A certain test preparation course is designed to help students improve their scores on the LSAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 6,16,19,12,15,14.
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal. Find the critical value that should be used in constructing the confidence interval.

Answers

Answer 1

Answer:

The critical value is [tex]T_c = 2.5706[/tex].

The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).

Step-by-step explanation:

Before building the confidence interval, we need to find the sample mean and the sample standard deviation:

Sample mean:

[tex]\overline{x} = \frac{6+16+19+12+15+14}{6} = 13.67[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(6-13.67)^2+(16-13.67)^2+(19-13.67)^2+(12-13.67)^2+(15-13.67)^2+(14-13.67)^2}{5}} = 4.4121[/tex]

Confidence interval:

We have the standard deviation for the sample, so the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 6 - 1 = 5

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.5706, that is, the critical value is [tex]T_c = 2.5706[/tex]

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.5706\frac{4.4121}{\sqrt{6}} = 4.63[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 13.67 - 4.63 = 9.04.

The upper end of the interval is the sample mean added to M. So it is 13.67 + 4.63 = 18.30.

The 90% confidence interval for the average net change in a student's score after completing the course is (9.04, 18.30).


Related Questions

3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}

A.657
B.2433
C. -843

Answers

Answer:

657

Step-by-step explanation:

pemdas

The value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

Hence option A is correct.

Given is an expression, 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]}, we need to simplify it,

Let's break down the expression step by step:

First, let's simplify the expression inside the innermost parentheses:

8 - 2 x 3 = 8 - 6 = 2

Next, let's simplify the expression inside the brackets:

3 x 23 - 2 = 69 - 2 = 67

Now, let's substitute the simplified expression inside the brackets back into the original expression:

(300 - 70 ÷ 5) - 67

Next, let's simplify the expression inside the remaining parentheses:

70 ÷ 5 = 14

Now, let's substitute the simplified expression inside the parentheses back into the expression:

(300 - 14) - 67

Next, let's simplify the expression inside the remaining parentheses:

300 - 14 = 286

Now, let's substitute the simplified expression inside the parentheses back into the expression:

286 - 67

Finally, let's perform the subtraction:

286 - 67 = 219

Now, let's multiply the result by 3:

3 x 219 = 657

Therefore, the value of the expression 3 x {(300 - 70 ÷ 5) - [3 x 23 - (8 - 2 x 3)]} is 657.

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The black graph is the graph of
y = f(x). Choose the equation for the
red graph.

a. y = f(x + 3)
b. y = f(x – 3)
c. y + 3 = f(x)
d. y - 3 = f(x)

Answers

9514 1404 393

Answer:

  b. y = f(x -3)

Step-by-step explanation:

The translation right h and up k units is ...

  y -k = f(x -h)

Here, the red graph is translated right 3 and up 0, so the translated function is ...

  y = f(x -3)

_____

Additional comment

You can check this if you like by listing a couple of corresponding points:

  y = f(x)

  1 = f(-3) . . . . left-most point on black graph.

The corresponding point on the red graph is (0, 1). Putting this into the equation (b), we get ...

  1 = f(0 -3) = f(-3) . . . . . correct value for f(-3)

e lifetimes of lightbulbs of a particular type are normally distributed with a mean of290 hours and astandard deviation of6 hours. What percentage of the bulbs have lifetimes that lie within 1 standarddeviation to either side of the mean

Answers

Answer:

Step-by-step explanation:

[tex]p(\overline{X}-\sigma \leq X \leq \overline{X}+\sigma)\\\\=p(\dfrac{\overline{X}-\sigma -\overline{X} }{\sigma} \leq Z \leq \dfrac{\overline{X}+\sigma -\overline{X} }{\sigma} )\\\\=p ( -1 \leq Z \leq 1)\\\\=2*(\ p (Z \leq 1)-0.5)\\\\=2*(0.8413-0.5)\\\\=0.6826\\\\\approx{68\%}[/tex]

What is the mean of 86, 80, and 95

Answers

87 is the mean.

To find the mean, you must

- add all of the numbers

- divide by the amount of numbers given

In this case, you would want to do (86 + 80 + 95)/3. This would give you an answer of 87.

