A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over the age of 55, 68 dream in black and white and among 288 people under the age of 25, 19 dream in black and white. Use a 0.05 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those underIdentify the test statistic?Identify the p value?Test the claim by constructing an appropriate confidence level?What is the conclusion base on the hypothesis test?What is the conclusion base on the confidence level?

Answers

Answer 1

Answer:

he proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Step-by-step explanation:

In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The hypothesis can be defined as follows:  

H₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. p₁ - p₂ ≤ 0.  

Hₐ: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. p₁ - p₂ > 0.  

The information provided is:

n₁ = 290

n₂ = 288

X₁ = 68

X₂ = 19

Compute the sample proportions and total proportions as follows:

 [tex]\hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}[/tex]

    [tex]=\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67[/tex]

The test statistic value is 5.67.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 [tex]p-value=P(Z>5.67)\\=1-P(Z<5.67)\\=1-\approx1\\=0[/tex]

The p-value of the test is quite small.

The null hypothesis will be rejected at 5% significance level.

Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The significance level of the test is 5%.

Then the confidence level will be:

Confidence level = 100% - Significance level

                             = 100% - 5%

                             = 95%

Compute the 95% confidence interval for the difference between proportions as follows:

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

The critical value of z for 95% confidence level is z = 1.96.

[tex]CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}[/tex]

      [tex]=(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)[/tex]

The null hypothesis would be rejected if the null value, i.e. (p₁ - p₂) ≤ 0 is not contained in the interval.

The 95% confidence interval consist of values greater than 0.

Thus, the null hypothesis will be rejected.

Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).


Related Questions

Please help quicklyyy!Zachary sold his stock in a computer company. He received $34 per share. This was $8 less
than twice what he paid for it. What was the price of the computer stock per share when he
bought it?

Answers

Answer:

Hey there!

Let x be the price he paid for.

2x-8=34

2x=42

x=21

He bought the stock for 21 dollars.

Hope this helps :)

Answer:

The price per share  when he bought it was 21

Step-by-step explanation:

Let x = price he paid for the stock

34 = 2x-8

Add 8 to each side

34+8 = 2x-8 +8

42 = 2x

Divide by 2

42/2 = 2x/2

21 = x

The price per share  when he bought it was 21

please help me Which of the following choices will evaluate the function ƒ(x) = -(-x), when x = -3? 3 -1 -3 None of these choices are correct.

Answers

Answer:

-3

Step-by-step explanation:

Given the function f(x) = -(-x)

we want to evaluate f(-3)

What we do simply here is substitute the value of -3 for x in the equation

That would be ;

f(-3) = -(-(-3)) = -(3) = -3

Tim wants to build a rectangular fence around his yard. He has 42 feet of fencing. If he wants the length to be twice the width, what is the largest possible length? Write an equation and solve.

Answers

Answer:

Rectangular fence dimensions:

x = 14 ft

w = 7  ft

A  = 98 ft²

Step-by-step explanation:

Rectangular fence dimensions:

x   length      and     w  width

Then   x  =  2*w      ⇒     w = x/2

Perimeter is

p = 2*x + 2*w

p = 2*x + 2* x/2

p = 2*x + x

3*x = 42

x = 14  ft      and     w = 14/2      ⇒     w = 7  ft

this diagram shows a scale drawing of a playground the scale is ___ 1:500 work out the perimeter of the real playground give your answer in meters

Answers

Answer:

The perimeter of the actual playground is 22000 units

Step-by-step explanation:

By measurement, the width of the scale drawing = 16 units

The breadth of the scale drawing = 6 units

Therefore, given that the scale is 1:500, we have that the actual dimensions of the playground are;

Actual width of the playground = 500×16 = 8,000 units

Actual breadth of the playground = 500×6 = 3,000 units

Therefore;

The perimeter of the actual playground = 2 × 8000 + 2 ×3000 =  22000 units.

For which quadratic equation is the axis of symmetry x = 3

a. y = -x2 + 3x + 5
b. y = -x2 + 6x + 2
c. y = x2 + 6x + 3
d. y = x2 + x + 3​

Answers

Answer:

b) y = -x2 + 6x + 2

Step-by-step explanation:

Please help me thank you

Answers

Answer:

B

Step-by-step explanation:

What are the coordinates of point P on the directed line segment from A to B such that P is One-fourth the length of the line segment from A to B?

Answers

Answer:

The answer is explained below

Step-by-step explanation:

The location of point A = (-5, -1) and point B = (4, 1).

To find the coordinate of the point that divides a line segment PQ with point P at [tex](x_1,y_1)[/tex] and point Q at [tex](x_2,y_2)[/tex] in the proportion a:b, we use the formula for the x and y coordinates:

[tex]x-coordinate:\\\frac{a}{a+b}(x_2-x_1)+x_1 \\\\While \ for\ y-coordinate:\\\frac{a}{a+b}(y_2-y_1)+y_1[/tex]

P is One-fourth the length of the line segment from A to B, Therefore AB is divided in the ratio 1:4. The location of point A = (-5, -1) and point B = (4, 1).Therefore:

[tex]x-coordinate:\\\frac{1}{1+3}(4-(-5))+(-5)=\frac{1}{4}(9)-5=-\frac{11}{4} \\\\While \ for\ y-coordinate:\\\frac{1}{1+3}(1-(-1))+(-1)=\frac{1}{4}(2)-1=\frac{-1}{2}[/tex]

Therefore the coordinate of P is (-11/4, -1/2)

Answer:

the coordinate of P is (-11/4, -1/2)

x= -11/4

y= -1/2

c on edu

Step-by-step explanation:

edu 2021

Please help me I will mark BRAINLIST :))))

Answers

Answer:

47%

Step-by-step explanation:

The total number of student is 4+6+2+2+3+4+6+3 = 30 students

P( male) = male / total

              = (4+6+2+2)/ total

               =14/30

                =.466666666

                46.66666%

To the nearest whole percent

                 47%

What is the difference from the point (-6,2) to the point (2,17)?

Answers

Answer: Distance is 17

Step-by-step explanation:

[tex]d = √((x2-x1)2 + (y2-y1)2)[/tex]

[tex](x2-x1) = (2 -6) = 8[/tex]

[tex](y2-y1) = (17 - 2) = 15[/tex]

Add them all together

[tex](8)2 + (15)2 = 64 + 225 = 289[/tex]

Square 289

[tex]\sqrt{289} =17[/tex]

Write in figures;Nine million twenty thousand four hundred and six and twenty seven thousandths.​

Answers

Answer:

9,020,406.27

Step-by-step explanation:

Answer:

9,020,406.27

Step-by-step explanation:

Nathaniel is using the quadratic formula to solve 0 = x2 + 5x - 6. His steps are shown below. Table showing 3 steps to solve an equation using the quadratic formula. What are the solutions to the equation?

Answers

Answer:

              [tex]\underline{x\in\left\{-6\,,\ 1\right\}}[/tex]

Step-by-step explanation:

[tex]x^2+5x-6=0\\\\a=1\,,\ \ b=5\,,\ \ c=-6\\\\x_1=\dfrac{-5-\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5-\sqrt{25+24}}2=\dfrac{-5-\sqrt{49}}2=\dfrac{-5-7}2=-6\\\\x_2=\dfrac{-5+\sqrt{5^2-4\cdot1\cdot(-6)}}{2\cdot1}=\dfrac{-5+7}2=1[/tex]

Answer:

Step-by-step explanation: Answer is B-6,1

Expected Value (50 points) Game: Roll two dice. Win a prize based on the sum of the dice. Cost of playing the game: $1 Prizes: Win $10 if your sum is odd. Win $5 if you roll a sum of 4 or 8. Win $50 if you roll a sum of 2 or 12. Explain HOW to find the expected value of playing this game. What is the expected value of playing this game? Show your work. (30 points)

Answers

Answer:

$7.89

Step-by-step explanation:

There are 36 possible outcomes when rolling two dice.

The sum will be odd if the first die is odd and the second is even or if the second is odd and the first is even. The probability of an odd sum is:

[tex]P(odd)=\frac{3}{6} *\frac{3}{6} +\frac{3}{6} *\frac{3}{6}\\P(odd)=0.5[/tex]

There is a probability of 1 in 2 of winning $10.

There are 8 ways to get a sum of 4 or 8 (1,3; 3,1; 2,2; 5,3; 3,5; 2,6; 6,2; 4,4). There is a probability of 8 in 36 or 2 in 9 of winning $5.

There are 2 ways to get a sum of 2 or 12 (1,1; 6,6). There is a probability of 2 in 36 or 1 in 18 of winning $50.

Any other outcome will not payout any amount.

The expected value is the sum of all possible payouts multiplied by their likelihood (including a 100% chance of paying $1 to play).

[tex]E=-1+10*\frac{1}{2} +5*\frac{2}{9}+50*\frac{1}{18}\\E=\$7.89[/tex]

The expected value is $7.89.

25x^2+58+16 how do you factor

Answers

Answer:

[tex](25x + 8)(x + 2)[/tex]

Step-by-step explanation:

[tex]25x^{2} + 58x + 16 = 25x^{2} + 50x + 8x + 16 = 25x(x + 2) + 8(x + 2) = (25x + 8)(x + 2)[/tex]

PLZ HELP ME I NEED THIS FAST WILL GIVE BRAINLIEST

Answers

Step-by-step explanation:

The formula the amusement parc use is  100y-39000=55(x-800)

The slope intercept form of a function is wriiten generally as:

y = mx+c

m is a slope c is a constant and represents the y-intercept x is a variable y is the input of the function

Let's rewrite our equation in the precedent form

100y-39000 = 55(x-800)100y -39000 = 55x-44000    add 39000 in both sides100y-39000+39000 = 55x-44000+39000100y = 55x-5000            divide both sides by 100y = 0.55x-50

The slope intercept form of this equation is:

y= 0.55x-50

Answer:

y=55x+38992

Explanation:

You have to turn the equation into the form y=mx+b

Step 1: Get y by itself(divide both sides by 100)

100y-39,000=55(x-800)

100/100y-39,000=55(x-800)/100

y-39,000=55(x-800)/100

Step 2: Get y by itself(+ 39000 to both sides)

y-39,000=55(x-800)/100

 +39,000=55x-800/100+39,000

y=55x-800/100=39,000

Step 3: Simplify

y=55x+38992

4⋅f(6)−6⋅g(5) need help asap

Answers

Answer:

6

Step-by-step explanation:

From the blue graph of f(x) we can see that the function value is -6 when x = 6.  Similarly, g(5) = -5.

Then:  4*f(6) - 6*g(5) becomes:

           4*(-6) - 6*(-5), or

              -24 +  30  = 6

The value of ⋅f(6)−6⋅g(5)= 6

What is Composition of function?

An operation where two functions say f and g generate a new function say h in such a way that h(x) = g(f(x)).

Given:

From the blue graph we can see that

f(x)= -6 when x = 6.

Similarly, g(5) = -5.

thus,

4*f(6) - 6*g(5)

=3 4*(-6) - 6*(-5)

=-24 +  30

= 6

Learn more about this concept here:

https://brainly.com/question/20379727

#SPJ2

Yasmin bought several items at the discount store. She paid 8.75 percent sales tax, an amount of $4.59, on the total amount of her purchase. What was the total amount of her purchase before tax was added? $40.16 $52.46 $190.63 $401.63

Answers

Answer:

  $52.46

Step-by-step explanation:

We are told that ...

  8.75% · purchase = $4.59

Dividing by the percentage, we have ...

  purchase = $4.59/0.0875 = $52.46

Yasmin's pre-tax total was $52.46.

Answer:

the correct answer is b aka 52.46

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1/8. There are 56 marbles in the bag and each is equally likely to be chosen. Work out how many red marbles there must be

Answers

Answer:

7 red marbles

Step-by-step explanation:

P( red) = red marbles / total marbles = 1/8

We know there are 56 marbles

red marbles/56 = 1/8

Multiply by 56

red marbles = 1/8 *56 = 7

There are 7 red marbles

Para medir la temperatura se pueden utilizar diferentes escalas, por ejemplo, la escala de grados Celsius (°C) y Fahrenheit (°F ). La relación entre estas escalas está dada por la expresión: C igual fracción numerador 5 por F menos 160 entre denominador 9 fin fracción ¿A cuántos grados Fahrenheit equivalen 62 °C?

Answers

Answer:

143.6F

Step-by-step explanation:

Entonces la ecuación establecida es;

C = [tex]\frac{5F-160}{9}[/tex]

Entonces, para resolver el Celsius, debes hacer de F el tema que hago a continuación.

[tex]C = \frac{5F - 160}{9}\\C * 9 =( \frac{5F-160}{9}) *9\\9C - 5F = 5F -160 - 5F\\9C-5F =-160 \\-5F = -160 - 9C\\\frac{-5F}{-5} = \frac{-160-9C}{-5}\\[/tex]

∴[tex]F = \frac{-160-9C}{-5}[/tex]

Ahora ingresamos los valores y resolvemos para F

F = [tex]\frac{-160 - 9(62)}{-5}[/tex]

  =[tex]\frac{-160-558}{-5}[/tex]

  = [tex]\frac{-718}{-5}[/tex]

  = 143.6

∴ 62C = 143.6F

Given: Parallelogram LMNO; MO ⊥ LN Prove: LMNO is a rhombus. Parallelogram L M N O is shown. Diagonals are drawn from point L to point N and from point M to point O and intersect at point P. A square is drawn around point P. Sides L M and O N are parallel and sides L O and M N are parallel. ♣: ♦: ♠: I WILL GIVE BRAINLIEST PLS ANSWER

Answers

The proofing is as follows:

Given that,

|LO|=|MN| and |LM|=|ON|

It means that  Opposite sides of a parallelogram are equa

Now, LN⊥OM

So,

∠LPO = ∠NPO = 90° ( by definition of perpendicular lines)

LPO ≅ ∠NPO (by definition of congruent angles)

|LP|=|PN| (diagonals of a parallelogram bisect each other)

based on this LMNO is a rhombus

Learn more: https://brainly.com/question/10046743?referrer=searchResults

Answer:

All right angles are congruent

Reflexive property

Opposite sides of a parallelogram are congruent

Step-by-step explanation:

That what i got on my assignment

Ewen has 48 whistle tiles and 16 blue tiles the cost of each white tile was £2 and the cost of each blue tile was £4 Work out the ratio of the total cost of the white tiles to the total cost of the blue tiles

Answers

Answer:

3:2

Step-by-step explanation:

Ewen has 48 white tiles and 16 blue tiles

The cost of each white tile was £2

The cost of each blue tile was £4

Therefore the total cost of 48 white tiles is

= 48×2

= £96

The total cost of 16 blue tiles is

= 16×4

= £64

The ratio of the total cost of the white tiles and blue tile can be calculated by dividing the cost of both tiles by their greatest common factor

The greatest common factor of £96 and £64 is 32

96/32 = 3

64/32= 2

Ratio= 3:2

Hence the ratio of the total cost of the white tiles to the blue tiles is 3:2

(-3)(-2)[-4-(-2)]
Slove the problem

Answers

Answer:

-12

Step-by-step explanation:

(-3)(-2)[-4-(-2)]

6[-4-(-2)]

6[-2]

-12

I NEED HELP PLEASE! THANKS :)

Answers

Answer:

A

Step-by-step explanation:

First, let's do the difference of two squares:

[tex](1-cos^4(\theta))=(1-cos^2(\theta))(1+cos^2(\theta))[/tex]

Note that [tex]sin^2(\theta)=1-cos^2(\theta)[/tex] (Pythagorean Identity)

Thus, we can substitute:

[tex]sin^2(\theta)(1+cos^2(\theta))[/tex]

Now, and I'm serious, you just have to use your creativity. After a while, you will find that:

[tex]sin^2(\theta)+cos^2(\theta)=1[/tex]

So:

[tex]1+sin^2(\theta)+cos^2(\theta)=1+1[/tex]

Thus, we have [tex]1+cos^2(\theta)=2-sin^2(\theta)[/tex]

Now, we can substitute:

[tex]sin^2(\theta)(2-sin^2(\theta))=2sin^2(\theta)-sin^4(\theta)[/tex]

first chance you get the best marks ​

Answers

Answer:

First box and last box.

