Given two independent random samples with the following results:n1=13x‾1=186s1=33 n2=13x‾2=171s2=23Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.Step 1 of 3 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Complete Question
Given two independent random samples with the following results:
[tex]n_2=13\ , \= x_2=171\ s_1=23[/tex]
Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 90% confidence interval. Round your answers to the nearest whole number.
Answer:
Step 1 of 3:
[tex]\= x_p = 15[/tex]
Step 2 of 3:
[tex]E =7.79[/tex]
Step 3 of 3:
[tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]
Step-by-step explanation:
Now considering the Step 1 of 3, the point estimate that should be used in constructing the confidence interval is mathematically represented as
[tex]\= x_p = \= x_1 - \= x_2[/tex]
=> [tex]\= x_p = 186 - 171[/tex]
=> [tex]\= x_p = 15[/tex]
Now considering the Step 2 of 3
Given that the confidence level is 90% then the level of significance is mathematically represented as
[tex]\alpha = (100-90)\%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
=> [tex]df = 13 + 13 - 2[/tex]
=> [tex]df = 24[/tex]
From the student t-distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24 \ is \ \ t_{\frac{\alpha }{2} ,df} = 1.711[/tex]
Generally the pooled variance is mathematically represented as
[tex]s_p^2 = \frac{ (13 -1 ) 33^2 + (13 -1 ) 23^2 }{(13 - 1 )(13 - 1)}[/tex]
[tex]s_p^2 = 134.83 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2} ,df } * \sqrt{\frac{s_p^2}{n_1} +\frac{s_p^2}{n_2} }[/tex]
=> [tex]E = 1.711* \sqrt{\frac{134.83}{13} +\frac{134.83}{13}}[/tex]
=> [tex]E =7.79[/tex]
Now considering the Step 3 of 3
Generally the 90% confidence interval is mathematically represented as
[tex]\= x_p -E < \mu_1 - \mu_2 < \= x_p +E[/tex]
=> [tex] 15 -7.79 < \mu_1 - \mu_2 < 15 +7.79[/tex]
=> [tex] 7.21 < \mu_1 - \mu_2 < 22.79[/tex]
Three students from a 16 student class will be selected to attend a meeting. 6 of the students are female
I think you want 8/3 or 2.666666 or mabye 37%
what is 2/3 + 1/2 equal?
Answer: To add fractions, find the LCD and then combine.
Exact Form:
7 /6
\(￣︶￣*\)) Hope this helps!!
Answer:
7/6
Step-by-step explanation:
2/3+1/2
4/6+3/6
4+3/6
7/6
6. How many 1/2 hour periods will make up 4 hours?
Answer: it will take 8 periods of 1/2 hour to make up 4 hours
Step-by-step explanation:
It will take 8 periods of 1/2 hour to make up 4 hours.
What are Arithmetic operations?Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.
Half an hour is 30 minutes,
There are 60 minutes in an hour.
4 hours=240 minutes.
240/30 = 8
Hence, 8 periods of 1/2 hour to make up 4 hours.
Learn more about Arithmetic operations
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When using the power rule, the original coefficient:__________a) Is multiplied by the original exponent.b) Only changes if the function is in terms of x.c) Is ignored
Answer:
a) Is multiplied by the original exponent.
Step-by-step explanation:
the power rule works like this:
you want to find the derivative of ax ⁿ
where n is the exponent and a is the coefficient
the derivative would equal (n ⋅ a)xⁿ⁻¹
e.g. you want to find the derivatives of 5x⁴
f'(x) = (4 ⋅ 5)x⁴⁻¹ = 20x³
f''(x) = (3 ⋅ 20)x³⁻¹ = 60x²
f'''(x) = (2 ⋅ 60)x²⁻¹ = 120x
f''''(x) = (1 ⋅ 120)x¹⁻¹ = 120
MATH please heeeeeeelp
Step-by-step explanation:
Its additive inverse!
Marty drew a model of the school library. The total area of the floor is 132 square
centimeters. What is the area of the shaded part of the model shown below?
10 centimeters
6 centimeters
Answer:
Step-by-step explanatio11n:
116
Which of the x-values are solutions to the following inequality
In science class, Sarah calculates the mass of a planet to be 918,000,000,000,000,000,000 kg. What is the mass of the planet in scientific notation? 91.8×1019 kg 9.18×10−20 kg 918×1018 kg 9.18×1020 kg
Answer:
Step-by-step explanation:
↘↘↘↙↙↖↗↙↖
I don't understand this
Answer:
tytytytyt
Step-by-step explanation:
Answer:
i don't either
Step-by-step explanation:
Joe borrowed $8,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 3 years?
