The appropriate statistical decision that researcher should use is that (d) Reject the null hypothesis with either a = 0.05 or a = 0.01
The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental data are reliable.
Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not.
According to the null hypothesis, there is no relationship between the independent variable and the measured event (the dependent variable). To test the null hypothesis, we don't have to think it's accurate. In contrast, you can suppose that a group of variables (dependent and independent) are connected.
According to the question ,
A researcher is testing a null hypothesis stating that for the general population there is no preference between the two leading brands of cola In a sample of n = 100 people, 35 preferred brand A and 65 preferred brand B.
The appropriate statistical decision is (d) Reject the null hypothesis with either a = 0.05 or a = 0.01
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Sample Response: First, I would write the rate as a fraction. Then I would divide the numerator by the denominator. Which key phrases did you use in your response? Find an equivalent ratio that compares a quantity to exactly one unit of another quantity. Write the rate as a fraction. Divide the numerator by the denominator.
The key phase that we see in our response is "Divide the numerator by the denominator" (option C).
What is a key phrase?A key phrase refers to a phrase that contains words that define the most important part of a text. A key phrase serves as a summary of a paragraph or larger text.
In this case, the key phrase would serve to establish what was the mathematical procedure that we carried out to solve a mathematical problem. According to the above, it can be inferred that the key phrase must contain the most precise information to describe this procedure.
Based on the above, the correct answer is "Divide the numerator by the denominator" because it exactly describes the procedure that was performed.
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Harrison deposits $345 in a savings account that earns 4.2% simple interest paid annually. How long will it take for the total amount in the account to reach $410?
PLEASE ASAP I HAVE THIS QUESTION ON A TEST HELLPP
The time required for the total amount in Harrison's account to reach $410 is 4.49 years.
What is time required to reached an accrued amount of $410?The simple interest formula is expressed as;
A = P( 1 + rt )
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given the data in the question;
Principal P = $345Interest rate r = 4.2% = 4.2/100 = 0.042Accrued amount A = $410Time t = ?Plug the given values into the above formula and solve for time t.
A = P( 1 + rt )
A/P = 1 + rt
A/P - 1 = rt
t = ( A/P - 1 ) / r
t = ( $410/$345 - 1 ) / 0.042
t = ( 13/69 ) / 0.042
t = 4.49 years
Therefore, the time needed to reach accrued amount is 4.49 years.
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Britney is buying a shirt and a hat at the mall. The shirt costs $31.18, and the hat costs $18.32. If Britney gives the sales clerk $100.00, how much change should she receive? (Ignore sales tax.)
The change she should receive is $50.50 and we can find it by using simple cost and price calculations.
What is selling price?
Selling price is the amount of money that a seller charges for a product or service. It is the amount of money that a buyer pays for a product or service. The selling price is determined by a variety of factors, such as the cost of production, the perceived value of the product or service, the market demand for the product or service, competitive pricing in the market, and the profit desired by the seller. The selling price may also be affected by the availability of financing options for buyers, taxes, and other applicable fees. The selling price is an important factor in marketing and promoting a product or service. It must be set at the right level to attract buyers and ensure that the seller can make a profit.
Selling price for a shirt = $31.18
Selling price for a hat = $18.32
Total amount she have = $100
Total selling price (for both) = $49.50
So, the remaining amount = $100 - $49.50
= $50.50
So, the change she should receive = $50.50
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In Bill the Boring's dryer there are 11 black shirts, 8 gray shirts, 12 black sweaters, and 10 gray sweaters. Bill is going to take one of these pieces of clothing
out of the dryer at random to check if his clothes are completely dry. What is the probability that the piece of clothing Bill takes out is gray or is a shirt?
Do not round intermediate computations, and round your answer to the nearest hundredth.
(If necessary, consult a list of formulas.)
Answer:
70.73%
29/41 = 0.7073...
Move the decimal over 2 places and get: 70.73
In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars. Five of the points are labeled A, B, C, D, and E, respectively.
E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven (thousands) Which of the five labeled points is the most influential with respect to a regression of trade-in value versus miles driven?
Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.
