A sample of 34 observations is selected from a normal population. The sample mean is 15, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.10 significance level. H0: μ ≤ 14 H1: μ > 14

Required:
a. Compute the value of the test statistic.
b. What is the p-value?

Answers

Answer 1

Answer:

1.944 ;

0.026

Step-by-step explanation:

Given :

Sample size, n = 34

Sample mean, xbar = 15

Population standard deviation, σ = 3

The hypothesis :

H0: μ ≤ 14

H1: μ > 14

The test statistic :

Test statistic = (xbar - μ) ÷ (σ/√(n))

Test statistic = (15 - 14) ÷ (3/√(34))

Test statistic = 1 / 0.5144957

Test statistic, Z = 1.944

The Pvalue :

Using the Pvalue from test statistic value :

Pvalue(1.944) = 0.026

Pvalue < α ; Reject H0


Related Questions

Emily, Yani and Joyce have a total of 3209 stickers. Yani has 2 times
as many stickers as Joyce. Emily has 279 more stickers than Yani. How
many more stickers does Emily have than Joyce?

Answers

Answer:

279+x

Step-by-step explanation:

Emily + Yani + Joyce=3209 stickers

if Yani has 2 times as many stickers as Joyce:this statement states that Joyce has x stickers and Yani has 2x stickers because x multiplied by 2

"Emily has 279 more stickers than Yani":therefore the equation for Emily will be ;279+2x

how many stickers does Emily have than Joyce:

(279+2x)-(x)

279+2x-x

=279+x

James purchased five acres of land fo 75,000 what was the cost per acre

Answers

Answer:

$15,000

Step-by-step explanation:

James purchased a total of 5 acres of land for a total price of $75,000. To find the cost of each individual acre, simply divide the total cost with the total amount of acres purchased:

[tex]\frac{total price of land bought}{total amount of acres} = \frac{75000}{5} = 15000[/tex]

The cost per individual acre, assuming all of them cost the same, is $15,000.

~

Answer:

15000

Step-by-step explanation:

Since

5 acres = 75000

therefore,

the cost price per acre would be

total cost price ➗ 5

7500/5= 15000

Suppose scores on exams in statistics are normally distributed with an unknown population mean and a population standard deviation of three points. A random sample of 36 scores is taken and gives a sample mean of 68. Find a 85 % confidence interval estimate for the population mean exam score. Explain what the confidence interval means​

Answers

this the answer of queastions

Step-by-step explanation:

67.18,68.82

Let mu be the true population mean of statistics exam scores. We have a large random samples of n=36 scores with a sample mean of 68.we know that the population standard deviation is sigma=3.A pivotal quantity is 3^sqrt(36)=(3/6)=68(1/2) which is approximately normally distributed. Therefore the 85%confidence interval is 68-(1/2)(1.6449), 68+(1/2)(1.6449) i.e (67.18,68.82)

‏ Lainey is looking for a new apartment and her realtor keeps calling her with new listings . The calls only take a few minutes , but a few minutes here and there are really starting to add up . She's having trouble concentrating on her work . What should Lainey do ? a ) Tell her realtor she can only receive text messages b ) Limit the time spent on each call c ) Turn off her phone until she is on a break d ) Call her realtor back when customers won't see her on the phone

Answers

Answer:

c ) Turn off her phone until she is on a break

(2+1/2) (2^2-1+1/4) find the expression in the form of cubes and differences of two terms.​

Answers

Answer:

Consider the following identity:

a³ - b³ = (a + b)(a² - ab + b²)

Let a = 2, b = 1/2

(2 + 1/2)(2² - 2*1/2 + 1/2²) = 2³ - (1/2)³ =8 - 1/8

Use the algebraic identity given below

[tex]\boxed{\sf a^3-b^3=(a+b)(a^2-ab+b^2)}[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-1+\dfrac{1}{4})[/tex]

[tex]\\ \sf\longmapsto (2+\dfrac{1}{2})(2^2-2\times \dfrac{1}{2}+\dfrac{1}{2}^2)[/tex]

Here a =2 and b=1/2

[tex]\\ \sf\longmapsto 2^3-\dfrac{1}{2}^3[/tex]

[tex]\\ \sf\longmapsto 8-\dfrac{1}{8}[/tex]

Can someone please help solve this equation thank you

Answers

Answer:

A and B

Step-by-step explanation:

Both points are in the shaded/blue zone

I hope this helps!

pls ❤ and give brainliest pls

Answer:

Yea both A and B are correct.

