An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $22.4 for a random sample of 2128 people. Assume the population standard deviation is known to be $9.3. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.
Answer:
[21.9, 22.9] in thousands of dollars
Step-by-step explanation:
The formula for Confidence Interval
= Mean ± z score × standard deviation/√n
Mean = $22.4
Standard deviation = $9.3
n = 2128
z score of 98% confidence interval = 2.326
Confidence Interval = 22.4 ± 2.326 × 9.3/√2128
= 22.4 ± 0.469
Confidence Interval =
22.4 - 0.469
= 21.931
≈ 21.9 in thousand of dollars
22.4 + 0.469
= 22.869
≈ 22.9 in thousands of dollars
Hence, the 98% confidence interval =
[21.9, 22.9] in thousands of dollars
Question 6 (1.25 points)
A researcher wants to test if the mean annual salary of all lawyers in a city is
different from $110,000. A random sample of 53 lawyers selected from the city
reveals a mean annual salary of $114,000. Assume that o = $17,000, and that the
test is to be made at the 1% significance level.
What is the value of the test statistic, z, rounded to three decimal places?
A
Answer:
Test statistic Z= 1.713
The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance
Null hypothesis is accepted
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
Step-by-step explanation:
Step(i):-
A researcher wants to test if the mean annual salary of all lawyers in a city is
different from $110,000
Mean of the Population μ = $110,000
Sample size 'n' = 53
Mean of the sample x⁻ = $114,000.
standard deviation of the Population = $17,000,
Level of significance = 0.01
Null hypothesis :
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
H₀: x⁻ = μ
Alternative Hypothesis : x⁻ ≠ μ
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{114000-110000}{\frac{17000}{\sqrt{53} } }[/tex]
Z = 1.7130
Tabulated value Z = 2.576 at 0.01 level of significance
The calculated Z- value = 1.7130 < 2.576 at 0.01 level of significance
Null hypothesis is accepted
There is no difference between the mean annual salary of all lawyers in a city is different from $110,000
Can someone show me how this worked out for the answer?
Answer: I'm not sure what you are asking?
what is the image of (6,-2) under the translation (x,y) (x-5,y-8)
Select the correct answer
Which statement best describes the graphed function?
ILL GIVE 15 PTS PLZ
Answer: the answer is a
Step-by-step explanation: learned about it in 9th grade
Answer:
it's a. the function has a relative maximum at (-2,4) and a relative minimum at (2,-4).
Find the equation of the line.
—————
The line is parallel to y =-6/7x +1 and passes through the point (-7,-3).
—————
The equation of the line is y=
Answer:
y = [tex]-\frac{6}{7}[/tex] x - 9
Step-by-step explanation:
Parallel lines have the same slopes and different y-intercept
m = [tex]-\frac{6}{7}[/tex]
y - (- 3) = [tex]-\frac{6}{7}[/tex] [x - (- 7)]
y + 3 = [tex]-\frac{6}{7}[/tex] (x + 7)
y + 3 = [tex]-\frac{6}{7}[/tex] x - 6
y = [tex]-\frac{6}{7}[/tex] x - 9
Which answers are examples of inductive reasoning?
Select each correct answer.
John saw wild turkeys in his yard during the past 3 years. He will see wild turkeys in his yard next year.
All right triangles have a 90° angle. Triangle ABC is a right triangle. Therefore, triangle ABC has a 90° angle.
The cinema charges $5 to see a movie. Four friends are going to the cinema to see a movie. Therefore, altogether they will pay $20 to see the movie.
Mrs. Smith notices that the first 10 students who enter her class are female. Therefore, she expects that all the students in her class will be female.
A
John will see a wild turkey in his yard next year
John saw wild turkeys in his yard during the past 3 years. He will see wild turkeys in his yard next year.
and
Mrs. Smith notices that the first 10 students who enter her cla$s are female. Therefore, she expects that all the students in her cla$s will be female.
Step-by-step explanation:
Hello!
First off, what is inductive and deductive reasoning?
Inductive is when you infer off of your observations. For example, "the last three cars I passed by were white, therefore the next car will also be white". The inductive reasoning is usually a broad guess. This could be right, but it isn't factual.
Deductive is when you infer based off of facts, or confirmed information. For example, "If you get 60% on a quiz, you pa$s the quiz. John got 80% percent on his quiz, therefore he passed." It is a confirmed fact that 60% is the pas$ing grade so if John got a 80%, that is more than 60% and he passes.
I hope the examples made sense!
I wrote about explaining the options but brainly is being sensitive
Please help!!!!!!!!!!
Step-by-step explanation:
3/1 x 5/6 = 15/6 = 2 3/6 = 2 1/2
answer is C
what is the slope of the line
Answer:
y-mx+b
Step-by-step explanation:
2/3 divided by 5 I Need answers
Answer:
Step-by-step explanation:
7.5
Answer:
if you divide [tex]\frac{2}{3}[/tex] by 5 the answer would be [tex]\frac{2}{15}[/tex]
10 workers produce 30 complex elements in 10 days. In how many days would 5
workers produce 24 elements?
Given:
10 workers produce 30 complex elements in 10 days.