"Information available from the question",
In the question:
In a study to determine whether miles driven is a good predictor of trade-in value, 11 cars of the same age, make, model, and condition were randomly selected. The following scatterplot shows trade-in value and mileage for those cars.
Five of the points are labeled A, B, C, D, and E, respectively.
E $6,500+ А $6,000 B $5,500+ $5,000+ $4,500+ Value $4,000 + + 50 60 70 80 90 100 Miles Driven
To find the which point is the most influential with respect to a regression of trade-in value versus miles driven?
Now, According to the question:
According to the points of labeled:
The correct answer is :
To see the figure.
Hence, Point E does not follow the trend with respect to the other data and is probably an outlier. The value of the car is much higher than other cars with similar miles driven.
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f ( x ) = − 2 x − 3 find f( 2 )
Answer:
The answer is (-7)
Step-by-step explanation:
f(x) = -2x - 3, if f(2)
f(2) = -2(2) - 3 = -4 - 3 = (-7)
Thus, The answer is (-7)
Graph triangle ABC with vertices
A( − 4, − 3), B(0, – 2),
and C(2, 2) and and its
image after a 90° clockwise
rotation about point C.
Check the picture below.
How can you check if a line belongs to a plane (Cartesian equation of the line and the equation of the plane is given)?
a) The line belongs to the plane.
b) The line does not belong to the plane.
How to verify if a line belongs or not to a plane?The equation of a line has the format given as follows:
[tex]\frac{x - x_1}{a} = \frac{y - y_1}{b} = \frac{z - z_1}{c}[/tex]
The equation of a plane has the format given as follows:
Ax + By + Cz + D = 0.
The line will belong to the plane if these two conditions are satisfied:
[tex]Ax_1 + By_1 + Cz_1 + D = 0[/tex]aA + bB + cC = 0.In standard format, the line for item a is given as follows:
[tex]\frac{x - 1}{4} = \frac{y + 2}{9.5} = \frac{z - 3}{1}[/tex]
Then the conditions are tested as follows:
3(1) - 2(-2) + 7(3) - 28 = 0.4 x 3 - 2 x 9.5 + 1 x 7 = 0.The two conditions are satisfied, hence the line belongs to the plane.
For item b, we have that:
(-2)(-6) + 1(8) - 5(-3) + 1 = 36.
First condition already not satisfied, hence the second does not need to be tested, meaning that the line does not belong to the plane.
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(See Example 12) A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. In how many ways can the executive committee be formed?
Since , A club has 42 members and 17 pledges. The club selects a 5-member executive committee composed of a chair and vice-chair, who must be members, and an advisory committee of 3 pledges. The executive committee can be formed in 850668 ways.
a. The number is ⁴²P₅ = 42!/37!
=42×41×40×39× 38 ×37!/37!
=102080160 ways.
b. The number is ⁴²C₅ = 42!/ 5! × 37!
=42× 41× 40× 39 ×38×37!/ 5×4×3×2×1 ×37!
= 850668 ways.
If you have trouble applying concepts, consider pure mathematics. Select 4 objects out of 24 to replace the first problem. Since there is a replacement, it is a permutation. So the answer is ⁴²P₅= 102080160 possibilities. Obviously there can't be a substitute for the next, so it's a combo. So the answer is ⁴²C₅= 850668 ways.