87 is the answer.
Mean is the same thing as average so you just all the given numbers and divide by the number of terms given (in this case 3 were given)

the graph of f(x)=6(.25)^x and its reflection across the y-axis , g(x), are shown. what is the domain of g(x)

Answers

9514 1404 393

Answer:

  all real numbers

Step-by-step explanation:

The domain of any exponential function is "all real numbers". Reflecting the graph across the y-axis, by replacing x by -x does not change that.

The domain of g(x) = f(-x) is all real numbers.

NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!

Chapter 11 part 2:

What are three different properties of logarithmic functions when encountering the operations of addition, subtraction, and multiplication? Provide an example of each.

Answers

The three main log rules you'll encounter are

log(A*B) = log(A) + log(B)log(A/B) = log(A) - log(B)log(A^B) = B*log(A)

The first rule allows us to go from a log of some product, to a sum of two logs. In short, we go from product to sum. The second rule allows us to go from a quotient to a difference. Lastly, the third rule allows to go from an exponential to a product.

Here are examples of each rule being used (in the exact order they were given earlier).

log(2*3) = log(2) + log(3)log(5/8) = log(5) - log(8)log(7^4) = 4*log(7)

----------------

Here's a slightly more complicated example where the log rules are used.

log(x^2y/z)

log(x^2y) - log(z)

log(x^2) + log(y) - log(z)

2*log(x) + log(y) - log(z)

Hopefully you can see which rules are being used for any given step. If not, then let me know and I'll go into more detail.

Someone help please

Answers

9514 1404 393

Answer:

  B.

Step-by-step explanation:

The relation between a function f(x) and its inverse g(x) is ...

  f(g(x)) = g(f(x)) = x

On can compute these functions of functions, or take an easier route and do the computation with a couple of numbers. It is often easiest to use x=0 or x=1. If we find g(f(x)) ≠ x, then we know the functions are not inverses. If we find g(f(x)) = x for one particular value of x, then we need to try at least one more to verify the relation.

__

If we call the two given functions f and g, then we have ...

  A. f(0) = -2/3, g(-2/3) ≠ 0 . . . . not inverses

__

  B. f(0) = -3/2, g(-3/2) = 0 . . . . possible inverses

     f(1) = 4/2 = 2, g(2) = 7/7 = 1 . . . . probable inverses

__

  C. f(0) = -2, g(-2) = 0 . . . . possible inverses

     f(1) = 1/2, g(1/2) = -5/3 . . . . not inverses

__

  D. f(0) = 5, g(5) = 27 . . . . not inverses

_____

Additional comment

Our assessment above is sufficiently convincing to let us choose an answer. If we want to verify the functions are inverses, we need to graph them or compute f(g(x)). The graph in the second attachment shows each appears to be the reflection of the other in the line y=x, as required of function inverses.

Help me please and thank you

Answers

Answer:

Option C is correct

Step-by-step explanation:

[tex]log( {10}^{3} )[/tex]

Use logarithm rules to move 3 out of the exponent.

[tex]3 \: log \: (10)[/tex]

Logarithm base 10 of 10 is 1.

[tex]3×1[/tex]

Multiply 3 by 1.

[tex]3[/tex]

Hope it is helpful....
C is the correct answer

Please due in 1 hour

Answers

I hope that helped you

9514 1404 393

Answer:

d + q = 440.10d +0.25q = 8.30

Step-by-step explanation:

The first equation describes the total number of coins. It says the sum of the numbers of dimes and quarters is 44, the total number of coins.

__

The second equation describes the total value of the coins. It will say that 0.10 times the number of dimes plus 0.25 times the number of quarters is 8.30, the total dollar value of the coins.

The two equations are ...

  d + q = 44

  0.10d +0.25q = 8.30

__

Additional comment

The solution can be found by substituting for d:

  0.10(44 -q) +0.25q = 8.30

  0.15q = 3.90

  q = 26

  d = 44 -26 = 18

Vinnie has 18 dimes and 26 quarters in his bag.

