the following information will be used for parts 1 and 2 of this assignment. in 1978 congress established a gas guzzler tax to discourage the production and purchase of fuel-inefficient vehicles. every vehicle currently produced is labeled as a guzzler if its fuel efficiency in mpg is below a certain amount. trucks, suvs and minivans were uncommon in 1978 so are exempt from the tax. if interested, read more: https://www.epa.gov/fueleconomy/gas-guzzler-tax each vehicle in the data set epafe2021data.csv has a projected annual fuel cost that estimates how much the vehicle will cost over a year in fuel. for example, the volkswagen passat has an estimated annual fuel cost of $1450. use the epafe2021data.csv dataset and the comparingtwomeans da6.r script to compare the average annual fuel cost in dollars between guzzlers and non-guzzlers from 2021 vehicles. part 1. (6 points) exploring the data. a. (2 points) visualize the data with a side by side boxplot. i. (1 point) paste the side-by-side box plot of the data. ii. (1 point) add a title and axis labels. iii. optional to change the color of the plot. b. (2 points) describe the distribution in context. is there visual evidence the average annual fuel cost is different between the guzzler and non-guzzler vehicles? explain. c. (2 points) provide an organized table of the summary statistics. include the sample means, standard deviations and sample sizes for each group. round to nearest whole number. mean standard deviation sample size guzzler non-guzzler
Answers
This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
A) 1: proportion of gas-guzzlers manufactured by American firms.
p2: proportion of gas-guzzlers manufactured by international firms.
In this way, the boundary of interest is p1 - p2.
B) H_0: p_1-p_2=0
H_1: p_1-p_2\neq0
C) The following requirements must be satisfied: n (1 p) 10 and np 10.
American Guzzlers do not meet this requirement because np = 7.
D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)
E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.
F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269
g. H0 should be rejected because the p-value is less than the 0.05 significance level.
There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.
Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
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Related Questions
Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 per job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this. 30 + 15 x greater-than-or-equal-to 90 which best describes the restrictions on the jobs deepak will accept?.
Answers
Deepak will work for at-least 4 hours in each job
Linear Inequality in one variable:
A linear inequality in one variable that can be written either in the form of,
a+bx<0
a+bx≤0
a+bx>0
a+bx≥0
where,
where a and b are real numbers and a≠0 a ≠ 0
For the given question,
Deepak charges $30 for each job he does plus an additional $15 for each hour he works.
He only accepts jobs if he will earn at least $90 per job.
If,
x is number of hours Deepak works in each job then,
required inequality can be written as,
30 + 15x [tex]\geq[/tex] 90
15x ≥ 90 - 30
15x ≥ 60
x ≥ 60/15
x ≥ 4
thus,
we conclude that Deepak will work for at-least 4 hours in each job.
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this was due last week pls help me
Answers
Answer:
X=-2
Step-by-step explanation:
5+0.1x=3(1-0.3x)
5+0.1x=3-0.9x
+0.9x +0.9x
5+x=3
-5. -5
x=-2
Hopes this helps
Answer:
the answer is B
Step-by-step explanation:
5+0.1x=3(1-0.3x)=}
5+0.1x=3-0.9x=}
0.1x+0.9x=3-5=}
x= - 2
A server at a restaurant is hoping for a 15% tip from a large party. The
party's bill at the end of the night was $312.00. Write a proportion and
describe how you would solve it to calculate the amount of the tip the
server hopes to receive. Be sure to state your final answer as an amount of
money, rounded to the nearest cent.
*Use the "/" on your keyboard as a fraction bar for ratios when writing the
proportion. For example: I can show that one-half and two-fourths are
proportional by typing "1/2 = 2/4" for the proportion.
Answers
$57 is the amount of the tip the server hopes to receive.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
A server at a restaurant is hoping for a 15% tip from a large party.
The party's bill at the end of the night was $312.00.
Now we need to find 15% of $312
15% is converted to decimal by dividing with 100
15/100=0.15
Now multiply 0.15 with 380
0.15×380
57
Hence $57 is the amount of the tip the server hopes to receive.