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seven teams play a soccer tournament in which each team plays every other team exactly once. no ties occur, each team has a 50% chance of winning each game it plays, and the outcomes of the games are independent. in each game, the winner is awarded 1 point and the loser gets 0 points. the total points are accumulated to decide the ranks of the teams. in the first game of the tournament, team a beats team b. the probability that team a finishes with more points than team $B$ is $m/n,$ where $m$ and $n$ are relatively prime positive integers. Find $m+n.$
The team a finishes with more points than team b with a probability of 319/512
seven teams play a soccer tournament in which each team plays every other team exactly once
in the first game of the tournament, team a beats team b
We need to find the probability that team a finishes with more points than team b
Both teams, a and b play 6 matches each
In the first match, a wins. Now they can play 5 matches each
Of the remaining 5 games
a win 0 and b win zero
P(a > b) = 5C1/2^5 x 5C1 / 2^5 = 1/1024
a win 1 and b win 1 or zero
P(a > b) = 5C1/2^5 x(5C0 + 5C1) / 2^5 = 30/1024
a win 2 and b win 2 or 1 or zero
P(a > b) = 5C2/2^5 x(5C0 + 5C1 + 5C2) / 2^5 = 160/1024
a win 3 and b win 3 or 2 or 1 or zero
P(a > b) = 5C3/2^5 x(5C0 + 5C1 + 5C2 + 5C3) / 2^5 = 260/1024
a win 4 and b win 4 or less
P(a > b) = 5C4/2^5 x(5C0 + 5C1 + 5C2 + 5C 3 + 5C4) / 2^5 = 155/1024
a win 5 and b win 5 or less
P(a > b) = 5C1/2^5 x(5C0 + 5C1+ 5C2 + 5C3 + 5C4 + 5C5) / 2^5 = 32/1024
P(a> b) = (1 + 30 + 160 + 260 + 155 + 32)/1024 = 638/1025 = 319/512
Therefore, the the probability that team a finishes with more points than team is 319/512
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question a newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. the editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. which of the following methods will achieve the desired sampling design?
Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
The correct option is (B).
Now, According to the question:
Stratified sampling design divides the given population into small sub-groups called strata. The members of each strata share some common features and at any particular time, a sample is randomly selected from each stratum which is then compared to the entire population. During random sampling, a number proportional to the stratum size is selected from all strata. The randomly selected samples from each strata are then combined to form a common random sample.
Considering that the editor wants to adopt stratified sampling, option B fits (Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.)
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The complete question is this:
A newspaper editor wants to investigate whether residents of the city support a proposal to build a new high school football stadium. The editor hires a polling firm to conduct a survey and requests that a sample of 500 residents be selected using a stratified sampling design based on voting districts within the city. Which of the following methods will achieve the desired sampling design?
(A) Send a survey to all city residents and use the first 500 returned surveys for the sample.
(B) Select a random sample from each voting district based on the proportion of city residents in the district so that a total of 500 is obtained.
(C) Select one voting district at random, and then select a random sample of 500 from the selected voting district.
(D) Alphabetize a list of all city residents, and then select the first 500 residents on the list, classifying those selected by voting district.
(E) Select the first 500 city residents who attend the next high school football game.
What ratio, a:b, is represented in the table?
a b
1.5 2.5
51 85
99 165
Answers
A 4:54:5
B 2:32:3
C 3:5
The ratio a : b represented in the table of values is (c) 3 : 5
How to determine the ratio a : b represented in the table of values?From the question, we have the following table of values that can be used in our computation:
a b
1.5 2.5
51 85
99 165
Remove the last two entries in the table
So, we have the following representation
a b
1.5 2.5
Express the remaining entries as a ratio
So, we have the following representation
Ratio = a : b
Substitute the known values in the above equation, so, we have the following representation
Ratio = 1.5 : 2.5
Divide the ratio by 0.5
So, we have the following representation
Ratio = 1.5/0.5 : 2.5/0,5
Evaluate the quotients
So, we have the following representation
Ratio = 3 : 5
Hence, the ratio is (c) 3 : 5
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3.79 divided by 4 answer
Answer:
0.9475
Hope this Helps!
Enter the letter only!
(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph thus option (B) will be correct.
What are coordinates?A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.
As per the given coordinates,
The coordinate is the representation of horizontal and vertical distinctions.
The (3,1) is the point that is 3 grid right or horizontal and 1 unit up or vertical from the origin.
Hence "(3,1),(4,-2),(-5,4),(4,-1),(-1,-2) match with the given coordinates of the graph".
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Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 171 in. Find the dimensions of the cylindrical package of greatest volume that may be sent via priority mail. (Hint: The length plus the girth is 2r + l.)
r =
l =
volume =
If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.
Given that,
The combined length and girth of a priority mail package cannot exceed 171 inches, according to postal standards.
We have to find calculate the size of the largest volume, cylindrical container that can be sent via priority mail.
We know that,
Let
Length= Breadth =x
Height=y
Volume can be written as
V=x²y
Now,
Combined length and girth is
7x+y=171
y=171-7x
V(x)=x²(171-7x)
V(x)=171x²-7x³
Differentiating with respect to x.
