The data below were obtained from an experiment were participants were given drinks with or without caffeine and then asked to tap their fingers. The data for 20 participants are below. Assume the number of taps per minute is normally distributed. The variance is unknown. Find a 95% CI for μ number of taps. Identify the pivot function used. 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242

Answers

Answer 1

Answer:

The  95% confidence interval is  [tex]244.26 < \mu < 246.95[/tex]  

The pivot function used is  

           [tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]

Step-by-step explanation:

From the question we are told that

  The  data given is 246 242 248 245 250 244 252 248 248 247 250 248 246 242 248 244 245 246 250 242

  The  sample  size is  [tex]n= 20[/tex]

   

Given that the confidence level is 95% then the level of significance is

      [tex]\alpha = (100 - 95)\%[/tex]

      [tex]\alpha = 0.05[/tex]

The  degree of freedom is mathematically represented as

    [tex]df = 20 -1[/tex]

    [tex]df = 19[/tex]

From the student t-distribution table  the critical value of  [tex]\frac{\alpha }{2}[/tex]  is  

          [tex]t_{\frac{\alpha }{2} , 19 } = 2.093[/tex]

The mean is mathematically represented as

          [tex]\= x = \frac{\sum x_i}{ n}[/tex]

         [tex]\= x = \frac{246+ 242 +248+245+ 250+ 244+252+ 248 +248 +247+ 250+ 248+ 246+ 242 +248 +244 +245 +246+ 250+ 242}{20}[/tex][tex]\= x = 246.6[/tex]

The standard deviation is mathematically represented as

            [tex]\sigma = \sqrt{\frac{\sum (x_i - \= x )^2)}{n} }[/tex]

           [tex]\sigma = \sqrt{\frac{(246- 246.6)^2 +(242- 246.6)^2 +(248- 246.6)^2 + (248- 245)^2+}{20} } \ ..[/tex]

             [tex]\ ...\sqrt{\frac{(250-246.6 )^2+ (244- 246.6)^2+(252- 246.6)^2+ (248- 246.6)^2+ (248- 246.6)^2+}{20} } \ ...[/tex]

              [tex]\ ..\sqrt{\frac{(247- 246.6)^2+ (250- 246.6)^2+ (248-246.6)^2+ (246-246.6)^2+ (242-246.6)^2+ (248-246.6)^2+ (244-246.6)^2+}{20} } \ ...[/tex]       [tex]\sqrt{\frac{ (245-246.6)^2+ (246-246.6)^2+ ( 246-246.6)^2 + ( 250-246.6)^2+ ( 242-246.6)^2 +( 246-246.6)^2+ ( 242-246.6)^2 }{20} }[/tex][tex]\sigma = 2.87411[/tex]

The margin of error is mathematically represented as

       [tex]E = t_{\frac{\alpha }{2} , 19} * \frac{\sigma }{\sqrt{n} }[/tex]

      [tex]E = 2.093 * \frac{2.87411 }{\sqrt{20} }[/tex]

      [tex]E = 1.345[/tex]

The 95% confidence interval is mathematically represented as

       [tex]\= x - E < \mu < \= x + E[/tex]

=>   [tex]245.6 - 1.345 < \mu <245.6 + 1.345[/tex]

=>    [tex]244.26 < \mu < 246.95[/tex]  

The pivot function used is  

           [tex]t = \frac{\=x - \mu}{ \frac{\sigma}{\sqrt{n} } }[/tex]

     


Related Questions

How do you do these questions? With step by step instructions please

Answers

Answer:         n = 3                                              n = 4                

               Upper Sum ≈ 3.41                      Upper Sum ≈ 3.25

               Lower Sum ≈ 2.15                      Lower Sum ≈ 2.25

Step-by-step explanation:

You are trying to find the area under the curve.  Area = height x width.

Height is the y-value at the given coordinate --> f(x)

Width is the distance between the x-values --> dx

n = 3

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 3 sections because n = 3 --> dx = 2/3

So the points we will evaluate is when x = {-1, -1/3, 1/3, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/3) = 1 + (-1/3)² = 1 + 1/9 --> 10/9

f(1/3) =  1 + (1/3)² = 1 + 1/9 --> 10/9

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/3}          f(-1) = 2                   f(-1/3) = 10/9

{-1/3, 1/3}        f(-1/3) = 10/9           f(0) = 1   (vertex lies in this interval)

{1/3, 1}             f(1) = 2                   f(1/3) = 10/9

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\quad A=\dfrac{2}{3}\bigg(2+\dfrac{10}{9}+2\bigg)\\\\.\qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{46}{9}\bigg)\\\\.\qquad \qquad \qquad =\dfrac{92}{27}\\\\.\qquad \qquad \qquad =\large\boxed{3.41}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{2}{3}\bigg(\dfrac{10}{9}+1+\dfrac{10}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{2}{3}\bigg(\dfrac{29}{9}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{58}{27}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.15}[/tex]

*****************************************************************************************

n = 4

First, let's figure out dx:  the distance from -1 to +1 is 2 units. We need to divide that into 4 sections because n = 4 --> dx = 2/4 = 1/2 (simplified)

So the points we will evaluate is when x = {-1, -1/2, 0, 1/2, 1}

For the upper sum, we find the max y-value for each interval

For the lower sum, we find the min y-value for each interval

Next, let's find the height for each of the x-values:

f(x) = 1 + x²

f(-1) = 1 + (-1)²   = 2

f(-1/2) = 1 + (-1/2)² = 1 + 1/4 --> 5/4

f(0) = 1 + (0)² = 1

f(1/2) =  1 + (1/2)² = 1 + 1/4 --> 5/4

f(1) = 1 + (1)²   = 2

Interval         Max                      Min

{-1, -1/2}          f(-1) = 2                   f(-1/2) = 5/4

{-1/2, 0}          f(-1/2) = 5/4            f(0) = 1  

{0, 1/2}           f(1/2) = 5/4             f(0) = 1

{1/2, 1}            f(1) = 2                   f(1/3) = 5/4

Now, let's find the Area: A = f(x) dx:

[tex]\text{Upper Sum:}\qquad A=\dfrac{1}{2}\bigg(2+\dfrac{5}{4}+\dfrac{5}{4}+2\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{26}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{13}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{3.25}[/tex]

[tex]\text{Lower Sum:}\qquad A=\dfrac{1}{2}\bigg(\dfrac{5}{4}+1+1+\dfrac{5}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{1}{2}\bigg(\dfrac{18}{4}\bigg)\\\\\\.\qquad \qquad \qquad \qquad =\dfrac{9}{4}\\\\\\.\qquad \qquad \qquad \qquad =\large\boxed{2.25}[/tex]

what is -3.5+(-4.9)=?What is the answer please?

Answers

Answer:

The answer is  -8.4

The probability of a student passing
an examination is 2/3
If the student
takes three examination, what is the
Probability that he will not
pass
any of them.​

Answers

Answer:  1/27

===============================================

Explanation:

2/3 is the probability of passing a test, so 1/3 is the probability of failing

Note how 2/3 and 1/3 add to 3/3 = 1 to represent 100%

The probability of failing 3 tests in a row is (1/3)^3 = (1/3)*(1/3)*(1/3) = 1/27 assuming each test event is independent from one another.

-------

Side note: the probability of passing at least one test is 1-1/27 = 26/27 and the probability of passing all three tests in a row is (2/3)^3 = 8/27

What is 30/35 in simplest form? ​

Answers

What is 30/35 Simplified? - 6/7 is the simplified fraction for 30/35.

Answer: 6/7

Step-by-step explanation:

I'm trying to find sin of (7pi/12) exactly using an angle of addition or subtraction formula could anyone help me​

Answers

Answer:

(√2 + √6)/4.

Step-by-step explanation:

Use the addition formula

sin (A+ B) = sinAcosB + cosAsinB

sin (7pi/12) =  sin( 3pi/12 + 4pi/12)

= sin(pi/4 + pi/3) =  sin pi/4 cos pi/3 + cos pi/4 sin pi/3

= 1/√2 * 1/2 + 1/√2 * √3/2     (using the 45-45-90 and 30-60-90 triangles)

= 1 / 2√2 + √3/2√2

=   √2/4 + √6/4

= (√2 + √6)/4

y varies inversely with x. If y = 5 when x = 60, find y when x = 150
pre cal

Answers

Answer:

y = 2  when x = 150

Step-by-step explanation:

Inverse variation is

xy = k

5*60 = k

300 = k

xy = 300

150y = 300

Divide by 150

150y/150 = 300/150

y = 2

T is the midpoint of SU, ST = 8x + 11 and TU = 12x-1, find the value of x.

Answers

Answer:

x = 3

Step-by-step explanation:

mid point means it bisects the segment into two equals halfs meaning

ST = TU

8x + 11 = 12x - 1

8x + 12 = 12x

12 = 4x

3 = x

Brayden is working two summer jobs, making $18 per hour lifeguarding and making $9 per hour clearing tables. In a given week, he can work no more than 19 total hours and must earn a minimum of $270. If Brayden worked 14 hours lifeguarding, determine the minimum number of whole hours clearing tables that he must work to meet his requirements. If there are no possible solutions, submit an empty answer.

Answers

Answer: The amount he earns from lifeguarding = $252 ($18×14). The total amount he needs to make a week is $270.

$270-$252=$18, he needs to earn $18 more from clearing tables.

$18÷9=2, so the minimum number of whole hours clearing tables is 2

A bag contains 6 RED beads, 3 BLUE beads, and 11 GREEN beads. If a single bead is picked at random, what is the probability that the bead is RED or GREEN?

Answers

Answer:

17/20

Step-by-step explanation:

Total no. of beads = 6 + 3 + 11 = 20

We need RED or GREEN bead .

So no. of beads needed = 6 + 11 = 17

So probability of getting GREEN or RED beads = 17/20

a vegetable farmer fills 2/3 of a crate with 5/7 of a pound of tomatoes. how many lbs can fit in one crate​

Answers

Answer:

1 1/14 lbs

Step-by-step explanation:

We can use ratios to solve

2/3 crate        1 crate

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

5/7 lb                 x lbs

Using cross products

2/3x = 5/7 *1

Multiply each side by 3/2

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

x = 15/14

x = 1 1/14

Answer:

[tex]\huge\boxed{\sf 1 \ crate = \frac{15}{14} \ lbs}[/tex]

Step-by-step explanation:

[tex]\sf \frac{2}{3}\ of \ a\ crate = \frac{5}{7} \ of \ a\ pound \\\\We \ need \ to \ find\ the \ weight \ of \ one \ crate\\\\So, Multiplying \ both \ sides \ by \ the\ reciprocal \ of \ \frac{2}{3} \ i.e. \frac{3}{2} \\\\1 \ crate = \frac{5}{7} * \frac{3}{2} \ lbs\\\\1 \ crate = \frac{5*3}{7*2} \ lbs\\\\1 \ crate = \frac{15}{14} \ lbs[/tex]

The grades in period 3 Algebra 2 have an average of 82% and vary by 12 percentage points. Formulate an absolute value equation that could be used to solve for the maximum and minimum grade.

|x______ | = _______

x = __________ (smaller number here)

x = _______ (larger nember here)

Blank 1:
Blank 2:
Blank 3:
Blank 4:

Answers

Answer:

[tex]|x - 85| = 12[/tex]

[tex]x = 73 \ (smaller\ number )[/tex]

[tex]x = 97 \ (larger \ number )[/tex]

Step-by-step explanation:

From the question we are told that

  The  grade is  [tex]k = 85\%[/tex]

   The  variation is  [tex]v = 12 \%[/tex]

Generally the absolute value equation is mathematically represented as

        [tex]|x - 85| = 12[/tex]

=>  [tex]x -85 = \pm 12[/tex]

So

    [tex]x = 85 + 12[/tex]

    [tex]x = 97 \ (larger \ number )[/tex]

And

     [tex]x = -12 + 85[/tex]

=>  [tex]x = 73 \ (smaller\ number )[/tex]

Write the equation of the line PERPENDICULAR to y = 3/2x + 6 that passes through the point (-3, 4).

Answers

Answer:

Step-by-step explanation:

perp. -2/3 slope

y - 4 = -2/3(x + 3)

y - 4 = -2/3x - 2

y = -2/3x + 2

A plane is a _____ figure

Answers

Answer:

bold

Step-by-step explanation:

hshsjjsududidididiidododododokdodkdjdndndnjdudududuididjdjdjd

A plane is a two dimensional figure.

Find a unit vector that is orthogonal to both i + j and i + k.

Answers

Answer: i - j - k

Step-by-step explanation:

Taking the cross product between two vectors will give you a third vector that is orthogonal(perpendicular) to both vectors.

<1,1,0> x <1,0,1>

[tex]det(\left[\begin{array}{ccc}i&j&k\\1&1&0\\1&0&1\end{array}\right] )[/tex]

the determinate of the matrix: <1,-(1),-1>

or: i - j - k

alex buys six equally priced candy bars for $9:00 what is the unit rate?

Answers

Answer:

$1.5 unit

Step-by-step explanation:

According to the given situation, the calculation of the unit rate is shown below:-

Candy bars = 6

Amount of candy bars = $9:00

Unit rate

[tex]= \frac{Amount\ of\ candy\ bars}{Number\ of\ candy\ bars}[/tex]

Now we will put the values into the above formula

[tex]= \frac{\$9:00}{6}[/tex]

Which gives result

= $1.5 unit

Therefore for computing the unit rate we simply divide the amount of candy bars by the number of candy bars.

When you woke up this morning, the temperature was -5.8°C. At noon, the temperature was 2.9°C. Which expression and statement describes the situation?

Answers

Answer:

-5.8<2.9

Step-by-step explanation:

do all sets have subsets?

Answers

Answer:

yes

Step-by-step explanation:

Amy, Ray, Kim, and Jamal are on a trivia team. They gain points for correct answers
and lose points for incorrect answers. During the contest, Amy gains 3 points, Ray loses
4 points, Kim loses 2 points, and Jamal gains 5 points. How many points does the team
have at the end of the contest?

Answers

Answer:

2 points

Step-by-step explanation:

0+3-4-2+5=2 points

Skip count by twos.
30,_ _ _ _ _ _ _ _ _,50.

Answers

30,32,34,36,38,40,42,44,46,48,50

An open top box is to be made by a 24 in by 24 in. by 36 in. piece of cardboard by removing a square from each corner of the box and folding up the flaps on each side. What size square should be cut out of each corner to get a box with the maximum volume?

Answers

Answer:

X= -12 +6√10

X= 6.973

Step-by-step explanation:

Volume of the box= (36-2x)(24-2x)x

Volume of the box

=( 864 -96x -4x²)x

But 864 -96x -4x²

=216 - 24x-x²

Solving for x quadratically

X= (24+12√10)/-2

X= -12 -6√10

X= -30.97

Or

X= (24-12√10)/-2

X= -12 +6√10

X= 6.973

X will definitely be a positive number

So X= -12 +6√10

X= 6.973

Increasing or decreasing the side length of the square that gives the

maximum volume, gives a volume that is less than the maximum.

The side length of the cut out square to get a box with the maximum volume is approximately 4.71 in.

Reasons:

The given dimensions of the box = 24 in. by 36 in.

Let x represent the dimensions of the square removed from the corners, we have;

Width of box = 24 - 2·x

Length of box = 36 - 2·x

Height of the box = x

Volume of a box = Width × Length × Height

Therefore;

Volume of the box, V = (24 - 2·x)·(36 - 2·x)·x = 4·x³ - 120·x² + 864·x

At the maximum or minimum point of the volume, we have;

[tex]\displaystyle \frac{dV}{dx} = \mathbf{ \frac{d}{dx} \left(4 \cdot x^3 - 120 \cdot x^2 + 864 \cdot x \right )} = 0[/tex]

Which gives;

12·x² - 240·x + 864 = 0

x² - 20·x + 72 = 0

Which gives;

[tex]\displaystyle x = \dfrac{20\pm \sqrt{(-20)^{2}-4\times 1\times 72}}{2\times 1} = \mathbf{10 \pm 2\cdot \sqrt{7}}[/tex]

At x = 10 + 2·√7, we have;

[tex]\displaystyle 10 + 2 \cdot \sqrt{7} > \frac{24}{2}[/tex]

2 × (10 + 2·√7) in. > 24 in. which is the width of the cardboard

Therefore, (10 + 2·√7) is too long to be cut from the cardboard

At x = 10 - 2·√7, we have;

V = 4·(10 - 2·√7)³ - 120·(10 - 2·√7)² + 864·(10 - 2·√7) ≈ 1,828.3

Therefore;

The maximum volume corresponds with a cut out square of side length x = 10 - 2·√7 inches  ≈ 4.71 inches

The size of the square to be cut out each corner is x ≈ 4.71 inches

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fatima bought an xbox game that is 38.00 plus 9% sales tax what is the sales tax on the xbox game that fatima purchased answer

Answers

The tax is $3.42.

I used proportions to find the answer.

Part Percent
——— = —————.
Whole 100

Then, cross multiply.

Part • 100
—————
Percent • Whole

Finally, divide the numerator by the denominator. If you apply these steps to your problem, you will get $3.42.

Find g(-2) + h(4) if g(x)= 5-2x and h(x) = - x2 pls help

Answers

Answer:

-7

Step-by-step explanation:

g(x)= 5-2x and h(x) = - x^2

g(-2) + h(4)

First find g(-2)

g(-2) = 5 -2(-2) = 5 +4 = 9

Then find h(4) = - 4^2 = -16

g(-2) + h(4) = 9-16 = -7

Answer:

-7

Step-by-step explanation:

Substitute -2 into g(x) equation,

g(x) = 5 - 2x

g(-2) = [5 - 2(-2)] = 9

Substitute 4 into h(x) equation,

h(x) = -x^2

h(4) = [-(4)^2] = -16

Therefore,

g(-2) + h(4) = 9 + (-16) = -7

Your math teacher is only giving three tests this quarter. They count equally and your quarter grade will be the average of the tests. You scored a 79% on the first test and an 84% on the second test. If your quarter grade is below a 75% you will be grounded from your phone. What scores will get you into trouble on your report card?

Answers

3 tests at 75% each = 3 x 75 = 225 total points

First two tests = 79 + 84 = 163

Third test needs to be at least: 225 - 163  = 62%

So any score less than 62 would get you into trouble.

There was 1 liter of water in the water bottle. Tom drank 200 milliliters of water. How many liters of water are left?

Answers

Answer:

.8L

Explanation:

Logic

The liters of water left are 0.8 liters.

What is an Equation?

An equation is a mathematical statement formed when two algebraic expressions are equated using an equal sign.

The equations are useful in the determination of unknown parameters.

The quantity of water in a water bottle is 1 liter.

The amount of water Tom drank is 200 milliliters.

Let x be the amount of water left in the bottle.

The liter has to be converted into milliliters.

1 liters = 1000 milliliters

The equation formed is,

1000 - 200 = x

x = 1000 - 200

x = 800 milliliters.

The water left in the water bottle is 800 milliliters.

1000 milliliters = 1 liters

800 milliliters = 0.8 liters

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Point R is on line segment QS. Given RS = 13 and QS = 20, determine the length of QR

Answers

Answer:

Length of QR = 7

Step-by-step explanation:

20 - 13 = 7

Emma and Clair are planning to sell lemonade on their street. They have two recipes to choose from. Emma’s recipe calls for the juice of 5 lemons and 2 cups of water. Clair’s recipe calls for the juice of 2 lemons and 1 cup of water. Why will the first recipe taste more “lemony”?

Answers

Answer:

Emma's recipe will be more lemony because

5/2=2.5

2/1=2

Step-by-step explanation:

Answer:

The ratio of lemon juice to water in Emma’s recipe is 5 to 2; the ratio in Clair’s recipe is 4 to 2. Emma’s recipe will taste more lemony because it has a greater ratio of lemon juice to water.

Step-by-step explanation:

Sample Answer

A factory worker can produce 28 toys in an eight hour day If there are 42 workers in total how many toys are produced every hour ​

Answers

Answer:

147 toys

Step-by-step explanation:

for 1 person, 28toys/8hours = 3.5toys/ 1hour

for 42 people, 42 * 3.5toys/ 1hour = 147 toys/hour

~Hope it Helps!~

Students in a large statistics class were randomly divided into two groups. The first group had a midterm exam that was printed on canary paper while the second group had the exam printed on pale green paper. The exam scores of the two groups were then then compared.This experiment was not blind because:_______a. Students were allowed to keep their eyes open while taking the exam.b. The exam was too long.c. The students knew whether or not music was playing while they were taking the exam.d. Some of the students did not study for the exam.e. Students were randomized into the two groups.

Answers

Answer:

e. Students were randomized into the two groups.

Step-by-step explanation:

What is the measure of r

Answers

130 degrees

360-100=260
260/2=103

Answer:

The two marks on the right and left side of the triangle means that it's an isosles triangle which means that the base angles are equal and any triangle in the world the sum of its angles is 180° and you have an angle with 100° so you should subtract 100 from 180 that gives 80° and dived 80 by 2 that gives you 40°

Glados
spent the day at the mall, First, she bought
three bikes for $10 each. Later, she found 22
dollar bills. Write the total change
an integer.
to Glado's
funds as an integer

Answers

Answer:

8

Step-by-step explanation:

Other Questions
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