To find:
The number of days, in which 5 workers produce 24 elements.
Solution:
According to the question, let as assume
[tex]n_1=10[/tex]
[tex]w_1=30[/tex]
[tex]d_1=10[/tex]
[tex]n_2=x[/tex]
[tex]w_2=24[/tex]
[tex]d_2=5[/tex]
where, n is number of workers, w is work done, and d is number of days.
We have, a formula,
[tex]\dfrac{n_1\times d_1}{w_1}=\dfrac{n_2\times d_2}{w_1}[/tex]
Substituting the values in the above formula, we get
[tex]\dfrac{10\times 10}{30}=\dfrac{x\times 5}{24}[/tex]
[tex]\dfrac{10}{3}=\dfrac{5x}{24}[/tex]
Isolate variable x.
[tex]\dfrac{10}{3}\times \dfrac{24}{5}=\dfrac{5x}{24}\times \dfrac{24}{5}[/tex]
[tex]\dfrac{240}{15}=x[/tex]
[tex]16=x[/tex]
Therefore, the required number of days is 16.
In parallelogram WXYZ, what are the coordinates of the point of intersection of WY and ZX?
Point of Intersection = ____ ____
Answer:
Point of intersection of WY and ZX is (3.5, 3.5).
Step-by-step explanation:
Since, diagonals of a parallelogram bisect each other,
Point of intersection of the diagonals will be midpoint of each diagonal.
By this property, midpoint (x, y) of the segment joining W(-2, 6) and Y(9, 1) will be,
[tex]x=\frac{x_1+x_2}{2}[/tex]
x = [tex]\frac{-2+9}{2}[/tex] = 3.5
Similarly, y-coordinate of the midpoint will be,
y = [tex]\frac{y_1+y_2}{2}[/tex]
y = [tex]\frac{6+1}{2}[/tex] = 3.5
Therefore, point of intersection of the diagonals of the given parallelogram will be (3.5, 3.5).
⚠️⚠️⚠️⚠️NEED HELP MARKING PEOPLE AS BRAINLIST!
I believe its a reflection
Sorry if im wrong
PLEASE HELP ME! ;)
What is the result when the number 20 is decreased by 10%?
Answer:
18 would be the number
Step-by-step explanation:
plz mark B R A I N L I E S T
Answer:
I think the answer is 18
Step-by-step explanation:
20-10%=18
You exercise for 4 minutes to burn off 60 calories. If you exercise for 60 minutes and burn off 900 calories, is that correct?
Answer:
4 minutes 60 calories
60 minutes ?
Using cross-multiplication, you can find the solution.
4x = 3600
x = 900
Yes its true, you can burn 900 calories in 4 minutes
In October of 2019, Gallup asked a random sample of 1,506 Americans which of two approaches to punishing murder they thought was better, the death penalty or life without possibility of parole. For the first time since Gallup began asking the question in 1985, a majority of Americans now say life imprisonment is a better approach for punishing murder than is the death penalty. According to the 2019 Gallup death-penalty poll, 60% percent of Americans asked to choose whether the death penalty or life without possibility of parole "is the better penalty for murder" chose the life-sentencing option. 36% favored the death penalty.
Required:
a. Find a 95% confidence interval for the proportion adults in the US that now believe life imprisonment is a better approach for punishing murder.
b. Interpret your interval above in the context of this problem.
c. Use your interval to find the margin of error associated with this confidence interval.
d. If we increase the level of confidence to 98%, will the interval be wider or narrower?
Answer:
a
The 95% confidence interval is [tex]0.5753< p <0.62474[/tex]
b
This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval
c
The margin of error is [tex]E = 0.02474 [/tex]
d
The confidence interval becomes wider
Step-by-step explanation:
From the question we are told that
The sample size is n = 1506
The sample proportion is [tex]\^ p = 0.60[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } [/tex]
=> [tex]E = 1.96 * \sqrt{\frac{0.60 (1- 0.60)}{1506} } [/tex]
=> [tex]E = 0.02474 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\^ p -E < p < \^ p +E[/tex]
=> [tex]0.60 - 0.02474 < p <0.60 + 0.02474[/tex]
=> [tex]0.5753< p <0.62474[/tex]
This 95% confidence interval tell us that there 95% confidence that the true proportion of adults in the US that now believe life imprisonment is a better approach for punishing murder lies within the interval
Generally the level of confidence varies directly with the critical value of [tex]\frac{\alpha }{2}[/tex] and this in turn varies directly with the margin of error which when sample proportion is constant it determines the width of the confidence interval so when the level of confidence increases the confidence interval becomes wider
If three servings of ice cream has 24g of fat, how many milligrams of fat does one serving have?
Answer:
600
Step-by-step explanation:
24 by 3 times 100
The number of milligrams of fat that one serving has is 8000 milligrams.
Firstly, it should be noted that
1000mg = 1 gram.
Since three servings of ice cream has 24g of fat, therefore, the fa that will be contained in each will be:
= 24/3
= 8g
Therefore, we'll convert 8 grams to milligrams and this will be:
= 8 × 1000
= 8000 milligrams.