V'(x)=343x-21x²
The maximum value
V'(x)=0
343x-21x²=0
7x(49-3x)=0
x=0
and
49-3x=0
3x=49
x=49/3
Once again differentiating with respect to x.
V''(x)=343-42x
V''(x)=343-42(0)=343>0(min)
V''(x)=343-42(49/3)=-343<0(max)
The maximum volume is
Vmax=V(49/3)=(49/3)(171-7(49/3))
Vmax=925
Therefore, If a priority mail package has a maximum combined length and girth of 171 inches and is rectangular in shape with a square cross section, the maximum volume allowed is 925.
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Please answer the question about nets
Answer:
Side h and side
If cabbage costs $0.39 per pound, then how many pounds of cabbage can you buy for $5.00? Explain why you can use division to solve this problem.
The amount of cabbage 12.82 pounds will be to buy for $5.00.
What is Division method?
Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The cabbage costs $0.39 per pound.
Now,
Since, The cabbage costs $0.39 per pound.
Hence, The amount of cabbage to buy for $5.00 = 1/0.39 × 5
= 12.82 pounds
Thus, The amount of cabbage 12.82 pounds will be to buy for $5.00.
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Solve the system of two linear equations by the method of elimination (also called addition method). For a dependent system, give the answer in the form of an ordered pair in terms of x. (If there is no solution, enter NO SOLUTION.) x - y = -15 -3x + 3y = 45 (x, y) =?
x - y = -15 -3x + 3y = 45 (x, y) = the system of two linear equations using the method of elimination ( 5, 45).
x - y = -15
-3x + 3y = 45
written as
3x - 3y = -15
+3x + 3y = 45
6x = 30
x = 5
Substitute x = 5 into either of the linear equations to find y.
x - y = -15
5 - y = -15
y = 45
Therefore, the solution is (5, 45).
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In a recent year, companies spent a total of $87.5 billion on newspaper, television, and radio ads. The total amount spent on television and
radio ads was only $2.9 billion more than the amount spent on newspaper ads alone. The amount spent on newspaper ads was $5.4 billion
more than what was spent on television ads. How much was spent on each form of advertising? (Hint: Let the variables represent numbers of
billions of dollars.)
How much was spent on newspaper ads? $
How much was spent on television ads? $
How much was spent on radio ads? $ billion
billion
billion
Answer:
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billionStep-by-step explanation:
You want the amount spent on ads in each medium given the total and relations between amounts spent for newspaper, television, and radio ads.
SetupLet n, t, r represent the amounts spent on ads in newspapers, television, and radio, respectively. The given relations tell you ....
n +t +r = 87.5
-n +t +r = 2.9
n -t = 5.4
SolutionThe augmented coefficient matrix can be reduced to row-echelon form using a suitable calculator or spreadsheet. This tells you the amounts spent in each medium. The attachment shows this.
newspaper ads: $42.3 billiontelevision ads: $36.9 billionradio ads: $8.3 billion__
Additional comment
The value of n can be found by subtracting the second equation from the first. That can be used in the third equation to find t, and both of those values can be used in either of the first two equations to find r.
Which system of linear inequalities has the point (3, -2) in its solution set?
y < -3; y ≤ 2/3x - 4
y > -3; y ≥ 2/3x - 4
y < -3; y ≥ 2/3x - 4
y > -2; y ≤ 2/3x - 4
The system that has linear inequalities has the point (3, -2) in its solution set is y > -3; y ≥ 2/3x - 4.
We know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)
In option B, we have
y > -3 ----> inequality A
y ≥ 2/3x - 4 ----> inequality B
In both inequality, change the values of x and y at the point (3, -2) and then compare the outcomes.
Inequality A
y > -3 ----> is true
Inequality B
y ≥ 2/3x - 4 ----> is true
Therefore
The ordered pair is a solution of the system B
As a result, the point (3, -2) in the solution set of the system with linear inequalities is y > -3; y 2/3x - 4.
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Write the following expression using the fewest possible terms.