Which equation represents an exponential function that passes through the point (2, 36)?
O f(x) = 4(3)
O fx) = 4(x)
O f(x) = 6(3)
O f(x) = 6(x)

Answers

Answer:              It would be the first equation because:

Step-by-step explanation:        

In order to be an exponential function, the X

variable has to be in the exponent, that eliminates

the second and fourth answers

       f(X) = 4(3)X

using the point (2,36)

  f(2) = 4 (3)2

         = 4 (9 )

         = 36

The equation which represents an exponential function is f ( x ) = 4 ( 3 )ˣ

What are the laws of exponents?

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the point on the graph be P ( 2 , 36 )

So , when x = 2 , the value of y = 36

f ( x ) = 4 ( 3 )ˣ   be equation (1)

when x = 2

f ( 2 ) = 4 ( 3 )²

f ( 2 ) = 4 x 9

f ( 2 ) = 36

Hence , the exponential equation is f ( x ) = 4 ( 3 )ˣ

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if 2/-5 x=-10/x what is the value of x​

Answers

Answer:

± 5

Step-by-step explanation:

2x/-5 = -10/x

2x^2 = 50

x^2 = 25

x = ± 5

Answer:

x=5

Step-by-step explanation:

Start with writing it like 2x/-5= -10/x

Then cross multiply: 2[tex]x^{2}[/tex]= 50

Divide by 2: [tex]x^{2}[/tex]=25

Square root of 25: 5

x=5

I’m new to this app and I need help with those two questions please help!!

Answers

y=x²-10x-7

a>0 so we will be looking for minimum

x=-b/2a=10/2=5

y=25-50-7=-32

Answer: (5;32)

y=-4x²-8x+1

а<0 so we will be looking for maximum

х=-b/2a=8/-8=-1

у=4+8+1=13

Maximum point (-1;13)

14. In a garden 746496 apple trees are arranged in such a way that, there are as inany rows as there are in a row. How many rows are there in the garden ​

Answers

Answer:

864

Step-by-step explanation:

do the square root of the total number

Explain why the equation x=x+1 is a contradiction

Answers

Answer:

It results in no solution.

Step-by-step explanation:

If you subtract x on both sides, this will leave you with 0 ≠ 3. The result is no solution. This is why it is contradictory.

Find the coordinates of the vertices of the figure after the given transformation: T<0,7>

A. X′(1,−1),L′(0,2),W′(2,1)
B. X′(−4,2),L′(−5,5),W′(−3,4)
C. X′(3,2),L′(2,5),W′(4,4)
D. X′(0,−3),L′(−1,0),W′(1,−1)

Answers

Answer: B

Step-by-step explanation:

Why did historians choose to study this topic?

f(x) = (2x – 1)(3x + 5)(x + 1) has zeros at I = -
1
cole
2= -1, and x =
What is the sign of f on the interval
5
<<
3
เล
?
Choose 1 answer:
А
f is always positive on the interval.
B
f is always negative on the interval.
f is sometimes positive and sometimes negative on the interval.

Answers

Interval of function f(x) is sometimes negative and sometimes positive.

What is interval of function?

The function interval is said to be positive if the value of the function f (x) increases with an increase in the value of x. In contrast, the function interval is said to be negative if the value of the function f (x) decreases with the increase in the value of x.

Given function,

f(x) = (2x – 1)(3x + 5)(x + 1),

Zeros of function,

x = 1/2 = 0.5

x = -5/3 = - 1.6667

x = -1

From the graph

Interval of function is negative between -∞ < x < -1.6667

Interval of graph is positive between -5/3 < x < -1

Interval of function is negative between -1 < x < 0.5

Interval of graph is positive 0.5 < x < ∞

Hence, f(x) has sometimes positive interval and sometimes negative interval.

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If side A is 10 inches long, and side B is 24 inches, find the length of the unknown side.

Answers

Step-by-step explanation:

Right Triangles and the Pythagorean Theorem. The Pythagorean Theorem, a2+b2=c2, a 2 + b 2 = c 2 , can be used to find the length of any side of a right triangle.

someone help me pls i need to pass summer school

Answers

16 to the 0 power 16 to the 0 power 16 to the 0 power 16 to the 0 power 16 to the 0 power

Answer:

A

Step-by-step explanation:

The be the inverse function the domain {4,5,6,7} becomes the range and the range {14,12,10,8} becomes the domain

14 → 4

12 →5

10 →6

8 →7

Help Please
2(-1+-4)-d^2

Answers

−d^2 + 7
Hope this helps !