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suppose that the ages of medical residents are normally distributed with a mean of 27 years and standard deviation 2 years. what percent of medical residents are less than 28 years old?
Answers
The percent of medical residents less than 28 years old is 69.15%.
For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.
First, solve for the z-score using the formula below.
z-score = (x – μ) / σ
where x = individual data value = 28
μ = mean = 27
σ = standard deviation = 2
z-score = (28 - 27) / 2
z-score = (1) / 2
z-score = 0.5
Find the probability that corresponds to the z-score in the z-table. (see attached images)
at z = 0.5, p = 0.6915
Multiply the probability by 100 to get the percentage.
% = p x 100
% = 0.6915 x 100
% = 69.15
Hence, the percent of medical residents that are less than 28 years old is 69.15%.
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a c-chart is used for multiple choice means. ranges. percent defective. fraction defective per unit. number of defects per unit.
Answers
A C - chart is used for Number of defects per unit.
What is C - chart?
In statistical quality control, the c-chart is a sort of control chart used to track "count"-type data, often the total number of nonconformities per unit. On rare occasions, it is also used to keep track of all the events that take place in a given period of time.
C-charts are used to assess if a process is predictable and stable as well as to track the results of process improvements before and after they have been made. The C - chart is particularly useful when there are few actual flaws in the subgroup but many potential for defects exist.
Count type data, such as the number of non-conformities per unit, are monitored using a statistical quality control chart known as a C-Chart.
Hence, a C - chart is used for Number of defects per unit.
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Instructions solve n given the equation -3(2n-3)=25 -8n
Answers
Answer:
n=7
Step-by-step explanation:
-6n-9=25-8n
2n=34
n=17
11) Chloe sells her "secret blend" of coffee, which sells for $21.84 per pound. To blend she uses "special dark"
which is $67 per pound and "lightly roasted" which is $14 per pound. She needs 100 pounds of "secret blend"
to sell. How much of each type does she need?
Answers
Answer:
ya poop in the coffee and then ya see how many pounds there is find the the type urself
Step-by-step explanation:
When written in scientific notation, the number 1,240,000 will have a
Choose... as the exponent on the power of 10.
Answers
Using scientific notation, the number 1240000 can be expressed as 1.24×10⁶
Scientific NotationScientific notation is a form of presenting very large numbers or very small numbers in a simpler form. As we know, the whole numbers can be extended till infinity, but we cannot write such huge numbers on a piece of paper. Also, the numbers which are present at the millions place after the decimal needed to be represented in a simpler form. Thus, it is difficult to represent a few numbers in their expanded form. Hence, we use scientific notations.
Converting the number 1,240,000 to scientific notation, we will get
1,240,000 = 1.24×10⁶
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A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour. Which equation represents how many grams of the compound will remain after 2 hours?
Answers
[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 5.8\%\to \frac{5.8}{100}\dotfill &0.058\\ t=\textit{hours}\dotfill &2\\ \end{cases} \\\\\\ ~\hfill A=100(1 - 0.058)^{2} ~\hfill[/tex]
The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A radioactive compound with mass 100 grams decays at a rate of 5.8% per hour.
And, Time = 4 hours
Now,
Since, We know that;
Amount for Exponential Decay is,
⇒ [tex]C = P (1 - r)^t[/tex]
Where, C is current amount, P is initial amount, r is rate and t is timeeee
Substitute all the values, we get;
The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
Thus, The equation represents the grams of the compound will remain after 2 hours will be;
⇒ C = 100 (1 - 0.058)²
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Applying the translation (x, y) → (x – 3, y + 7) maps the point (–4, 7) onto the point ________.
A)
(14, –7)
B)
(–7, 14)
C)
(7, –14)
D)
(14, 7)
Answers
Answer:
B
Step-by-step explanation:
The rule means to subtract 3 from the x-coordinate and add 7 to the y-coordinate.
A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used. Find the dimensions of the playground that will enclose the greatest total area.
Answers
The greatest total area, length will be 300 ft. and width will be 200 ft.
Given,
In the question:
A rectangular playground is to be fenced off and divided into two parts by a fence parallel to one side of the playground. 1200 feet of fencing is used.