(−3x − 12) + (16 + 8x)
5x + 4
5x + (−4)
11x + 28
11x + (−4)
Therefore option a) 5x+4 is the simplified form of the equation.
What is equation?Equations in mathematics are logical statements with two algebraic expressions on either side of the equals (=) symbol. The equality of the expressions on the left and right in relation to one another is shown. LHS = RHS (left hand side = right hand side) is the first step in any mathematical equation. You can solve equations to determine a variable's or quantity's value. It is not an equation if the statement lacks the "equal to" sign. It will be thought of as a phrase. Later on in this essay, there will be an explanation of the distinctions between an expression and an equation.
Here,
Given:
=>(−3x − 12) + (16 + 8x)
=> -3x-12+16+8x
=> 5x+4
So 5x+4 is the simplified form of the equation
Therefore option a) 5x+4 is the simplified form of the equation
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What is the probability of getting a queen if a card is drawn out from a pack of 52 cards?; What is the probability of getting a 9 from a deck of 52 cards?; Which explains the most likely reason for the discrepancy between Josh's predicted and actual results?; What is the probability of getting 8 from the of card?
The probability of getting a queen if a card is drawn out from a pack of 52 cards is 1/13
Probability is the chance of an event to occur with respect to the given conditions.
Probability of an event P(E) = number of favorable outcomes (n)/total number of outcomes(N)
P(E) = n/N
Total cards in a pack (N) = 52
Number of queens (n) = 4
P(getting a queen from pack of cards) = Number of queens/Total cards in a pack
P(E) = n/N
P(E) = 4/52
P(E) = 1/13
Hence, the probability of the given event is 1/13.
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What is ASA congruence rule Class 7?
The ASA (angle-side-angle) congruence rule states that two triangles are congruent if two angles and the side between them are equal in both triangles.
What is ASA congruence rule Class 7?The ASA congruence rule is a fundamental rule of geometry that states that two triangles are congruent when two angles and the side between them are equal in both triangles. This rule is especially important when solving geometry problems, as it can help determine the size and shape of a triangle.
The ASA congruence rule is applicable to all triangles, regardless of their size or shape, and can be used to find the missing angles or sides of a triangle. By applying the ASA congruence rule, students can gain a better understanding of the properties of triangles and other geometric shapes.
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If g(t) varies inversely with t and g(t)=9 when t=4. Find the value of g(t) when t=2
The value of g(t) is 18 when x is 2.
What is proportionality?Proportionality is defined as, the fact or quality of being in proper balance or relation as to size or quantity, degree, severity, etc
Given that, g(t) varies inversely with t and g(t)=9 when t=4.
According to question,
g(t) ∝ 1/t
Let k be constant of proportionality, then,
g(t) = k/t
Solving for k, we get,
9 = k/4
k = 36
When, t = 2, then
g(t) = 36/2
g(t) = 18
Hence, The value of g(t) is 18 when x is 2.
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A 224-inch pipe is cut into two pieces. One piece is three times the length of the other. Find the length of the shorter piece.
The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.
Given that,
Cut into two halves is a 224-inch pipe. The length of one component is three times that of the other.
We have to determine the shorter piece's length.
We know that,
Let's use the variable L to represent the longer pipe and the variable S to represent the shorter pipe.
Since the pipe will be the sum of L and S, we can create the following equation:
L+S=224
The longer piece is three times the shorter piece, which is another thing we know.
L=3S
Substituting the second equation for the first equation
L+S=224
3S+S=224
4S=224
S=224/4
S=56
The shorter piece is 56 inches.
The lengthier component should be used to replace the following:
L=3S
L=3(56)
L=168
The longer piece is 180 inches.
Therefore, The shorter piece is 56 inches and the longer piece is 180 inches when cut into two halves is a 224-inch pipe.
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19 ÷ 359 with remainder
Answer: 18 with a remainder of 17
Step-by-step explanation:
which expression can be used to find 20 percent of 92?; which expression gives the best estimate of 45 percent of 76?; what is 50 percent of 62? 0.31 3.1 31 310; what is 60 percent of 92?; which expression can be used to find 12 percent of $98?; which expression can be used to find 38 percent of 22?; which correctly explains how to estimate 55 percent of 64?; 20% of 190
The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.