Step-by-step explanation:

It is the first box.

Distribute 7 to the first number

7 * -3/4 = -21/4

-21/4 = 5  -1/4

Distribute 7 to the second number

7 * -3

= -21

Put the numbers together

5  -1/4x  -21 is the answer.

It is also the last box.

They separated the parenthesis.

So it is still 7 * -3/4

and

7*-3.

Hope this helps,

Kavitha

how to find the angel in trigonometry when all the lengths of the right angled triangle already given.

Answers

Answer:

The three trigonometric ratios can be used to calculate the size of an angle in a right-angled triangle

Use rule ; SOHCAHTOA .Where sin x = opp/hyp

cos x = adj/hyp

tan x= opp/adj

Substitute the given values for the three sides

into any of the above rules

[tex]example = Hyp = 2\\opp = 1\\sin- x = 1/2\\x = sin^{-1} 1/2\\x = 30[/tex]

Step-by-step explanation:

I Hope It Helps :)

Hi can someone please help meee

Brian plays basketball. In the past he has made 4 out of every 5 free throws. What is the probability, as a decimal, that Brian will make the next two free throws?

Answers

Answer:

0.64

Step-by-step explanation:

4 out of 5 free throws is 0.8 as a decimal.

The probability that Brian will make 2 free throws is 0.8 for the first one, and then 0.8 of that for the second one. That means you multiply the two to get your answer and 0.8 times 0.8 = 0.64.

de un tanque lleno de agua se utiliza la cuarta parte para lavar ropa, los 5/ 6 del resto para cocinar y aun quedan 100 litros de agua ¿ cuantos litros de agua tenia el tanque?¿ cuantos litros de agua se utilizan para cocinar?

Answers

Answer:

a. 800 litros

b. 500 litros

Step-by-step explanation:

Aquí, se nos dice que 1/4 del total se usa para lavar la ropa.

Lo que queda sería 1-1 / 4 = 3/4 Fuera de esto, 5/6 se usa para cocinar.

La fracción utilizada para cocinar es 5/6 * 3/4 ​​= 15/24 = 5/8

Y todavía nos quedan 100 litros.

La cantidad utilizada ya sería 1/4 + 5/8 = (2 + 5) / 8 = 7/8

Entonces la fracción no utilizada = 1-7 / 8 = 1/8

Ahora, es este 1/8 que corresponde a 100 litros.

Digamos que el volumen total es x litros inicialmente, Eso significa 1/8 * x = 100 x / 8 = 100 x = 800 litros

La fracción utilizada para cocinar es 5/8 del total, por lo que el valor sería 5/8 * 800 = 500 litros

Find the area of the shaded region where a = -1.88 and b = 2.12. Note: the graph may not be drawn to scale. Write only a number as your answer. Round to 4 decimal places (for example 0.6148). Do not write as a percentage. (picture in attachment)

Answers

Answer:

0.0471

Step-by-step explanation:

Here, we want to find the area of the shaded region.

The area of the shade region = 1- area of the unshaded region

The area of the unshaded region is as follows;

P(b) - P(a)

and that is;

P(-1.88<x<2.12) = 0.95294 from z table

So the area of the shaded region = 1-0.95294 =

0.04706 = 0.0471 to 4 d.p

To solve 6x=30, Keith divided both sides of the equation by 6. Which property justify this step

Answers

Answer:

6x to find x on it's own you need to divide by the number infront,

Step-by-step explanation:

Keith divides both side of the equation by 6 in order to make x the subject of the equation. The opposite of multiplication is division

Pleas answer this question now fast in two minutes

Answers

Answer:

3

Step-by-step explanation:

Adjacent angles have a common side and no common interior points.

I need help with this problem, the picture is attached below. Select the following numbers that cannot represent the area of a polygon.

Answers

Answer:

-200, 0 and -5

Step-by-step explanation:

Area can never be zero or negative.

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