Now, According to the question:
Lets assume, the length of the playground is l ft. and width is w ft.
Suppose, the playground is divided into two parts by a fence parallel to width. That means the length of the divider fence will be w ft.
So, the total length of the fence needed = (2l+ 3w)ft.
It is given in the question that 1200 feet of fencing is used.
2l + 3w = 1200
2l = 1200 - 3w
l = 600 - [tex]\frac{3}{2}w[/tex] ......(1)
Now, the area of the playground....
A = l × w
A = ( 600 - [tex]\frac{3}{2}w[/tex] ) × w
A = 600w - [tex]\frac{3}{2}w^2[/tex]
Taking derivative on both side in respect of "w" ,
we will get:
dA/dw = 600 - [tex]\frac{3}{2} (2w)[/tex]
dA/dw = 600 - 3w
A will be maximum when dA/dw = 0
600 - 3w = 0
600 = 3w
w = 600/3
w = 200
Now plugging this w = 200 into equation (1)...
l = 600 - [tex]\frac{3}{2}[/tex] × 200
l = 600 - 300
l = 300
Hence, for the greatest total area, length will be 300 ft. and width will be 200 ft.
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The dictionary wa about 1 kg and a paperclip weigh about 1 g how many paper clip would equal the weight of a dictionary
Answers
1000 paperclips would weigh equal to the dictionary.
Weight of the dictionary = 1 kg
weight of one paper clip = 1 gm
according to the mathematical conversion system of weights
1 kilogram = 1000 grams
on the basis of the statement
1 gram is the weight of = 1 clip
so , 1000gm would be the weight of = 1 x 1000
1000 gm would be the weight of = 1000 clips
to weigh equal to the dictionary , we would require 1000 clips .
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a rectangular container with a square base and open top must have volume of 16 \text{} cubic meters. if material for the base costs $8 per square meter, and material for the sides costs $2 \text{} per square meter, find the dimensions of the container so that the cost of material to make it will be a minimum. as your answer, please input the value of the minimal cost.
Answers
The minimal cost of the box is $96.
Given data;
The volume of the box (v) = x²y
Given that, volume = 16 m³
So, 16 = x²y
y = 16/x² → (I)
Material for the base costs $8 per square meter, and material for the sides costs $2 per square meter.
Total cost (C) = 8 (x²) + 2*(xy)(4)
= 8x² + 8xy
Using (I),
C(x) = 8x² + 8x(16/x²)
C (^) = 8x² + 128/x
Now find critical points from
∴ [tex]\frac{d}{dx} = [8x^2+\frac{128}{x} ]=0[/tex]
x³ = 8
x = 2
So, the minimal cost will be given by x= 2,
Now, y = 16/x²
= 16/4
= 4
Dimension of the box that minimizes the cost is;
height = 4m, width=2m and breadth = 12m
Now,
Minimum cost = 8 (2)² + 128/2 = 32 + 64
= 96
Hence, The minimal cost of the box is $96.
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10 Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.
a Use a mapping to write this as a function.
Dakarai's answer was -1.2.
b Use inverse functions to work out the number Dakarai thought of. Show all your working.
Answers
a) The function that represents the given situation is (x - 11) ÷ 4 = -1.2 and the number thought by Dakari is 6.2
b) The inverse function (y - 11) ÷ 4 = -1.2
Function:
The function that is from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.
Given,
Dakarai thought of a number. He subtracted 11 from the number then divided the result by 4.
Here we need to find the following
a) function that map the function and the number though by Dakarai
b) inverse of the function
Let us consider the number thought by Dakarai as "x"
First, he subtracted 11 from the number,
So it can be written as,
=> x - 11
After that, he divided it by 4
So, the it can be written as,
=> (x - 11) ÷ 4
Now, the result was -1.2
So the function is
=> (x - 11) ÷ 4 = -1.2
Now we have to solve this equation, in order to find the value of x,
=> (x - 11) ÷ 4 = -1.2
=> x - 11 = -1.2 × 4
=> x - 11 = -4.8
=> x = -4.8 + 11
Therefore, the value of x is 6.2
And the inverse of the function can be written as by change the x as y,
Then we get,
=> (y - 11) ÷ 4 = -1.2
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Find the image of 4(3, 7) under a translation along the vector (-4, 2).
A'(7,5)
A'(1,-9)
A'(-1,9)
4'(-7,-5)
Answers
The image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).
Given:
A(3,7) under a translation along the vector (-4, 2).
A' = A + (-4,2)
= (3,7) + (-4,2)
= (3+(-4), 7+2)
= (3-4, 9)
= (-1, 9)
Therefore the image of A(3, 7) under a translation along the vector (-4, 2) is A'(-1,9).
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or
The radius of a semicircle is 2 millimeters. What is the semicircle's area?
Answers
The area of the semi circle with radius 2mm is 2[tex]\pi[/tex][tex]mm^{2}[/tex]
What is a semi-circle?A semicircle is formed when a lining passing through the centre touches the two ends on the circle. Thus, by joining two semicircles we get a circular shape.
When a circle is cut into two halves or when the circumference of a circle is divided by 2, we get a semicircular shape.
Area of a semi-circle = [tex]\frac{\pi r^{2} }{2}[/tex]
but radius r = 2mm
substitute r into the area equation, we have
Area of semicircle = [tex]\frac{\pi 2^{2} }{2}[/tex]
Area of semicircle is = 2[tex]\pi[/tex][tex]mm^{2}[/tex]
In conclusion the area of the semicircle is 2[tex]\pi[/tex][tex]mm^{2}[/tex]
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i really need help with this pls
Answers
Hope you understand;)
Answer:
B. x=3/k
Step-by-step explanation:
5kx+6=7kx
first you can simplify the kx terms
6=7kx-5kx
6=2kx
now get x by itself
6/2k=x
3/k=x
Find the length of the third side. If necessary, round to the nearest tenth.
Answers
Answer: 17.9
Step-by-step explanation:
Answer: 17.9
Step-by-step explanation:
a = 11c = 21b = ?[tex]a^{2} +b^{2} =c^{2} \\b^{2}=c^{2}-a^{2} =21^2-11^2=441-121=320\\b=\sqrt{320} =17.8885438[/tex]
Rounded to the nearest tenth would be 17.9.
If y = cos x, how many periods will there be between -5pi and 9pi ?
Answers
Answer:
7 periods.
Step-by-step explanation:
The cosine function is periodic, meaning it repeats forever.
Standard form of a cosine function:
[tex]f(x) = A \cos(B(x + C)) + D[/tex]
where:
A = amplitude (height from the mid-line to the peak).2π/B = period (horizontal distance between consecutive peaks).C = phase shift (horizontal shift - positive is to the left).D = vertical shift.Therefore, for y = cos x:
Amplitude = 1Period = 2πPhase shift = 0Vertical shift = 0The maximum of the function is when x = 0 + 2πn.
The minimum of the function is when x = π + 2πn.
To find the number of periods, first find the difference between the two given values:
⇒ 9π - (-5π) = 9π + 5π = 14π
As the period of the function is 2π, then the number of periods is:
⇒ 14π ÷ 2π = 7 periods.
which ratios are proportional ? (A. 2/3 = 3/4) (B. 5/6 = 11/12) (C. 6/9 = 9/12) (D. 3/5 = 9/15).
Answers
Answer:
D
Step-by-step explanation:
[tex]\frac{3}{5}[/tex] = [tex]\frac{9}{15}[/tex] It is the only one that you can multiply the top and the bottom of the fraction with the same number to get an equivalent fractions. Multiply the top and the bottom of the first fraction by 3 to get the top and the bottom of the second fraction.
In ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°. Find the area of ΔHIJ, to the nearest square centimeter.
Answers
The area of the triangle ΔHIJ is 42805 square centimeters.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a given ΔABC can be obtained by (1/2)×a×c×sin(∅/2)
where sin(Ф/2) is the included angle.
Given, ΔHIJ, h = 730 cm, i = 390 cm and ∠J=35°.
∴ The area of the ΔHIJ is (1/2)×730×390×sin(35/2) square centimeter.
= 142,350×sin(17.5) square centimeter.
= 42805 square centimeters.
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Which equation can be solved by using this system of equations?
[y-3x³-7x² +5
[y=7x²+2x
3x³-7x²+5=0
3x³-7x² +5-7x4 + 2x
7x²+2x=0
7x4+3x3-7x²+2x+5=0
Answers
The equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
We are given;
y = 3x³ - 7x² + 5
y = 7x^4 + 2x
We will solve the given equation by substitution method:
Using the substitution method, let us substitute y = 7x^4 + 2x in the equation y = 3x³ - 7x² + 5, we get,
3x³ - 7x² + 5 = 7x^4 + 2x
So, 3x³ - 7x² + 5 = 7x^4 + 2x will be solved by using the given system of equations.
Thus, the equation which can be solved by using the given system of equations; y = 3x³ - 7x² + 5 and y = 7x^4 + 2x is 3x³ - 7x² + 5 = 7x^4 + 2x. Option B is correct.
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2.5 ( x + 8 ) = 3.5x - 4
Answers
Answer:
x = 20
Step-by-step explanation:
Expanding the bracket on the right gives us :
2.5x + 20 = 3.5x - 4
Subtract 2.5x from both sides :
20 = x - 4
Add 4 to both sides :
20 = x
x = 20
Hope this helped and have a good day
the united nations stores data about energy production from animal waste and the use around the world. the following data set gives information for converting animal waste into electricity. country or area commodity - transaction year quantity unit united states animal waste - transformation in electricity 2014 171907 terajoules united states animal waste - transformation in electricity 2013 149233 terajoules united states animal waste - transformation in electricity 2012 104847 terajoules united states animal waste - transformation in electricity 2011 141347 terajoules united states animal waste - transformation in electricity 2003 185912 terajoules united states animal waste - transformation in electricity 2002 197120 terajoules united states animal waste - transformation in electricity 2001 104725 terajoules united states animal waste - transformation in electricity 2000 126745 terajoules united states animal waste - transformation in electricity 1999 133206 terajoules united states animal waste - transformation in electricity 1998 224425 terajoules united states animal waste - transformation in electricity 1997 129113 terajoules united states animal waste - transformation in electricity 1996 5274 terajoules united states animal waste - transformation in electricity 1993 21748 terajoules united states animal waste - transformation in electricity 1992 242924 terajoules united states animal waste - transformation in electricity 1991 210448 terajoules united states animal waste - transformation in electricity 1990 215437 terajoules what is the slope of the linear equation of the entire data set? round to nearest hundredth. provide your answer below:
Answers
The slope of the linear equation of the entire data set is -720.98
1. Bring data in to excel sheet
2.Select both x and y variable and insert scatter plot chart. Select any data point in the chart and add trend line. In the format trend line option choose "Linear" and also select "Display an equation on chart" & "Display R-squared value on chart"
To find: What is the slope of the linear equation of the entire data set? Round to nearest hundredth.
Regression equation : y = -720.98x + 15,90,277.32
Slope = -720.98 (Round to nearest hundredth.)
Intercept = 15,90,277.32
So, the slope of the linear equation of the entire data set is -720.98
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Which inequality represents all possible values for x in -2x>-48?
A X <-24
BX<24
CX-24
DX> 24
Answers
Answer:
Step-by-step explanation:
An inequality which represents all possible values for x in -2x>-48 is: B. x < 24.
What is an inequality?In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data such as integers, and variables in an equation based on any of the following inequality symbols:
Greater than (>).Less than (<).Greater than or equal to (≥).Less than or equal to (≤).Next, we would find the solution and possible values to this given inequality as follows:
-2x > -48
Dividing both sides of the inequality by -2, we have:
-2x/-2 > -48/-2
x < 48/2
x < 24.
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What is the solution to |x-9| -3 < 1
Answers
Answer:
[tex]x < 13[/tex] and [tex]x > 5[/tex]
Step-by-step explanation:
Take a look at the attachments...