Answer:
$1680
Step-by-step explanation:
make use of the simple interest formula:
PRT/100
P is the principle ($8000)
R is the rate of interest (7%)
T is the time (3)
= 8000*7*3 / 100
1680
which of the following is NOT true?
If the endpoints of a segment are (3,0), and (0, 3), the length of the segment is approximately 4.24 units.
If the endpoints of a segment are (3,-3), and (5,-5), the length of the segment is approximately 4.24 units.
The Pythagorean Theorem can be used to find the length of a segment.
The Distance Formula can be used to find the length of a segment.
Answer:
The answer is: If the endpoints of a segment are (3,-3), and (5,-5), the length of the segment is approximately 4.24 units.
Step-by-step explanation:
The value of x in the equation (12x − 36) = 5x + 18 is .
Answer:
[tex]x = \frac{54}{7} [/tex]Step-by-step explanation:
(12x − 36) = 5x + 18
First of all remove the parenthesis
That's
12x - 36 = 5x + 18
Next subtract 5x from both sides of the equation
We have
12x - 5x - 36 = 5x - 5x + 18
7x - 36 = 18
Add 36 to both sides of the equation
That's
7x + 36 - 36 = 18 + 36
7x = 54
Divide both sides by 7
[tex] \frac{7x}{7} = \frac{54}{7} [/tex]
We have the final answer as
[tex]x = \frac{54}{7} [/tex]
Hope this helps you
Answer: x=54/7
Step-by-step explanation:
To find the value of x, we need to use algebraic properties to isolate x.
12x-36=5x+18 [subtract both sides by 5x]
7x-36=18 [add both sides by 36]
7x=54 [divide both sides by 7]
x=54/7
Now, we know that x=54/7.
The center of circle P is at (-3, 8) and the radius is 12
units. Find its equation.
Answer:
The answer is
x² + y² + 6x - 16y - 71 =0Step-by-step explanation:
The equation of a circle is given by
( x - a)² + ( y - b)² = r²where ( a , b) is the center of the circle and
r is the radius
From the question the center is
P (-3, 8) and radius = 12
Substitute the values into the above formula and solve
That's
( x + 3)² + ( y - 8) = 12²
Expand the terms
That's
x² + 6x + 9 + y² - 16y + 64 = 144
Arrange the terms
x² + y² + 6x - 16y + 9 + 64 - 144 = 0
We have the final answer as
x² + y² + 6x - 16y - 71 =0Hope this helps you
7. Identify the explicit formula for the sequence given by the recursive formula
Answer: B) f(n) = 30 - 8(n - 1)
Step-by-step explanation:
Explicit formula is of the form: [tex]a_n=a_1+d(n-1)[/tex] where
[tex]a_1[/tex] is the first term d is the difference between consecutive termsGiven: f(1) = 30 --> this represents the first term [tex]a_1[/tex] = 30
f(n - 1) - 8 --> this means the previous term minus 8 thus d = -8
[tex]a_n[/tex] = 30 + (-8)(n - 1)
= 30 - 8(n - 1)
Answer:
B. f(n) = 30 – 8(n – 1)
Step-by-step explanation:
got it right on test
a rectangular with a perimeter of 32 cm has a base of x-3 cm and a height of 2x+7 cm what are the length in cm of the rectangle base an height
Answer:
Step-by-step explanation:
Perimeter = 32
length = x - 3
width = 2x + 7
Perimeter = 2* Length + 2* width
Perimeter = 2*(x-3) + 2(2x + 7) = 32 Remove the brackets.
2x - 6 + 4x + 14 = 32 Combine
6x + 8 = 32 Subtract 1 from both sides
6x = 32 - 8
6x = 24 Divide by 6
x = 24/6
x = 4
So the base = x - 3 = 4 - 3 = 1
The height = 2*4 + 7 = 8 + 7 = 15
(Multiple choice)
The quotient of a number and 17 is 118.82.
