Answer:
He lost $5.
Step-by-step explanation:
When the customer gives him the $20, the salesman does not gain any money because it is fake.
Then, he gets real money summing up to $20. So he gains that, but then gives $5 away. Now he has $15.
Then, the lady tells him the $20 bill is fake, so he must give the lady $20. So, 15 - 20 = -5. He lost $5.
Answer: He lost $35. $15 for the pair of shoes and $20 for having to repay the joined store for the counterfit money.
Step-by-step explanation:
Nancy shot a 24 on 4 holes of golf. At this rate, what can she expect her score to be if she plays all 18 holes?
Answer:
108
Step-by-step explanation:
"At this rate, ..." means we're to assume Nancy's score is proportional to the number of holes:
score/18 = 24/4
Multiplying by 18, we get ...
score = 18(24/4) = 18(6) = 108
Nancy can expect a score of 108 on 18 holes.
The range of the secant function is?
Answer:
1. Where are the vertical asymptotes on the graph of the secant function?
choice A: x = π /2 + nπ
2. The range of the secant function is
answer: y ≤ -1 or y ≥ 1
3. What is the period of the secant function?
Choice C : 2π
Step-by-step explanation:
there are 3 questions on this page.
correct on edge
The range of secant is y ≤ -1 or y ≥ 1.
What is a range in the function?The range of a function is the set of its possible output values.
As we know the vertical asymptotes of the secant function
x = π /2 + nπ
and, The range of the secant function is
y ≤ -1 or y ≥ 1
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A company issues 7% bonds with a par value of $200,000 at par on January 1. The market rate on the date of issuance was 6%. The bonds pay interest semiannually on January 1 and July 1. The cash paid on July 1 to the bond holder(s) is:
Answer:
The cash paid to the bondholder on July 1 is Z = $7000
Step-by-step explanation:
From the question we are told that
The percentage bond issued by the company is [tex]n = 7[/tex]%
The par value of the bond is [tex]V =[/tex]$200,000
The market rate is [tex]r = 6[/tex]%
So we are told that the bonds pay interest semiannually on January 1 and July
So the cash paid to the bondholder on July 1 is mathematically evaluated as
Z = [tex]V * \frac{7}{100} * \frac{1}{2}[/tex]
substituting value
Z = [tex]200000 * \frac{7}{100} * \frac{1}{2}[/tex]
Z = $7000
Final answer:
The cash paid on July 1 to bondholders for the company's 7% bonds with a par value of $200,000 is $7,000. This is calculated by first determining the annual interest payment and then dividing by two for the semiannual payment.
Explanation:
Understanding Bond Interest Payments
The question revolves around how much cash is paid to bondholders on July 1 for a company that issued 7% bonds with a par value of $200,000 at par when the market rate was 6%. Since the bonds were issued at par, this implies that the bond's stated interest rate matches the market interest rate at the time of issuance. However, the market rate later does not affect the fixed payments of a bond issued at par.
The interest payment for this bond would be calculated using the face value and the stated annual interest rate, which is then divided by two since interest is paid semiannually. The calculation is as follows:
Calculate the annual interest payment: $200,000 (par value) × 7% (interest rate) = $14,000.Divide the annual interest by two for the semiannual payment: $14,000 ÷ 2 = $7,000.Therefore, the cash paid on July 1 to the bond holder(s) is $7,000.
Translate the sentence into an inequality.
Six subtracted from c is at least 20.
Answer:
6 - c </= 20
Step-by-step explanation:
What are the me and you
What are the x- and y-coordinates of point E, which partitions
the directed line segment from A to B into a ratio of 1:2?
x = ( min )(x2 – x1) + x1
v = l m on Jiva – vi] + vi
(0, 1)
0 (-1,3)
* (-2,5)
(1,0)
Complete question:
What are the x- and y- coordinates of point E, which partitions the directed line segment from [tex]A\:(- 4,\:9) \:to\: B\:(2,\:- 3)[/tex] into a ratio of 1 : 2.