Given that,
Finding the expression that can be utilised to find
20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98.
What is percentage?From the Latin word "per centum," which means "by the hundred," the word "percentage" was borrowed. The denominator of percents is 100, making them fractions. In other words, it is the relationship between a part and a whole in which the value of the whole is consistently set to 100.
Take
20% of 92
Multiply 20%×92
=18.4
45% of 76
Multiply 45% ×76
=34.2
50% of 62
Multiply 50%×62
=31
60% of 92
Multiply 60%×92
=55.2
12% of 98
Multiply 12%×98
=11.76
Therefore,
The solved expression we get for 20% of 92, 45% of 76, 50% of 62, 60% of 92 and 12% of 98 is the numbers 18.4, 34.2,31,55.2 and 11.76.
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cost per pound ($) ingredient beginning ending quantity (pounds) per 100 pounds of product a 2.50 3.95 25 b 8.75 9.90 15 c 0.99 0.95 50
The relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
In the given question we have to compute the price relatives for the three ingredients A, B and C.
Now finding the relative price using the formula.
Relative Price(RP) = Ending Cost(E)/Beginning Cost(B) *100
Now from the given table;
Ingredient Beginning(B) Ending(E) E/B E/B*100
A 2.50 3.95 1.58 158
B 8.75 9.90 1.131 131.1
C 0.99 0.95 0.96 96
Hence, the relative price of ingredient A is 158, ingredient B is 131.1 and ingredient C is 96.
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The right question is
A chemical company produces a special industrial chemical that is a blend of three chemical ingredients. The beginning-year cost per pound, the ending-year cost per pound, and the blend proportions follow. (Round your answers to the nearest integer.)
Cost per Pound ($)
Ingredient Beginning Ending Quantity (pounds) per 100
Pounds of Product
A 2.50 3.95 25
B 8.75 9.90 15
C 0.99 0.95 70
Compute the price relatives for the three ingredients.
Item Price Relative
A
B
C
You have been given the task of organizing a poll regarding an upcoming election. The object is to estimate the proportion of the country that will vote to keep the current government in power. You have been told to collect a sample and find a 95% confidence interval for the proportion. This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74. a) Calculate the minimum sample size that is required in this survey. Give your answer as a whole number. Someone working on your team reports that the information suggesting that the proportion of people that will vote to keep the current government is equal to 0.74 is out of date. In fact, some recent events in politics mean that there is no safe guess at what the proportion might be. b) Based on this new information, calculate the minimum sample size that is required in this survey. Give your answer as a whole number.
The confidence interval for the task of organizing the poll for the upcoming elections be,
(222.117 , 257.883)
Given, You have been given the task of organizing a poll regarding an upcoming election.
The object is to estimate the proportion of the country that will vote to keep the current government in power.
You have been told to collect a sample and find a 95% confidence interval for the proportion.
This interval is allowed to have a margin of error of 3%. A preliminary investigation suggests that the proportion of people that will vote to keep the current government is 0.74.
We have to find the confidence interval,
Subtract 1 from your sample size. 10 – 1 = 9.
Subtract the confidence level from 1, then divide by two.
(1 – .95) / 2 = .025
For 9 degrees of freedom df and α = 0.025, margin of error is 2.262.
Divide your sample standard deviation by the square root of your sample size.
25 / √(10) = 7.90569415
Now, Multiply 2.262 × 7.90569415 = 17.8826802
For the lower end of the range
240 – 17.8826802 = 222.117
For the upper end of the range
240 + 17.8826802 = 257.883
Hence, the confidence interval be (222.117 , 257.883)
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Suppose a math class contains 40 students, 23 females (five of whom speak French) and 17 males (six of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is male.
6/11 is the probability that a randomly selected student speaks French, given that the student is male
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
There are 11 members who speak french and 5 are females in 11 members
5/11
p(a given b) = p(a and b) / p(b).
6 of the people in the group are men that speak french, then the probability of (a and b) becomes 6/40
probability that a person speaks french is 11/40
p(a given b)=6/40/11/40
=6/40×40/11=6/11
Hence, 6/11 is the probability that a randomly selected student speaks French, given that the student is male.
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