The probability of type ii error at the 5% significance level is 49.5%
Probability:
In statistics, the number of possible way of occurring an particular event is referred as probability.
Given,
The manager of a firm wants to determine if the average hourly wage for semi-skilled workers is $9 in the capital district. in order to do so, she takes a random sample of 100 hourly wages and finds that the sample mean is $8 and the sample standard deviation is $2. the hypotheses to be tested are: h subscript 0 : mu equals 9 h subscript 1 : mu not equal to 9 assume that the actual average is $8.8.
Here we need to find the probability of type ii error at the 5% significance level.
While we looking into the give question, we have identified the following,
Semi skilled worker hourly wages = $9
Number of samples = 100
sample mean = $8
Standard deviation = $2
Hypotheses
H₀ : μ = 9
H₁ : μ ≠ 9
Significance level = 5%
Therefore, the type II error is calculated as,
=> P [(100 - 9/(2/√100)) ≥ (9 - 8)/(2/√100))] = 1 - 5
When we simplify this one then we get, the probability as 49.5%.
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If a 16-foot utility pole is connected to a cable
that is attached to the ground 12 feet from the
base of the pole, find then length of the cable?
Answer:20 ft
Step-by-step explanation:
Using Pythagoras' Theorem:
[tex]h^{2} = a^{2} +b^{2} \\h^{2} = 16^{2} +12^{2} \\h^{2} = 256+144h^{2} = 400\\\\[/tex]
Now you want to get h alone. To do that you need to get rid of the squared by finding the square root of 400.
[tex]h=\sqrt{400}\\h=20[/tex]
louisa walks from her school 40 feet south and then walks 100 feet east. what is the shortest distsnce louisa is from her school? round to the nearest tenth
The shortest distance Louisa is from her school is 107.7 feet
How to determine the shortest distance from her school?From the question, we have the following parameters that can be used in our computation:
East = 100 feet
South = 40 feet
The shortest distance from her school is calculated using the following theorem
Shortest distance = √(East² + South²)
Substitute the known values
Shortest distance = √(100² + 40²)
Evaluate
Shortest distance = 107.7
Hence, the shortest distance = 107.7 feet
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let n be a positive integer and suppose n distinct lines are drawn in the plane. no two of these lines are parallel, and no three of these lines intersect at a common point. prove that these lines divide the plane into n 0 c n 1 c n 2 regions.
There are 0 lines, 1 regions, and no line junctions. There are always k+1k+1 regions and kk intersections added whenever a line is added and crosses k other lines.
Another perspective is that k+1k+1 areas are added for each line and k intersections added (the number of added lines and intersections).Consequently, the total number of regions is 1 plus the sum of the number of lines and junctions.The number of intersections is 1 + the number of lines. There are (n2) (n2) crossovers with nn lines (if no two lines are parallel and no three lines are coincident). Therefore, there are (n2) +n+1=n(n1)/2+n+1=n2+n+2/2 areas instead of (n2) +n+1=n(n1)/2+n+1=n2+n+2/2).
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in order to calculate the correlation between two variables related to the same sample what do you need to calculate first?
In order to calculate the correlation between two variables related to the same sample you need to calculate first the mean of each variable.
Before determining the correlation, the covariance of the two variables in the issue must always be computed. The standard deviation of each variable is then needed. The correlation analysis is calculated by dividing the covariance even by combination of a standard deviations of two or more variables.
A correlation is a statistical measurement of the two-variable connection. The measure works best with parameters that have a linear connection with one another.
The degree of the relationship between two variables is examined using correlation. To get the correlation between two variables, divided the covariance value by the standard deviation of both variables. Correlation analysis for two variables in the same sample should be performed. If you run a survey with two factors, a responder should be able to answer both variables at a glance. Furthermore, other participants' replies to the parameter might be evaluated for a correlation test.
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I need help with a linear equation.
The slope (-8) of the linear equation that is represented by the table, is the amount Austin pays each week, which is $8.
What is the Slope of a Linear Equation?A linear equation which is given as y = mx + b, has a slope value which represents the change in y over a change in x and is given by the value of m in the linear equation.
If a table is said to represent a linear equation, the slope of the linear equation, which can also be called the unit rate, can be found by using two pairs of values from the table to calculate the change in y over the change in x.
Given that the table above represents a linear equation where L is dependent on the value of t, it means that slope of the linear equation represents the amount Austin paid back each week.
Find the slope using two points, (2, 24) and (4, 8):
Slope (m) = (24 - 8) / (2 - 4)
m = 16/-2
m = -8
Therefore, this means that Austin pays $8 every week.
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9. What is the distance between the coordinates (9, -2) and
(9,8)?