Hope this helps! :)
1. a car manufacturer is concerned about poor customer satisfaction at one of its dealerships. the management decides to evaluate the satisfaction surveys of its next 62 customers. the dealership will be fined if the number of customers who report favorably is between 45 and 50. the dealership will be dissolved if fewer than 45 customers report favorably. it is known that 84% of the dealership's customers report favorably on satisfaction surveys. a. what is the probability that the dealership will be fined? b. what is the probability that the dealership will be dissolved?
Answers
Probability that the dealership will be fined is 0.157
Probability that the dealership will be dissolved is 0.158
the management decides to evaluate the satisfaction surveys = 62 customers
the sample mean is 0.84
we solve this using sampling distribution of the proportion
standard deviation of the sample is [tex]\sqrt{\frac{PQ}{n} }[/tex] P = 0.84 Q= 0.16 n= 62
[tex]\sqrt{\frac{0.84*0.16}{62} }[/tex] = 0.04
mean(P) = 0.84
standard deviation = 0.04
45/62 = 0.72
50/62 = 0.80
(a) the probability that the dealership will be fined
p(45 < x < 50) = p(x< 50) - p(x<45)
Z-value for 50 is (0.80- 0.84)/0.04 = -1
p(x<50)= 0.1586
Z-value for 45 is (0.72-0.84)/0.04 = -3
p(x<45) = 0.0013
p(45 < x < 50) = 0.1586-0.0013 = 0.1573
(b) the probability that the dealership will be dissolved
p(x<45) = 0.1586
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Can someone help me with this?
Answers
Using multiplication or division, we can have either of the numbers from the operation.
Multiplication and Division of Numbersmultiplication is the repeated addition of numbers. But the rules for multiplication of integers are different from that of addition. It includes three possibilities. They are:
Multiplication between two positive numbers,Multiplication between two negative numbers; andMultiplication between a positive number and a negative number.The product of two integers with similar sign numbers will always be positive. This means the product of two positive numbers or two negative numbers will always be positive. While the product of a positive number and a negative number (integers with different signs) will always be negative.
In this case, the three numbers are interconnected via arithmetic operation.
135 ÷ 15 = 9
9 × 15 = 135
135 ÷ 9 = 15
So, which ever way we go with, these numbers are connected to each other.
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The difference between the digits of a two digit
number is 1. The number itself is 1 more than 5 times
the Sum of Its digit. If the units digit is greater than
the tens digit, find the number.
Answers
Answer:
56
Step-by-step explanation:
Number with two digits = 10y + x
x > y
x-y = 1
10y + x = 5(x+y) + 1
x = y + 1
10y + y + 1 = 5(y+1 +y) + 1
11y + 1 = 5(2y+1) + 1
11y + 1 = 10y + 5 + 1
11y - 10y = 5
y = 5
x = 5 + 1 = 6
In a study of cell phone usage and brain hemispheric dominance, an internet survey was e-mailed to subjects randomly selected from an online group involved with ears. There were surveys returned. Use a 0. 01 significance level to test the claim that the return rate is less than 20%. Use the p-value method and use the normal distribution as an approximation to the binomial distribution.
Answers
The value of z statistics is -1.878,
Given,
In the question:
Number of random sample selected, n = 6967
Number of surveys returned, x = 1331
Now, According to the question:
Estimated proportion of return rate;
To find the value of p = 1331/6967 = 0.192
Significance level, ∝ = 0.01
z would represent the statistic
We investigate the assertion that the return rate is less than 20%, and the following hypotheses are tested:
Null hypothesis, p₀ ≥ 0.2
Alternative hypothesis, p₀ < 0.2
The statistics, z = (p - p₀) / √(p₀(1 - p₀)/n)
z = (0.191 - 0.2) / √(0.2(1 - 0.2)/6967) = -1.878
Using the alternative hypothesis and the following probability, we can now get the p value:
p value = p(z < - 1.878) = 0.0302
We fail to reject the null hypothesis when the p value exceeds the significance level of 0.01 and there is insufficient evidence to support the conclusion that the return rate is less than 20% at 1% of significance.
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