Answer:
(C) (-2,5)
Step-by-step explanation:
[tex]x = (\dfrac{m}{m+n}) (x_2-x_1) + x_1\\\\y = (\dfrac{m}{m+n}) (y_2-y_1) + y_1[/tex]
[tex](x_1,y_1)=(- 4,\:9),(x_2,y_2)=B\:(2,\:- 3)[/tex]
m=1, n=2
[tex]x = \left(\dfrac{1}{1+2}\right) (2-(-4)) + (-4)\\=\left(\dfrac{1}{3}\right) (2+4)-4\\=\left(\dfrac{6}{3}\right)-4=2-4\\x=-2[/tex]
[tex]y = \left(\dfrac{1}{1+2}\right) (-3-9) + 9\\=\left(\dfrac{1}{3}\right) (-12)+9\\=\left(-\dfrac{12}{3}\right)+9=-4+9\\y=5[/tex]
The x- and y-coordinates of the point E is (-2,5)
A major building contractor has 10 new floor plans that she would like to start using in the homes she builds. She wants to know whether her homes will sell for a higher price in the city or the suburbs. She builds two homes—one in the city and one in the suburbs—for each of the 10 floor plans. She uses the same real estate agency to sell all 20 homes and then she calculates the difference in selling price (city – suburb) for each of the floor plans. What is the most appropriate test to analyze her data? a. Two Proportion Z Test b. One Sample T Test c. One Proportion Z Test d. Independent Samples T Test e. Paired T Test
Answer: d. Independent Samples T Test
Step-by-step explanation: Independent Samples T Test is commonly used when you want to compare the means of two independent groups and determine if there is evidence that the the associated means are significantly different.
For this test, the data must have: continuous dependent variable; independent variable is categorical (two or more groups); cases that have values on both variables; the obervations are independent, i.e. the groups don't interfere on each other; random sample of data for the population; normal distribution of the dependent variable for each group; homogeneity of variances and no outliers.
Each groups should have at least 6 subjects and have the same number of individuals in each group.
The hypothesis in this test can be expressed as:
H₀: μ1 = μ2 or μ1 - μ2 = 0
H₁: μ1 ≠ μ2 or μ1 - μ2 ≠ 0
Will give brainliest please explain how
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = [tex]2^{\frac{5}{2} }[/tex] = [tex]2^{x}[/tex]
x = 5/2
Answer:
x = 5/4
Step-by-step explanation:
√2+√2+√2+√2 = 2^x
4√2 = 2^x
4√2 = =
x = 5/2
x/-4=-16. Solve for x.
Answer:
64
Step-by-step explanation:
16 *4 is 64 so 64 divide by -4 equals -16.
Hope this helps.
Answer: 64
Step-by-step explanation: Since x is being divided by -4, to solve for x, multiply both sides of the equation by -4.
On the left side, the -4's will cancel
and on the right side, -16(-4) is 64.
So x = 64.
Please do not try to do this problem in your head.
Show the work that it takes to get x by itself.
g a. What is a residual? b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? a. What is a residual? A. A residual is a value that is determined exactly, without any error. B. A residual is the amount that one variable changes when the other variable changes by exactly one unit. C. A residual is a value of yminusModifyingAbove y with caret, which is the difference between an observed value of y and a predicted value of y. D. A residual is a point that has a strong effect on the regression equation. b. In what sense is the regression line the straight line that "best" fits the points in a scatterplot? The regression line has the property that the ▼ sum of squares sum of the residuals is the ▼ lowest highest possible sum.
Answer:
for the first question we have the "c” as the correct option
residual is a value of y -y^ which is the difference between an observed value of y and predicted value of y
The residual is a value of y -y ^ which is the difference between an observed value of y and predicted value of y, so answer A is false in The residual mo has errors, option B is false because it is not defined as the quantity that changes a variable and it is false that the residual is a point that has a strong effect on the regression
for question two the correct answer is:
the best fitting straight regression line at the scatter plot points is
b) sum of squares and lowest
The residual is the value obtained by subtracting the actual and the predicted value. Therefore, the residual of a linear model can be defined thus ;
Y_actual - Y_predictedThe line if best fit, defines the line which best fits or models a data. It is the line in the the sum of the square is lowest as it tries to minimize the sum of squared error.