Answer:
10
Step-by-step explanation:
if u got up 10 from (9,-2) you will get to (9,8)
mary lee's natural food store sells a combination of teas. the most popular is a mixture of a tea that sells for per pound with one that sells for per pound. if she needs of tea that will sell for per pound, how many pounds of each tea should she use?
She may thus combine 21 pounds of tea priced at $3 and 14 pounds of tea priced at $2 to create tea that costs $2.6 per pound.
What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: (Number/variable, Math Operator, Number/variable) is an expression.
Here,
Let 3x be the pounds of tea for $3 and 2x be the pounds of tea for $2.
Total required pounds=35
3x+2x=35
x=35/5
x=7
So, She can add 21 pounds of tea for $3 and 14 pounds of tea for $2 to make the tea that is $2.6 per pound.
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Is 700% of 6 less than 10,greater than 10 but less than 100,or greater than 100?
Greater than 100. 700% of 6 is 42.
PLS HELP!!! I really need help!
Use substitution to solve the system.
5x + 4y = 9
-2x + y = -14
Answer:
x=9/5 − 4y/5
x = 7 + y/2
Step-by-step explanation:
Move all terms that don't contain x to the right side and solve.
Solve using substitution.
y = –7x − 8
y = 2x + 10
12 is 30% of what number?
Answer: 3.6
Step-by-step explanation:
Step 1: 30/100 = x/12
Step 2: Multiply 12x30 and then divide it by 100
The figure is made up of a cone and a cylinder.
To the nearest whole number, what is the volume of this figure?
Use 3.14 to approximate π . Round only your final answer to the nearest whole number.
Enter your answer in the box.
The volume of the composite shape is 38mm³(nearest whole number)
What is a composite solid?A composite shape can be defines as a shape created with two or more basic shapes. We often refer to composite shapes as compound and complex shapes.
The volume of a the composite solid above = volume of cone + volume of cylinder
volume of cone = 1/3πr²h
=1/3×3.14×2²×3
= 12.56mm³
volume of the cylinder = πr²h
= 3.14×2²×2
= 25.12mm³
therefore the volume of the shape = 12.56+25.12
= 37.68mm³
= 38mm³( nearest whole number)
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expected counts 153 94.5 63 49.5 45 45 enter the test statistic - round to 4 decimal places. test statistic
On solving the provided question, we got that - 0.000005178 as the P-value,the null hypothesis is a common statistical theory that contends that no statistical relationship
How do you define a null hypothesis?Using a single observed variable to compare two sets of observed data and measured phenomena, the null hypothesis is a common statistical theory that contends that no statistical relationship and significance exists.
h0; no change in beverage preferences
h1: alterations in drink preferences
alpha = 0.05
We find the test statistics' solution.
The attachment underwent the chsquare test.
Chi-square: (O-E)2/E
Chi square is 32.30188.
[tex]number of degrees of freedom = n-1 = 6-1 = 5[/tex]
I determined the p value using the chi distribution tool in Excel.
CHIDIST(3.20188, 5) =
0.000005178 as the P-value
We reject the null hypothesis since the pvalue is less than 0.05 and come to the conclusion that there is enough evidence to support the shift in drink preferences.
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PLS ACTUALLY ANSWER BOTH REASONS !!!!! 100 PTS CHOICES ARE THE SAME FOR BOTH
The blanks in this two-column proof should be completed (filled) as follows:
Statements Reasons_______________
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
What is the Right Triangles Similarity Theorem?In Mathematics, the Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two (2) triangles that are formed would be similar to each other, as well as the original triangle.
What is CPCTC?In Mathematics, CPCTC is an acronym for corresponding parts of congruent triangles are congruent and it states that the corresponding angles and side lengths of two (2) or more triangles are congruent if they are both congruent i.e AD ≅ CD.
Additionally, HL is an acronym for hypotenuse leg and it states that if the hypotenuse and one (1) leg in a right-angled triangle are congruent to the hypotenuse and leg of another right-angled triangle, then the two (2) triangles would be congruent i.e ΔADB ≅ ΔCDB.
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Answer:
ΔADB ≅ ΔCDB HL.
AD ≅ CD CPCTC.
Step-by-step explanation:
or what the guy said on top :D
a bathtub filled with 55 gallons of water is drained. the water drains at a rate of 5 gallons per minute. the function f(x)=-5x+55 represents the volume of water in the tub as it drains. how many minutes has passed if the tub still has more than 20 gallons of water remaining in it.
f-1(x)=1\5x-11
Step-by-step explanation:
please help me with my homework Find the value of x in the parallelogram
Adjacent angles of a parallelogram are supplementary.
[tex]x+2x=180 \\ \\ 3x=180 \\ \\ x=\boxed{60}[/tex]
The money
m
(in £) Noah has to spend each week is his wage
w
(in £) subtract the tax
t
(in £) he pays on his income. Enter a formula for the money he can spend and enter how much he has to spend if he earns £160 a week and pays £55 in tax.