Therefore, a serving has 8000 milligrams.
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107 is what percent of 160.9?
(HELP NOW PLS)
Answer:
66.5%
Step-by-step explanation:
107/160.9 = 0.665001 = 66.5%
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t2 + 35, y = ln(t2 + 35), z = t; (6, ln(36), 1)
Answer:
Attached below is the detailed solution
answer : x(t), y(t), z(t) = ( 6 + t/6, In (36) + t/18, 1 + t )
Step-by-step explanation:
x = [tex]\sqrt{t^2 + 35 }[/tex] , y = In(t^2 + 35 ), Z = t;(6, ln(36), 1)
Determine the parametric equations for the tangent line to the curve with the above given parametric equations
attached below is the detailed solution
what do you think was the porpuse of this advertisement?
Answer:
The purpose of advertising is to inform the consumers about their product and convince customers that a company's services or products are the best, enhance the image of the company, point out and create a need for products or services, demonstrate new uses for established products, announce new products and programs.
Please help i will give brainlest!
Answer:
6×1+9×1/10+4×1/100+7×1/1000
Step-by-step explanation:
what will be the 40th term in the sequence defined by an=-12+4(n-2)
Answer:
140
Explanation:
an=-12+4(n-2)
an=-12+4([40]-2)
an=-12+4(38)
an=-152-12
an=140
The 40th term in the sequence defined by aₙ= -12+4(n-2) is 140
using AP formula,
aₙ = a + (n - 1)d
where
a = first term
d = common difference
n = number of terms
Therefore,
aₙ = -12 + 4(n-2)
n = 40
a₄₀ = -12 + 4(40 - 2)
a₄₀ = -12 + 4(38)
a₄₀ = -12 + 152
a₄₀ = 140
The 40th term of the sequence is 140.
learn more about arithmetic progression here: https://brainly.com/question/22069667?referrer=searchResults
PLEASE HELP ME SIMPLIFY THIS PLEASE SHOW WORK TO! THANK YOU 3/4x + 11 - 5 1/2 + 1/4x
Answer:
x-29/2
Step-by-step explanation:
Find the whole, given the part and the percent. 50% of what number is 60
Answer:
50% of 120 is 60
Step-by-step explanation:
So 60 is half of 120, and 60 times 2 is 50 :)
(Brainliest?)
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Let x as that number ,
So :
[tex] \frac{50}{100} x = 60 \\ [/tex]
[tex] \frac{1}{2} x = 60 \\ [/tex]
Multiply sides by 2
[tex]2 \times \frac{1}{2} x = 2 \times 60 \\ [/tex]
[tex]x = 120[/tex]
Thus that number is 120 .
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Find the slope for the line that passes thru the points (-2, 7) and (4, 18)
Answer:
[tex]m=\frac{11}{6}[/tex]
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASAlg I
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Step-by-step explanation:
Step 1: Define
Point (-2, 7)
Point (4, 18)
Step 2: Solve for slope m
Substitute: [tex]m=\frac{18-7}{4+2}[/tex]Subtract/Add: [tex]m=\frac{11}{6}[/tex]Answer:
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Find the value of x.
The angle measures of 2 x degrees, 90 degrees, and x degrees sum to 180 degrees.
Answer:
x = 30°
Step-by-step explanation:
2x + 90 + x = 180
3x = 90
x = 30
Topic: Angles
If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{x = 30 \degree}}}}[/tex]
♨ Step - by - step explanation
☯ Given angles :
2x° , 90° , x°☯ To find :
Value of x✎ Set up an equation and solve for x :
[tex] \sf{2x \degree \: + 90 \degree \: + \: x \degree = 180 \degree}[/tex]Add the like terms. Remember that Only coefficients of like terms can be added or subtracted.
➺ [tex] \sf{3x \degree + 90 \degree = 180 \degree}[/tex]
Move 90° to right hand side and change it's sign
➺ [tex] \sf{3x \degree = 180 \degree - 90 \degree}[/tex]
Subtract 90° from 180°
➺ [tex] \sf{3x \degree = 90 \degree}[/tex]
Divide both sides by 3
➺ [tex] \sf{ \frac{3x \degree}{3} = \frac{90 \degree }{3} }[/tex]
➺ [tex] \boxed{ \sf{x = 30 \degree}}[/tex]
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❑ Rules for solving an equation
If an equation contains fractions , multiply each term by the LCM of denominators.Remove the brackets, if any.Collect the terms with the variable to the left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '.Simplify and get the single term on each side.Divide each side by the coefficient of variable and then get the value of variable.Hope I helped!
Have a wonderful time ! ツ
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I GIVE CROWN
HELP ONLY SERIOUS HELP NOT FOR POINTS
This is one I’m stuck on
Answer:
1.109
2.264
3.462
Step-by-step explanation:
Jose uses 1/5 cup of red paint for every 3/5 cup of blue paint to make purple paint. Enter the number of cups of red paint Evelyn uses for 1 cup of blue paint.
Please help this is due tomorrow!!
What is the length of the line segment with endpoints (11, −4) and (−12, −4) ?
Answer:
23 units on the x axis
Step-by-step explanation: