\\+(0\cdot 0.324135)\\\\=0.002916+0.030618+0.11907+0.18522+0\\\\=0.337824\\\\\approx 0.338[/tex]
Thus, the expected number of available places when the limousine departs is 0.338.
Health insurers are beginning to offer telemedicine services online that replace the common office visit. Wellpoint provides a video service that allows subscribers to connect with a physician online and receive prescribed treatments. Wellpoint claims that users of its LiveHealth Online service saved a significant amount of money on a typical visit. The data shown below ($), for a sample of 20 online doctor visits, are consistent with the savings per visit reported by Wellpoint.
90 34 41106 84 5355 48 4175 49 9792 73 7480 94 10256 83
Required:
Assuming the population is roughly symmetric, construct a 95% confidence interval for the mean savings for a televisit to the doctor as opposed to an office visit (to 2 decimals).
Answer:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
Step-by-step explanation:
Information given
90 34 41 106 84 53 55 48 41 75 49 97 92 73 74 80 94 102 56 83
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
[tex]\bar X=71.35[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s=22.48 represent the sample standard deviation
n=20 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=20-1=19[/tex]
Since the Confidence is 0.95 or 95%, the significance is [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.093[/tex]
And replacing we got:
[tex]71.35-2.093\frac{22.48}{\sqrt{20}}=60.83[/tex]
[tex]71.35+2.093\frac{22.48}{\sqrt{20}}=81.87[/tex]
A plane flies 240 miles due north, then 320 miles due west. How
many miles must it fly to return to its starting point by the shortest
route? (Enter your answer without units.)
Answer: The distance of the shortest route of return is 400
Step-by-step explanation:
The direction of travel of the plane forms a right angle triangle ABC as shown in the attached photo. C represents the starting point of the plane. To determine the distance of the shortest by which the plane can return to its starting point, BC, we would apply the Pythagorean theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
BC² = 320² + 240²
BC² = 160000
BC = √160000
BC = 400
Find the domain and range of the following function ƒ(x) = 5|x - 2| + 4 Domain: [4,8) Range: (-∞,∞) Domain: (4,∞) Range: (-∞,∞) Domain: (-∞,∞) Range: [4,∞) Domain: (-∞,∞) Range: (4,∞)
Answer:
Step-by-step explanation:
Hi,
the function is defined for all reals so the domain is [tex]]-\infty;+\infty[[/tex]
for x real
|x| >= 0
so f(x) >= 4
so the range is [tex][4;+\infty[[/tex]
do not hesitate if you need any further explanation
hope this helps
Answer:
Domain: (-∞,∞) Range: (4,∞)
find the quotient of (5+4i)/(6+8i) ans express in simplest forms
Answer:
Your correct answer is 31/50 + -4/25 i
Step-by-step explanation:
5+4i/6+8i = 31/50 + -4/25 i
Renee is making a scale diagram of her MP3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the MP3 player is 4 centimeters, and the width is 7 centimeters. This is , and the scale factor is .
Answer:
2
Step-by-step explanation:
Scale Factor = [tex]\frac{AnySideOfDiagram}{AnySideOfMP3Player}[/tex]
So,
Scale Factor = [tex]\frac{8}{4} = \frac{14}{7}[/tex] = 2
So,
The scale factor is 2
Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.
n=55,
x=33,
p=0.55
p(3)=_________
Answer:
P(33) = 0.0826
Step-by-step explanation:
The binomial distribution in this case has parameters n=55 and p=0.55.
The probability that k successes happen with these parameters can be calculated as:
[tex]P(x=k) = \dbinom{n}{k} p^{k}(1-p)^{n-k}\\\\\\P(x=k) = \dbinom{55}{k} 0.55^{k} 0.45^{55-k}\\\\\\[/tex]
We have to calculate the probability fo X=33 succesess.
This can be calculated using the formula above as:
[tex]P(x=33) = \dbinom{55}{33} p^{33}(1-p)^{22}\\\\\\P(x=33) =1300853625660220*0.0000000027*0.0000000235\\\\\\P(x=33) =0.0826\\\\\\[/tex]
Assume that you plan to use a significance level of α = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate. Round your answer to the nearest thousandth.
n1 = 677 n2 = 3377
x1 = 172 x2 = 654
Answer:
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal
Step-by-step explanation:
Given first sample size n₁ = 677
First sample proportion
[tex]p^{-} _{1} = \frac{x_{1} }{n_{1} } = \frac{172}{677} = 0.254[/tex]
Given second sample size n₂ = 3377
second sample proportion
[tex]p^{-} _{2} = \frac{x_{2} }{n_{2} } = \frac{654}{3377} = 0.1936[/tex]
Null Hypothesis : H₀ : p₁ = p₂.
Alternative Hypothesis : H₁ : p₁ ≠ p₂.
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{P Q(\frac{1}{n_{1} } +\frac{1}{n_{2} }) } }[/tex]
where
[tex]P = \frac{n_{1} p_{1} + n_{2} p_{2} }{n_{1}+n_{2} } = \frac{677 X 0.254+3377 X 0.1936}{677+3377}[/tex]
P = 0.2036
Q = 1 - P = 1 - 0.2036 = 0.7964
[tex]Z = \frac{0.254- 0.1936 }{\sqrt{0.2036 X 0.7964(\frac{1}{677 } +\frac{1}{3377 }) } }[/tex]
Z = 3.775
Critical value ∝=0.05
Z- value = 1.96
The calculated value Z = 3.775 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
The Two Population proportion are not equal