If Noah earns £160 a week and pays £55 in tax, he has £160 - £55 = £160-£55 = £105 to spend.
What is meant by subtraction?Subtraction is a mathematical procedure that includes subtracting one number from another. For example, if we have five apples and subtract three of them, we are left with two apples. Beginning with the bigger number and deducting the smaller number from it is how subtraction is done. Subtraction is denoted by the minus symbol (-). A difference is the outcome of a subtractive operation.
We may better grasp how to solve issues requiring the removal of one or more elements from a set by understanding the fundamental mathematical formula of subtraction. It is employed in many different scenarios, such as when we need to subtract incomes on a regular basis.
How to solve?
The formula for the money Noah has to spend each week is m = w - t.
£160 - £55 = £160 - £55 = £105
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urgent help needed the question is written in the image below plss
#1= 36
#2=81
#3= 32
#4=125
20 chairs at four tables equals how many chairs per table
Answer:
5 chairs per table.
Step-by-step explanation:
Need help, please!
Is a^+b^6 = (a²+b²)(a^4-a²b^2+b^4) an identity? Explain or show your reasoning.
Expression a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴) is an identity, by left-hand term and right-hand term property.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations,
The given expression is,
a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)
To prove that the given expression is an identity,
Solve left-hand term,
Substitute a² = x, b² = y
a⁶ + b⁶
= x³ + y³
Use formula x³ + y³ = (x + y)(x² - x y + y²)
= (x + y)(x² - x y + y²)
Again substitute x = a², y = b², expression will be,
= (a² + b²)(a⁴ - a²b² + b⁴)
Hence, a⁶ + b⁶ = (a² + b²)(a⁴ - a²b² + b⁴)
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21 out of 300 equals what percent
Answer:
7%
Step-by-step explanation:
When trying to figure out percentages, we can try to use a proportional relationship. Percent means out of a hundred, and since we don't know the percentage on top, we can mark it as ?.
21/300 = ?/100
To figure this out quickly, we can try figuring out how many times we need to multiply or divide to get to the next number. Between 21 and ?, we can't do anything because we are unsure of what ? is.
Between 300 and 100, we can notice that to get to 100, we must divide by 3. 300/3 = 100
This means that the first ratio is three times the amount of the second ratio, which means that the second ratio is 1/3 of the first.
We can multiply 21 by 1/3 (or divide by 3), which will get us to 7.
7/100 = 0.07 = 7%
You and a classmate have been paired to solve an equation. Your partner says they got an answer but the solution they found does not work when they checked it. Here is their work:
6 (8-3x )− 3 (9x−1 )+ 60
54 - 18x = −27x − 3 + 60
54 - 18x = −27x + 57
-18x = -27x + 3
9x = 3
x= 1/3
Explain all of the mistakes your partner made and how to correct them. After correcting the mistakes, write the correct answer for this equation.
The mistake are shown below and the correct steps are shown below.
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;
The expression is,
⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60
And, All the steps are;
⇒ 6 (8 - 3x ) = - 3 (9x - 1 ) + 60
⇒ 54 - 18x = −27x − 3 + 60
⇒ 54 - 18x = −27x + 57
⇒ -18x = -27x + 3
⇒ 9x = 3
⇒ x= 1/3
Now,
Since, The expression is,
⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60
Cleary, In the second step 2; your partner doing mistake.
So, All the correct steps are;
⇒ 6 (8 - 3x) = - 3 (9x - 1) + 60
⇒ 48 - 18x = - 27x + 3 + 60
⇒ 48 - 18x = - 27x + 63
⇒ 27x - 18x = 63 - 48
⇒ 9x = 15
⇒ x = 15/9
⇒ x = 5/3
Thus, The correct value is;
⇒ x = 5/3
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help w this, dont guess
Quickly and fast which expression is equivalent to 4(3/4y - 2 + 1/2y? choose all that apply
a.4y-8
b.5y-8
c.3y-8+2y
d.-3y
e.3y+8+2y
f.5y+8
Answer: 2y4 + 4y2
Step-by-step explanation:
2y3 + 4y2
2y4 + 4y2✔
1/2y3 + 1y2
1/2y4 + 4y2
the regression equation netincome = 2,277 + .0307 revenue was estimated from a sample of 100 leading world companies (variables are in millions of dollars). (a-1) calculate the residual for the x, y pair ($41,078, $8,301).
From a sample of 100 leading world companies we can estimate the residual value is 4,762.9054 .
It is given that,
Regression equation net income = 2277+0.0307
From a sample of 100 leading world companies we can estimate the revenue.
(a-1)
for the (x,y) pair, x = $41,078 and y = $8,301 or it is represented as ($41,078 , $8,301)
then the above (x,y) pair's residual value is e = y - ÿ
ÿ = 2277+0.307x
= 2277+0.0307(41078)
= 2277+1261.0946
= 3538.0946
Thus, e = y - ÿ
so, e = 8301 - 3538.0946
= 4762.9054
Hence, the residual value = 4,762.9054
To calculate the correlations between a dependent variable and one or more independent variables, a statistical technique grouping together several statistical techniques known as regression analysis is utilized. Revenue is the entire amount of money received from the sale of goods or services related to a company's main operations. Revenue, also known as gross sales, is often referred to as the "top line" because it appears at the top of the income statement. The residual value, also known as salvage value, is the estimated value of a fixed asset at the end of its useful life or lease term.
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The following information was collected from a simple random sample of a population. 9 13 15 15 21 24 The point estimate of the population standard deviation is Select one: O a. 59.1. O b. 7.688. O C. 7.018. O d. 49.25.
The point estimate of the population standard deviation is Select one is 5.4558.
Given data
9,13,15,15,21,24
We have to find first mean
Here n=6
[tex]$\begin{aligned} \text { mean } \bar{x} & =\frac{\sum x_i}{n} \\ & =\frac{9+13+15+15+21+24}{6} \\ & =\frac{97}{6} \\ & =16.166\end{aligned}$[/tex]
[tex]$\therefore$[/tex] Standard deviation
[tex]S=\sqrt{\frac{\sum\left(x_i-x\right)^2}{n-1}}$$[/tex]
S= root (9-16.(66)^2+(13-16.166)^2+(15-16.166)^2+(15-16.166)^2+(21-16.166)^2+(25- 16.166)^2/(6-1)
[tex]\begin{aligned}& =\sqrt{\frac{148.833336}{5}} \\& =\sqrt{29.7666} \\& =5.4558\end{aligned}[/tex]
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Answer:
Step-by-step explanation:
b) 7.688 The point estimate of the population standard deviation is 7.688. The point estimate of a population parameter is the estimate of the population parameter based on a single sample. In this case, the point estimate of the population standard deviation is the sample standard deviation, which is a measure of the spread or variability of the sample data. To calculate the sample standard deviation, we need to first calculate the sample mean, which is the average of the values in the sample. In this case, the sample mean is (9 + 13 + 15 + 15 + 21 + 24)/6 = 14.5. We can then use this value to calculate the sample standard deviation, which is √(((9-14.5)² + (13-14.5)² + (15-14.5)² + (15-14.5)² + (21-14.5)² + (24-14.5)²)/6) = 7.688. This is the point estimate of the population standard deviation. The other answer choices are not the sample standard deviation.
does someone mind helping me with this question? Thank you!
Answer:
50,000
Step-by-step explanation:
1,750 x 2 = 3,500
25,000 x 2 = 50,000
i need help asap !!!!!!
Answer: A and C is incorrect, the middle is 14. The minimum is 13. The max is 16.
Step-by-step explanation: B is correct
there is no 12
please
help I will give brainly
The distance AC to be covered for the given triangle will be 429.94 meters.
What is a triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices.
Triangle is a very common figure to deal with our daily life for example in our daily life to measure the height of any tower then there is a huge application of the right angle triangle.
As per the given triangle,
By cosine law,
Cos∠ABC = (220² + 430² - AC²)/(2 × 220 × 430)
Cos∠ABC = (233300 - AC²)/189200
Cos(180° - 75°) = (233300 - AC²)/189200
(233300 - AC²) = -48968.56
AC² = 184331.4367
AC = 429.94 meter
Hence "The distance AC to be covered for the given triangle will be 429.94 meters".
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x −y. (b)arex y andx−y independent?
⇒ Yes X+Y and X-Y are independent
What is covariance?
Covariance is a measure of the combined variability of two random variables used in probability theory and statistics. The covariance is positive if the greater values of one variable primarily match the greater values of the other variable, and the same is true for the lesser values.
Define U=X+Y, V=X−Y
Then, [tex]x=\frac{(U+V)}{2}[/tex], and
[tex]Y=\frac{(U-V)}{2}[/tex]
Find the Jacobian J for the transformation.
Then, fU,V(u,v)= fX(x=(u+v)/2) fY(y=(u−v)/2)|J|
You will find that fU,V(u,v) factors into a function of u alone and a function of v alone. Thus, by the Factorization thm, U and V are independent.
b) Yes X+Y and X-Y are independent
a) Since , X+Y and X-Y are independent,
COV(X+Y , X-Y) = 0 Answer
Cov(X+Y , X-Y) = 0
b)
Yes these are independent
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