Can someone help me with this plz

Answers

Answer:

170.7

Step-by-step explanation:

We are aware that the base is a square, with side lengths 8cm, and we are given that the height is 8 cm. Since the volume of a square based pyramid is 1/3 x base area x height, we receive 1.3 x 64 x 8 which is 512/3 which is in turn 170.666 recurring. However, since this question asks you to round the the nearest tenth, you get 170.7

Answer:

171

Step by step explanation:

Volume = lwh/3
= 8 x 8 x 8
≈171 km^3

Each time Kristine gets paid, she spends $20 and saves the rest. If the amount Kristine earns is represented by x and the amount she saves is represented by y, which graph models her savings?
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (5, 100) and (10, 200).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 1) and (40, 2).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (0, 20) and (10, 30).
A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Answers

Answer:

A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Step-by-step explanation:

If Kristine spends $20 and saves the rest when she gets paid, the amount she saves should always be 20 less than the amount she earned.

The points (20, 0) and (25, 5) accurately represent this, where x is how much she earns and y is how much she saves.

(20, 0) represents her earning $20 and saving $0, because she spends $20 every time she gets paid.

(25, 5) represents her earning $25 and saving $5, because she spent $20.

So, the correct graph is A graph titled Kristine's Savings has money earned on the x-axis and money saved on the y-axis. A line goes through points (20, 0) and (25, 5).

Answer:

d

Step-by-step explanation:

find the derivative of y=(x³-5)⁴(x⁴+3)⁵ ​

Answers

Answer:

[tex]12x^{2} (x^{3}-5)^{3} (x^{4}+3)^{5} +20x^{3} (x^{3}-5)^{4} (x^{4}+3)^{4}[/tex]

Step-by-step explanation:

The Online Exam from Applied Statistics consists of 6 questions. Statistics show that there is a 75% chance that the student will answer to any one of Exam problems correctly. If the number of attempts for each question is unlimited, find the following probabilities

a. The student will correctly answer the first question after the 4th attempt.
b. The student will correctly answer three questions after 10 total attempts.
c. What is the average number and SD of attempts up to when the student answers all the questions correctly?

Answers

Solution :

a). The probability that the student will [tex]\text{correctly answer}[/tex] the 1st question after the 4th attempt.

P (correct in the 4th attempt)

= [tex]$(1-0.75)^3 \times 0.75$[/tex]

= 0.01171875

b). The probability that the student will [tex]\text{correctly answer}[/tex] 3 questions after 10 total attempts.

P( X = 3) for X = B in (n = 10, p = 0.75)

= [tex]$C(10,30) \times 0.75^3 \times 0.25^7$[/tex]

= 0.0031

c). The mean and the standard deviation for the number of attempts up to when the students gets all the questions correct is :

There are = 6 success, p = 0.75.

Therefore, this is a case of a negative binomial distribution.

[tex]$E(X)=\frac{k}{p}$[/tex]

         [tex]$=\frac{6}{0.75}$[/tex]

         = 8

So, [tex]$\sigma = \frac{\sqrt{k(1-p)}}{p}$[/tex]

     [tex]$\sigma = \frac{\sqrt{6(1-0.75)}}{0.75}$[/tex]

        = 1.6330

Instructions: Find the missing side. Round your answer to the nearest tenth.
22
58°

Answers

Answer:

x = 19.2

Step-by-step explanation:

tan(58)=x/12

x=12×tan(58)

x=19.2

Answered by GAUTHMATH

The diameters of ball bearings are distributed normally. The mean diameter is 7373 millimeters and the variance is 44. Find the probability that the diameter of a selected bearing is less than 7676 millimeters. Round your answer to four decimal places.

Answers

Answer:

0.9332

Step-by-step explanation:

We are given that

Mean diameter, [tex]\mu=73[/tex]

Variance, [tex]\sigma^2=4[/tex]

We have to find the probability that the diameter of a selected bearing is less than 76.