Step-by-step explanation:

if you can see you can put (-12,0) inside the shaded triangle also for (-10,1)

you can give brainlist to the person above :D

look at the image for the question

Answers

Answer:

117.8

Step-by-step explanation:

surface area = πr²+πrl, where r = radius and l = slant height

so,

πr²+πrl

= π×3²+π×3×9.5

= 75π/2

= 117.8 (rounded to the nearest tenth)

Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the outer function y = f(u).] $ y = e^{{\color{red}5}\sqrt{x}} $

Answers

Answer:

The answer is "[tex]\frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]".

Step-by-step explanation:

Given:

[tex]y = e^{{\color{\red}5}\sqrt{x}}[/tex]

let

[tex]\to t= 5\sqrt{x}\\\\\frac{dt}{dx}= 5 \frac{1}{2\sqrt{x}}\\\\\frac{dt}{dx}= \frac{5}{2\sqrt{x}}\\\\[/tex]

and

[tex]\to y=e^t\\\\\to \frac{dy}{dt}=e^t\\[/tex]

[tex]\to \frac{dy}{dt}=e^{5\sqrt{x} }\\[/tex]

So,

[tex]\to \frac{dy}{dx}= \frac{dy}{dt} \times \frac{dt}{dx}[/tex]

         [tex]=e^{5\sqrt{x} }\times \frac{5}{2\sqrt{x}}\\\\= \frac{5 e^{5\sqrt{x} }}{2\sqrt{x}}[/tex]

OR

[tex]\to g(x) = 5\sqrt{x} \\\\\to f(x) = e^{(x)}\\\\[/tex]

Derivate:  

[tex]\to f''g' = \frac{e^{(5\sqrt{x})}5}{(2\sqrt{x})}[/tex]

3 log2 (x+1) - 2 = 13​

Answers

Answer:

Hello,

Answer 31

Step-by-step explanation:

[tex]3*log_2(x+1)-2=13\\\\3*log_2(x+1)=13+2\\\\log_2(x+1)=5\\\\\\x+1=2^5\\\\x=32-1\\\\\boxed{x=31}\\[/tex]

5 Cece draws these two figures to prove there is more
than one parallelogram with a 40° angle between a
2-cm side and a 6-cm side. Is Cece correct? Explain.
2 cm
40
4.
2 cm

Answers

Answer:

chash greatly ta 45uerywryrsyrsyrs

look at the image below

Answers

Answer:

117.8

Step-by-step explanation:

Surface area = πr²+πrl (whee r = radius and l = slant height)

= π×3²+π×3×9.5

= 75π/2

= 117.8

An object travels along the x-axis so that its position after t seconds is given by x(t) = 2t2 – 5t – 18 for all times t such that t ≥ 0.

Which inequality describes all times t for which the object is traveling toward the right?

Answers

the function is given, and it's value is where the object is ("how far to the right").

so as long as it rises (going more right), this will be apply.

in the screenshot I graphed the function. of course t is graphed as x and "along the x-axis" is graphed as y, but the pattern is the same anyways.

for the first 1.25 seconds the object goes to the left, and after that always to the right.

since we look at t to calculate x, t effectively takes the role of the important variable that is normally given to x. the calculation pattern are just the same. so let's find the lowest point of this function by calculating it out.

x(t) = 2t² – 5t – 18

x'(t) = 4t -5

x'(t) = 0

0 = 4t -5

5 = 4t

1.25 = t

plugging it into the second derivative

x''(t) = 4

x''(1.25) = 4

it's positive, so at t=1.25 there is a low point

(of course the second derivative is constant anyways.)

the object is traveling toward the right

the object is traveling toward the rightfor t > 1.25

The object is moving to the right, for t > 1.25, the object is moving in a rightward direction.

What is inequality?