A. it can be solved with division property of equality.
B. It can be solved with the multiplication property of equality
C. The equation should x/17=118.82
D.x=7
E. X=2020
Answer:
C. The equation should x/17=118.82
Step-by-step explanation:
We know that
Dividend ÷ Divisor = Quotient
Dividend/Divisor = Quotient
From the question, we are told that:
The quotient of a number and 17 is 118.82
Let us represent the unknown number as x = Dividend
17 = Divisor
Quotient = 118.82
Hence,
x / 17 = 118.82
Cross Multiply
x = 17 × 118.82
x = 2019.94
The correct answer = Option C. The equation should x/17=118.82
Which number is not equal to one of the following expressions
Answer:150,000
Step-by-step explanation:
1500×10=15000
150,000÷100=1500
1500÷10=150
So 150,000 is not an answer in one the expressions
Answer:150,000
Step-by-step explanation:
Earth is 149 597 890 km from the sun. Pluto is about 39.5 times farther away from the sun than earth. how far is pluto from the sun? round your answer to three digits and express it in scientific notation.
Answer:
39.5 astronomical units
Suppose we want a 99% confidence interval for the average amount spent on books by freshmen in their first year at college. The amount spent has a normal distribution with standard deviation $34. (a) How large should the sample be to guarantee the margin of error will be no more than $3?(b) If we wanted a smaller margin of error, we would need a sample. (Enter: ''LARGER'', ''SMALLER'' or ''SAME SIZE'', without the quotes.)
Answer:
a) 855
b) We would need a Larger sample.
Step-by-step explanation:
(a) How large should the sample be to guarantee the margin of error will be no more than $3?
The formula for Margin of Error = z × Standard deviation/√sample size
z = z score of 99% confidence interval = 2.58
Standard deviation = $34
Sample size = n = unknown
Margin of Error = $3
√n = z × Standard deviation/Margin of Error
Square both sides
n = (z × standard deviation/Margin of Error)²
n =( 2.58 ×34/ 3)²
n = (29.24)²
n = 854.9776
Approximately, the size of the sample be to guarantee the margin of error will be no more than $3 is 855
(b) If we wanted a smaller margin of error, we would need a sample. (Enter: ''LARGER'', ''SMALLER'' or ''SAME SIZE'', without the quotes.)
We would need a Larger sample.
This is because, the larger the sample, the smaller the margin of Emerror and the smaller the sample, the larger the margin of error. Therefore, for the question b, we would be needing a larger sample.
3/7➗4/5= How do you solve this problem, step by step?
A car is traveling down a highway at a constant speed, described by the equation d=65t, where d represents the distance, in miles, that the car travels at this speed in t hours. How many miles does the car travel in 1.5 hours?
Answer:
A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels - 1138… ... How many miles does it take the car to travel 26 miles at this speed? c. ... the distance, in miles, that the car travels at this speed in t hours.
Step-by-step explanation:
Hope this helps
(15.x + 79)
(5x + 61)
Answer:
A) 15x +79 = z
B) 15x +79 + 5x + 61 = 180
20x + 140 = 180
20x = 40
x = 2
Then using equation A)
A) 15 * 2 + 79 = z
30 + 79 =z
z = 109
Step-by-step explanation:
Please help quick !!!!!! Simplify 6(x + 4).
Answer:
6(x + 4)
opening brackets
=6x+24 is the answer
Step-by-step explanation:
22 must lie between the whole numbers
and
Please help!! What is the quotient??
At the city museum, child admission is $5.20 and adult admission is $9.20. On Friday, 157 tickets were sold for a total sales of $1068.40. How many adult tickets were sold that day?
solve for x 4 - (x + 2) < -3(x + 4)
in 4 - (x + 2) < -3(x + 4), x < -7
isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
x<-7
Step-by-step explanation:
Use inverse operations to solve
4 - ( x + 2 ) < -3 ( x+ 4)
first distribute the (-) sign and the (-3)
4 -x -2 < -3x -12
simplify
2 -x < -3x -12
simplify again, with inverse operations
2 -x < -3x -12
+3x +3x
2 + 2x < -12
-2 -2
2x < -14
/2 /2
x<-7
Is - 6/5 rational or irrational?
Answer:
lt is rational number .
If you get this you are a critical thinker. I enter the garden. There are 34 people. You kill 30. How many people are in the garden. Good luck! If you get it correct your answer will be deleted and I will message you to continue the game. Don't play if you are not going to continue.
Answer:
35 counting yourself.........34 not