Standard deviation, [tex]\sigma=\sqrt{variance}=\sqrt{4}=2[/tex]

[tex]P(x<76)=P(\frac{x-\mu}{\sigma}<\frac{76-73}{2})[/tex]

[tex]P(x<76)=P(Z<\frac{3}{2})[/tex]

Where [tex]Z=\frac{x-\mu}{\sigma}[/tex]

[tex]P(x<76)=P(Z<1.5)[/tex]

[tex]P(x<76)=0.9332[/tex]

Hence, the probability that the diameter of a selected bearing is less than 76=0.9332

−12x+y=10 in slope-intercept form

Answers

Answer:

y=12x+10

Step-by-step explanation:

Slope-intercept form is y=mx+b

1. Add -12x to both sides of the equation

identify an equation in point slope form for the line perpendicular to the y=-1/2x+11 that passes through (4,-8). a. y+8=1/2(x-4) b. y-4=2(x+8) c. y-8=1/2(x+4) d. y+8=2(x-4)

Answers

Answer:

d. y+8=2(x-4)

Step-by-step explanation:

There are 2 important parts to this question. First, understanding which slopes are perpendicular. The negative reciprocal of a number will be perpendicular to it. So, since the original slope is -1/2 the new slope should be 2.

Then, remember what the point-slope formula is. The point-slope formula is: [tex]y-y_{2}=m(x-x_{2})[/tex]. So if you plug in the point and slope the new equation looks like, [tex]y--8=2(x-4)[/tex]. Then, simplify for the final answer of [tex]y+8=2(x-4)[/tex].

I need help with ged

Answers

Answer:

General Educational Development (GED) tests

What do subject do you need help?

Step-by-step explanation:

The GED® exam is made up of 4 subjects, broken into separate exams: Mathematical Reasoning, Reasoning Through Language Arts, Social Studies, and Science.

Your car can go 2/7 of the way on 3/8 of a tank of gas how far can you go on the remaining gas?
A proportion that can be used is a/b=c/d

Answers

Answer:

10/21 of the distance

Step-by-step explanation:

2/7 distance

------------------

3/8 tank

The rest of the tank is 8/8 - 3/8 = 5/8

2/7 distance         x

------------------ = ----------------------

3/8 tank              5/8 tank

Using cross products

2/7 * 5/8 = 3/8x

10/56 = 3/8x

Multiply each side by 8/3

10/56 * 8/3 = 3/8x * 8/3

10/3 * 8/56=x

10/3 * 1/7 =x

10/21 =x

10/21 of the distance

i need help with this question asapppppp

Answers

9514 1404 393

Answer:

  $11,680.58

Step-by-step explanation:

Usually, I would say copy the example, using 70,000 instead of 55,000. However, the example you show has a couple of errors in it. You need to do what it says, not follow what it did.

__

The first 48,535 is taxed at 15%, so the tax is 0.15×48535 = 7280.25.

The next (70,000 -48,535) = 21,465 is taxed at 20.5%, so the tax is ...

  0.205×21,465 = 4400.325 ≈ 4400.33

The the total tax due on $70,000 is ...

  $7280.25 +4400.33 = $11,680.58 . . . . tax due on $70,000

_____

Additional comments

The example shown has a couple of errors. The tax on the excess amount is figured at 2.05%, not 20.5%, and the 132.53 value from that is shown as 132.23.

__

Any tax table like this one can be reduced to a set of simpler formulas. Here are the formulas for the brackets shown in your tax table.

  ≤ 48535 -- income × 0.15

  ≤ 97069 -- income × 0.205 -2669.425

  ≤ 150,473 -- income × 0.26 -8008.22

  ≤ 214,368 -- income × 0.29 -12,522.41

  > 214,368 -- income × 0.33 -21,097.13

In this case, the second row of this simpler table would give the tax on $70,000 as ...

  tax = 70,000 × 0.205 -2669.425

  tax = 14350 -2669.425 = 11680.575 ≈ 11,680.58 . . . same as above

Other Questions
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