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

We have:

An object travels along the x-axis so that its position after t seconds is given by:

x(t) = 2t² – 5t – 18

x'(t) = 4t - 5

x'(t) = 0

4t -5 = 0

t = 5/4 = 1.25 seconds

x''(t) = 4

x''(1.25) = 4

x''(1.25) > 0

At t = 1.25 the object travels at a low point.

Thus, the object is moving to the right, for t > 1.25, the object is moving in a rightward direction.

Learn more about the inequality here:

brainly.com/question/19491153

#SPJ2

the mean salary if of 5 employees is $35900. the median is $37000. the mode is $382000. If the median payed employee gets a $3100 raise, then…
New median:
New mode:

Answers

Answer:

Step-by-step explanation:

New median:40100

New mode:385100

Solve (2x – 1)2 = 9. Question 11 options: A) x = 2, –1 B) x = 2, 1 C) x = –2, –1 D) x = –2, 1

Answers

Answer:

(2x – 1)2 = 9

4x-2=9

4x=9+2

4x=11

x=11/4

x=2.75

NEED HALP!!! Find the ordered pair $(s,t)$ that satisfies the system

Answers

Answer:

(-8/7 ; 5/7)

Step-by-step explanation:

5t + 1/2s = 3 - - - (1)

3t - 6s = 9 - - - - - (2)

Multiply (1) by 12 and (2) by 1

Add the result to eliminate s

60t + 6s = 36

3t - 6s = 9

____________

63t = 45

t = 45 / 63

t = 5/7

Put t = 5/7 in either (1) or (2) to obtain the value of s

3(5/7) - 6s = 9

15/7 - 6s = 9

-6s = 9 - 15/7

-6s = (63 - 15)/7

-6s = 48/7

s = 48/7 * - 1/6

s = - 8/7

The midpoint of has coordinates of (4, -9). The endpoint A has coordinates (-3, -5). What are the coordinates of B?

Answers

9514 1404 393

Answer:

  (11, -13)

Step-by-step explanation:

If midpoint M is halfway between A and B:

  M = (A +B)/2

Then B is ...

  B = 2M -A

  B = 2(4, -9) -(-3, -5) = (8+3, -18+5)

  B = (11, -13)

Answer:

Use the midpoint formula:

[tex]midpoint=(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2})[/tex]

Endpoint A = (x₁, y₁) = (-3, -5)Endpoint B = (x₂, y₂)Midpoint = (4, -9)

Substitute in the values:

[tex](4, -9)=(\frac{-3+x_{2}}{2} +\frac{-5+y_{2}}{2} )[/tex]

[tex]4=\frac{-3+x_{2}}{2} \\4(2)=-3+x_{2}\\8+3=x_{2}\\x_{2}=11[/tex]      [tex]-9=\frac{-5+y_{2}}{2} \\(-9)(2)=-5+y_{2}\\-18+5=y_{2}\\y_{2}=-13[/tex]

Therefore, Point B = (11, -13)

the age of furaha is 1/2 of the age of her aunt if the sum of their ages is 54 years. find the age of her aunt

Answers

Answer:

I think it is twenty seven

Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.

Answers

Answer:

rectangle

Step-by-step explanation:

Perimeter of 20 feet

rectangle (square is technically a rectangle):

sides 5 and 5

5*5 = 25ft²

Circle:

20/(2π) = 3.18309...

3.1809...²π = 31.831ft²

Max area of rectangle (i.e. square) has a smaller area than a circle.

Two sides of a triangle have lengths 13 m and 19 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)

Answers

Answer:

The third side is increasing at an approximate rate of about 0.444 meters per minute.

Step-by-step explanation:

We are given a triangle with two sides having constant lengths of 13 m and 19 m. The angle between them is increasing at a rate of 2° per minute and we want to find the rate at which the third side of the triangle is increasing when the angle is 60°.

Let the angle between the two given sides be θ and let the third side be c.

Essentially, given dθ/dt = 2°/min and θ = 60°, we want to find dc/dt.

First, convert the degrees into radians:

[tex]\displaystyle 2^\circ \cdot \frac{\pi \text{ rad}}{180^\circ} = \frac{\pi}{90}\text{ rad}[/tex]

Hence, dθ/dt = π/90.

From the Law of Cosines:

[tex]\displaystyle c^2 = a^2 + b^2 - 2ab\cos \theta[/tex]

Since a = 13 and b = 19:

[tex]\displaystyle c^2 = (13)^2 + (19)^2 - 2(13)(19)\cos \theta[/tex]

Simplify:

[tex]\displaystyle c^2 = 530 - 494\cos \theta[/tex]

Take the derivative of both sides with respect to t:

[tex]\displaystyle \frac{d}{dt}\left[c^2\right] = \frac{d}{dt}\left[ 530 - 494\cos \theta\right][/tex]

Implicitly differentiate:

[tex]\displaystyle 2c\frac{dc}{dt} = 494\sin\theta \frac{d\theta}{dt}[/tex]

We want to find dc/dt given that dθ/dt = π/90 and when θ = 60° or π/3. First, find c:

[tex]\displaystyle \begin{aligned} c &= \sqrt{530 - 494\cos \theta}\\ \\ &=\sqrt{530 -494\cos \frac{\pi}{3} \\ \\ &= \sqrt{530 - 494\left(\frac{1}{2}\right)} \\ \\&= \sqrt{283\end{aligned}[/tex]

Substitute:

[tex]\displaystyle 2\left(\sqrt{283}\right) \frac{dc}{dt} = 494\sin\left(\frac{\pi}{3}\right)\left(\frac{\pi}{90}\right)[/tex]

Solve for dc/dt:

[tex]\displaystyle \frac{dc}{dt} = \frac{494\sin \dfrac{\pi}{3} \cdot \dfrac{\pi}{90}}{2\sqrt{283}}[/tex]

Evaluate. Hence:

[tex]\displaystyle \begin{aligned} \frac{dc}{dt} &= \frac{494\left(\dfrac{\sqrt{3}}{2} \right)\cdot \dfrac{\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{\dfrac{247\sqrt{3}\pi}{90}}{2\sqrt{283}}\\ \\ &= \frac{247\sqrt{3}\pi}{180\sqrt{283}} \\ \\ &\approx 0.444\text{ m/min}\end{aligned}[/tex]

The third side is increasing at an approximate rate of about 0.444 meters per minute.

9514 1404 393

Answer:

  0.444 m/min

Step-by-step explanation:

I find this kind of question to be answered easily by a graphing calculator.

The length of the third side can be found using the law of cosines. If the angle of interest is C, the two given sides 'a' and 'b', then the third side is ...

  c = √(a² +b² -2ab·cos(C))

Since C is a function of time, its value in degrees can be written ...

  C = 60° +2t° . . . . . where t is in minutes, and t=0 is the time of interest

Using a=13, and b=19, the length of the third side is ...

  c(t) = √(13² +19² -2·13·19·cos(60° +2t°))

Most graphing calculators are able to compute a numerical value of the derivative of a function. Here, we use the Desmos calculator for that. (Angles are set to degrees.) It tells us the rate of change of side 'c' is ...

  0.443855627418 m/min ≈ 0.444 m/min

_____

Additional comment

At that time, the length of the third side is about 16.823 m.

__

c(t) reduces to √(530 -494cos(π/90·t +π/3))

Then the derivative is ...

  [tex]c'(t)=\dfrac{494\sin{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}\right)}\cdot\dfrac{\pi}{90}}{2\sqrt{530-494\cos{\left(\dfrac{\pi}{90}t+\dfrac{\pi}{3}}}\right)}}}\\\\c'(0)=\dfrac{247\pi\sqrt{3}}{180\sqrt{283}}\approx0.443855...\ \text{m/min}[/tex]

Determine what type of model best fits the given situation:

A. linear
B. exponential
O c. quadratic
D. none of these
Reset Selection

Answers

C. Quadratic. The graph is a parabola

Damaged items are marked down 25% to 40%. A newspaper coupon holder; to an additional 10% markdown of the new price due to the damage. What is the lowest price of a damaged item that was originally marked GHC100?
A GHC 35.60
B GH 5000
C. GHC 18.00
D. GHC 40.80
E GHC 23.40​

Answers

Markdown is the difference (at sale) between the price an item is placed at for retail sale, and the actual price the item is sold

The correct option is; B. GHC 50.00

The reason for choosing option B is as follows;