Therefore, the correct options are C and (sum of square ; lowest)
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What algebraic expression must be subtracted from the sum of Y squared plus 5Y -1 and 3Y squared minus 2Y +4 to give you 2Y squared plus 7Y -2
Answer:
The required expression is:
2Y² - 4Y + 5
Step-by-step explanation:
Given the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
= 4Y² + 3Y + 3
Subtracting (2Y² - 4Y + 5), we have
2Y² + 7Y - 2
Therefore, the expression:
2Y² - 4Y + 5
must be subtracted from the expression:
(Y² + 5Y - 1) + (3Y² - 2Y + 4)
to give the expression:
2Y² + 7Y - 2
1+2x-3x-4 I need it please
Answer:
Simplified as -3 - x
Step-by-step explanation:
I know, you want to simplify this answer.
So.
1 + 2x - 3x - 4 = 1 - x - 4 = -3 - x
382
Which equation represents a circle with a center at (-3, -5) and a radius of 6 units?
(x-3)2 + (y – 5)2 = 6
(x - 3)2 + (x - 5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
Answer:
(x+3)^2 + (y+5)^2 = 36
Step-by-step explanation:
We can write the equation of a circle as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
(x--3)^2 + (y--5)^2 = 6^2
(x+3)^2 + (y+5)^2 = 36
What is the domain of the function Y equals cube root x
Final answer:
The domain of the function y = x^(1/3) (cube root of x) is all real numbers, which is expressed as (-∞, +∞).
Explanation:
The domain of a function describes all the possible values of 'x' for which the function is defined. In the case of the function y = cubic root of x, which is written as y = x^(1/3), the function is defined for all real numbers because you can take the cubic root of any real number, negative, positive, or zero. Hence, the domain of the function y = x^(1/3) is all real numbers, which mathematically is expressed as (-∞, +∞). This is different from the function y = x^2, where the domain must often be restricted to nonnegative numbers to have a well-defined real inverse function.
10 percent of what number is 350
Answer:
3500
Step-by-step explanation:
multiply 10*350
In this exercise, we consider finding the first five coefficients in the series solution of the first-order linear initial value problem (x²+2)y′′ − 6y = 0 subject to the initial condition y(0) = 1, y′(0) = 2. Since the equation has an ordinary point at x=0 and it has a power series solution in the form y = Lim(n=0→[infinity])Σ cₙxⁿ.(1) Insert the formal power series into the differential equation and derive the recurrence relation: cn= __________cₙ₋₂ for n=2,3,⋯ The solution to this initial value problem can be written in the form y(x)= c₀y₁(x)+c₁y₂(x) where c₀ and c₁ are determined from the initial conditions. The function y₁(x) is an even function and y₂(x) is an odd function. For this example, from the initial conditions, we have c₀ = ______ and c₁ = ______. The function y₁(x) is an infinite series y₁(x) = 1+ Lim(n=1→[infinity])Σ aₙx²ⁿNote that the constant c₀ has been factored out. (2) Use the recurrence relation to find the first few coefficients of the infinite series: a₂ = _______, a₄ = _______, a₆ = _______, a₈ = _______.Note that the constant c₀ has been factored out. Finally the polynomial y₂(x)= _______NOTE: The function y₂(x) is an odd degree polynomial with first term x. In other words, note that the constant c₁ has been factored out.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached images for the step by step explanation for the answer to the question
What is better, X-Box or Playstation?! Im thinking about buying one of them. Plz help me decide. !WILL MARK BRAINLIEST!
Answer:
playstation
Step-by-step explanation:
literally everybody owns one lol
Answer:
well i have both
Step-by-step explanation:
heres some pros and cons
PS4 or Xbox One: which one will you choose?
Both Microsoft and Sony's current generation of gaming consoles inspire fierce loyalty from their respective camps. This means, if you're not already Team PlayStation or Team Xbox, it can be difficult to make a decision between the two.
To help you make the impossible choice between Microsoft and Sony's current offerings, we've made a comprehensive list of all the key differences – as well as the similarities – to keep in mind when buying an Xbox One or PS4.
There's certainly no doubt that the PlayStation 4 has taken the lead in sales, but both have their pros and cons – and the mid-gen refresh has certainly given us a lot more to think about when weighing those up.
UPOOD
The area of a square is given by s2 and the perimeter is given by 4s, where s is the side length of the square,
If the side length of a square is 4 inches, its area is
16.6 square inches and its perimeter is
074 Inches.
Reset
Next
Answer:
If the side length of a square is 4 inches, it's Area is 16 inches, and Perimeter is 16 inches.
Step-by-step explanation:
Given that the Area = s²
Perimeter = 4s
Side length of the square = s
If the length of a square is 4 inches, then applying the above formulas, we have
s = 4 inches
Area = 4² = 16 inches
Perimeter = 4s = 4×4 = 16 inches
Final answer:
The area of a square with a side length of 4 inches is 16 square inches and its perimeter is 16 inches. Doubling the side length to 8 inches yields an area that is four times greater, 64 square inches, due to the squared relationship between side length and area.
Explanation:
Understanding Square Area and Perimeter
A student has posed a question about the properties of squares. We are given that the side length of a square is 4 inches. From this, we can calculate the square's area and perimeter. The area of a square is found by squaring the length of its side (s2), which in this case would be 4 inches × 4 inches = 16 square inches. The perimeter is the length around the square, calculated by multiplying the side's length by 4, yielding 4 inches × 4 = 16 inches.
By understanding the formulas for area (s2) and perimeter (4s), students can solve many geometrical problems related to squares. For instance, if the dimensions of a square are to be doubled, the new side length would be 4 inches × 2 = 8 inches, resulting in an area of 8 inches × 8 inches = 64 square inches, which is four times the original area, demonstrating that the area scales with the square of the linear dimensions.
Solve: tan(x)-cos^2(x)=sin^2(x)
Answer:
x = 45 degrees +180 n where n is an integer
Step-by-step explanation:
tan(x)-cos^2(x)=sin^2(x)
Add cos^2(x) to each side
tan(x)-cos^2(x)+ cos^2(x)=sin^2(x)+ cos^2(x)
tan(x)=sin^2(x)+ cos^2(x)
We know that sin^2(x)+ cos^2(x) = 1
tan (x) =1
Take the inverse tan of each side
tan ^-1 ( tan x) = tan ^-1 (1)
x = 45 degrees +180 n where n is an integer
Answer:
Pi/4+kpi
Step-by-step explanation:
X= 45 degrees and on unit circle that is pi/4
Europeans have been more skeptical than Americans about the use of genetic engineering to improve foods. A sample survey gathered responses from random samples of 824 Americans and 12268 Europeans. (The European sample was larger because Europe is divided into many nations.) Subjects were asked to consider the following issue: Using modern biotechnology in the production of foods, for example to make them higher in protein, keep longer, or change in taste. They were asked if they considered this "risky for society." In all, 432 of Americans and 7629 of Europeans thought the application was risky.
Give a 98% confidence interval for the percent difference (±0.1) between Europe (call them group 1) and the United States:
Answer:
The 98% confidence interval = (-0.14, -0.056)
Explanations:
From the calculations done in the file attached to this solution
Proportions of Americans that considered the application risky = 0.524
Proportions of Americans that did not considerthe application risky = 0.476
Proportions of Europeans that considered the application risky = 0.622
Proportions of Europeans that did not consider the application risky = 0.377
Standard error of the sample proportion using the formula written in the attached file = 0.018
The 98% confidence interval is also calculated as in the attached file and gotten as (-0.14, -0.056)
Rachel bought two coloring books.
One had 134 pictures and the other
had 309. After one week she had
already colored 145 of the pictures,
How many pictures does she still have
to color?
Answer:
298 pictures
Step-by-step explanation:
One coloring book has 134 pictures, and other one has 309 pictures. The total will be addition:
134 + 309 = 443 pictures
Rachel colored 145 of them all, so subtract 145 from 443:
443 - 145 = 298
She still has 298 pictures left.
Answer:
298
Step-by-step explanation:
Total pictures:
134 + 309
443
Already coloured: 145
To be coloured: 443 - 145
= 298
You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 99% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $ 12 comma 260 with a standard deviation of $ 800. Suppose that the interval is calculated to be (11693 comma 12827 ). How could the sample size and the confidence coefficient be altered in order to guarantee a decrease in the width of the interval?
Answer:
If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:
[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The width of the confidence interval is just defined as two times the margin of error:
[tex] Width = 2ME[/tex]
And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%
By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.
Step-by-step explanation:
For this case w ehave the following info given from the problem
[tex] n =17[/tex] represent the sample size for the cars selected
[tex]\bar X = 12260[/tex] represent the average price for the cars sold
[tex] s= 800[/tex] represent the standard deviation for the solds
And we have a 99% confidence interval for the true average price for the cars given:
[tex]11693 \leq \mu \leq 12827[/tex]
And we know that the confidence interval for the true mean is given by this formula:
[tex] \bar X \pm t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
If we want to guarantee a decrease in the width of the confidence interval we need to analyze the margin of error given by:
[tex] ME = t_{\alpha/2} \frac{s}{\sqrt{n}}[/tex]
The width of the confidence interval is just defined as two times the margin of error:
[tex] Width = 2ME[/tex]
And then we can decrease this width of the interval we need to increase the sample size in order to have a greater number in the denominator for the margin of error and that implies a reduction in this width for the confidence interval at the confidence level fixed of 99%.
By the other hand if we increase the confidence level then the width would be larger and in the other case when we decrease the confidence level the width would be lower.
Your Cabaret nightspot "Jazz on Jupiter" has become an expensive proposition: You are paying monthly costs of $70,000 just to keep the place running. On top of that, your regular cabaret artist is charging you $2900 per performance, and your jazz ensemble is charging $800 per hour. Set up a (monthly) cost function for the scenario. (Let C represent the monthly cost in dollars, x represent the number of performances by the cabaret artist per month and y represent the number of hours of jazz per month.) C(x, y)
Answer:
The monthly cost function for the scenario C(x,y) is;
C(x,y) = 70,000 + 2900x + 800y
Step-by-step explanation:
Let C represent the monthly cost in dollars.
x represent the number of performances by the cabaret artist per month
and y represent the number of hours of jazz per month
Given;
monthly costs of $70,000
regular cabaret artist is charging you $2900 per performance.
Per month = $2900x
your jazz ensemble is charging $800 per hour.
Per month = $800y
The monthly cost function for the scenario C(x,y) is the sum of all the costs;
C(x,y) = 70,000 + 2900x + 800y
(1) Saad had a box that is 15cm by 20cm by 22cm. What is the volume of the box?
(2) jake is redoing her kitchen. It measures 18ft by 19 ft. If wallpaper costs $1.29 per foot, how much will it cost her to wallpaper the kitchen?
Answer:
Question1:volume=6600cm^3
Question2:cost=$441.18
Step-by-step explanation:
Question 1:
volume=length x width x height
Volume=15 x 20 x 22
Volume=6600cm^3
Question 2:
area of kitchen=length x width
Area of kitchen=18 x 19
Area of kitchen=342ft^2
$1.29 for 1ft^2
$b for 342ft^2
$b=342 x1.29
$b=$441.18
Which statement(s) could describe the graph of a nonproportional relationship? Select all that apply
Answer:
A. The positive y-intercept.
D. The y-intercept is negative.
Step-by-step explanation:
The proportional relationship is defined by the graph passing through the origin i.e. the y-intercept is equal to zero.
The equation of y proportional to x relationship is y = kx, which again denotes that the graph passes through the origin (0,0).
Now, the statements that can describe the graph of a non-proportional relationship are
A. The positive y-intercept.
D. The y-intercept is negative. (Answer)
The statements that could describe the graph of a nonproportional relationship include:
A. The positive y-intercept.D. The y-intercept is negative.It should be noted that the proportional relationship is defined by the graph passing through the origin. The equation of y proportional to x relationship is y = kx.
From the information given, the relationship shows that the positive y-intercept and the y-intercept is negative.
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the height of the two triangular faces is 5.2 centimeters. the surface area of the triangular prism is ____ square centimeters.
The surface area of the triangular prism is 171.2 square centimeters.
From the given triangular prism,
Area of base (rectangle) = Length×Breadth
= 8×6=48 square centimeter
So, area of 3 congruent rectangles = 3×48
= 144 square centimeter
Here, area of a triangle = 1/2 × Base × Height
= 1/2 ×6×5.2
= 15.6 square centimeter
So, area of 2 congruent triangles= 2×15.6
= 31.2 square centimeter
Total surface area = 144+31.2
= 171.2 square centimeter
Therefore, the surface area of the triangular prism is 171.2 square centimeters.
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What is the relationship between 1 and 2
Answer:
they are a complimentary couple since both offer examples of their own qualities. Both types are highly dutiful and are attracted to each other
Step-by-step explanation:
hope this helps
~berrian
Final answer:
The relationship between 1 and 2 in mathematics can refer to causality, ratios, probability, physical properties in physics, or reciprocal relationships, depending on the context.
Explanation:
The relationship between 1 and 2 can refer to various mathematical concepts, depending on the context in which these numbers are being used. Here are a few examples:
Causality: In a simple model with objects A and B, an arrow from A to B implies that A is the cause and B is the effect. It's a directional relationship.
Ratio: When we say the ratio between two quantities is 1:2, it implies for every unit of the first quantity, there are two units of the second quantity. In this case, RP1 to Rp2 is 1:2.
Probability: In the context of dice, if the first value is 2, the ratio could describe the possible outcomes when rolling two dice.
Physical properties: Mathematical relationships can be determined for variable pairs in physics such as Pressure (P) versus number of moles (n), or volume (V) versus temperature (T).
Reciprocity: In some mathematical expressions, swapping the subscripts '1' and '2' does not change the relationship, indicating a reciprocal or bidirectional relationship between the two.
Understanding these relationships requires recognizing the context and the mathematical principles that govern them.
What percent is 7 out of 40?
Answer:
17.5%
Step-by-step explanation:
Convert fraction (ratio) 7 / 40 Answer: 17.5%
Answer:
17.5
Step-by-step explanation:
7/40 = 17.5
Hope this helps! Please mark brainliest :)
Which expression is the result of
10x2 + 50x = ?
Step-by-step explanation:
10x2 + 50x
10x ( x +5)
Is the result
If f[6} = x ^ -2x , find: f [6} =
Answer:
1/ 6^12
Step-by-step explanation:
f[x} = x ^ (-2x)
f(6) = 6 ^ (-2*6)
= 6 ^ -12
We know the negative exponent moves it to the denominator
= 1/ 6^12
A study in 2010 reported that 3 in 4 adults in a relationship met their significant other using an online dating site. Recently a popular magazine 'People' claimed that that number has changed. To test this claim a telephone survey of 600 randomly selected adults in a relationship was completed. Of the 600 adults, 480 said that they met their significant other using an online dating site. Does this provide evidence that the proportion has changed? Use α = 0.05, to test the magazine's claim. Conditions: 1. The sample is 2. n p 0 ( 1 − p 0 ) 10 3. n 0.05 N Hypotheses: H 0 : p 0.75 H 1 : p 0.75 Test Statistic: The test statistic is a test statistic. The value of the test statistic is . p-value: The value of the p-value is . Decision: Because the p-value is than α = 0.05, we the null hypothesis. Conclusion: The data the claim that the proportion has changed
Answer:
Step-by-step explanation:
From the given information,
The required correct answers are,
1. The sample is:
b) simple random sample
2. np0 (1-p0) ___ 10
a) greater than or equal to
3. n ___ 0.05N
b) less than or equal to
Hypotheses:
4. H0:p___0.75
d) =
5. H1:p___0.75
a) ≠
6. The test statistic is a
a) z test statistic
7. test statistic=2.8284
8. p-value=0.0047
Decision:
Because p-value less than Alpha=0.05, we reject null hypothesis.
Conclusion:
The data support the claim that the proportion has changed.
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
p = 3/4 = 0.75
For the alternative hypothesis,
p ≠ 0.75
Considering the population proportion, probability of success, p = 0.75
q = probability of failure = 1 - p
q = 1 - 0.75 = 0.25
Considering the sample,
Sample proportion, P = x/n
Where
x = number of success = 480
n = number of samples = 600
P = 480/600 = 0.8
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.8 - 0.75)/√(0.75 × 0.25)/480 = 2.53
Recall, population proportion, P = 0.75
The difference between sample proportion and population proportion(P - p) is 0.8 - 0.75 = 0.05
Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.75 - 0.05 = 0.7
the p for the right tail is 0.75 + 0.05 = 0.8
These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area
From the normal distribution table, the area above the test z score in the right tail 1 - 0.9943 = 0.0057
We would double this area to include the area in the left tail of z = - 2.53. Thus
p = 0.0057 × 2 = 0.0114
Because alpha, 0.05 > than the p value, 0.0114, then we would reject the null hypothesis.
Therefore, at 5% significance level, this data provide evidence that the proportion has changed.