The known parameters

The percentage by which damaged items are marked down = 25% to 40%

The percentage markdown offered by the newspaper coupon = 10%

The original marked price of the item = GHC 100

Strategy:

Apply the damaged items and coupon markdown percentages to the original marked price of GHC100 sum the results to find the total markdown

Solution:

Markdown due to damage:

Given that the item is damaged, to have the lowest price, we apply the largest markdown of 40%;

40% is removed from the price to which the item marked down due to damage, as follows;

The markdown due to damage = 40/100 × GHC 100 = GHC 40

Markdown due to Coupon Holder:

The markdown the coupon holder is to get = 10% off the retail price

Given that the damage is not mentioned in the newspaper, we have;

∴ The markdown the coupon holder is to get = 10/100 × GHC 100 = GHC 10

Total markdown:

The total markdown is therefore equal to GHC 40 + GHC 10 = GHC 50

The Lowest Price of A Damaged Items marked GHC100:

The lowest price of the item = Original price - Maximum markdown

The lowest price of the item = GHC 100 - GHC 50 = GHC 50

Learn more about markdown and markup concepts here;

https://brainly.com/question/20705786

pls help Describe how to find the product of the two terms 3x^2y^5 and 4x^3y^7

Answers

Answer:

12 x^5y^12

Step-by-step explanation:

3x^2y^5 * 4x^3y^7

Multiply the constants

3*4 = 12

Multiply the x terms

x^2 * x^3

We know a^b* a^c = a^(b+c)

x^(2+3) = x^5

Multiply the y terms

y^6 * y^7 = y&(5+7) = y^12

Put them back together

12 x^5y^12

The answer above me is correct

Please help me with this on the image

Answers

Answer:

a) Obtuse angle b) Reflex angle

find the quotient 1/5 / (-5/7) =

Answers

Answer:

-7/25

Step-by-step explanation:

1/5 ÷ (-5/7)

Copy dot flip

1/5 * -7/5

-7/25

Given the function f(x) = -5x + 2, find the range ofly for x = -1, 0, 1.
O 7, 2, -3
O 7, 2, 3
O-7, -2, 3
0-7, -2, -3

Answers

Answer:

A

Step-by-step explanation:

f(-1)=7, f(0)=2, f(1)=-3

Please help meeee
Find the value of d.
A. 47
B. 56
C. 75
D. 30

Answers

Answer:

56

Step-by-step explanation:

Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)

75 = 1/2 (94+d)

Multiply by 2

75*2 = 94+d

150 = 94+d

Subtract 94 from each side

150-94 = d

56=d

Use the point-slope formula to determine the equation of the line that has a slope of 1⁄2 and passes through point (0, 0).

Answers

Answer:

y-0 = 1/2(x-0)

y = 1/2(x)

Step-by-step explanation:

Point slope form is

y-y1 = m(x-x1)

where m is the slope and (x1,y1) is a point on the line

y-0 = 1/2(x-0)

y = 1/2(x)

solve for x ! please help (show work)

Answers

Answer:

x = 1/2

Step-by-step explanation:

8(-2x+1) =0

Divide each side by 8

-2x+1 = 0

Add 2x to each side

-2x+1+2x = 2x

1 = 2x

Divide by 2

1/2 = 2x/2

1/2 =x

Answer:

1/2

Step-by-step explanation:

8(-2x+1)=0

Use distributive property first

-16x+8=0

Subtract 8 on both sides

-16x=-8

Divide both sides by -16 to get x by itself

x=0.5

Which is also equal to 1/2

Therefore, x is equal to 1/2

The quotient of -8 and the sum of a and b

Answers

Hi! I'm happy to help!

To solve this, you need to know what all of the terms mean. Quotient means division, and sum means addition. Knowing this we can set up our expression.

Because there is an operation inside of an operation (addition inside of division) we use parenthesis.

-8÷(a+b)

I hope this was helpful, keep learning! :D

Quy tắc suy luận nào là cơ sở của suy diễn sau: "Biết rằng: 2 đường thẳng d và d' song song hoặc cắt nhau. Ta đã có d không song song với d'. Vậy d cắt d'
Select one:
a. Luật loại trừ
b. Luật rút gọn
c. Luật phản chứng
d. Luật tách rời

Answers

Answer: a

Step-by-step explanation:

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