Assume the competing hypotheses take the following form: H0: µ1 – µ2 = 0, HA: µ1 – µ2 ≠ 0, where µ1 is the population mean for population 1 and µ2 is the population mean for population 2. Also assume that the populations are normally distributed and that the observations in the two samples are independent. The population variances are not known but are assumed equal. Which of the following expressions is appropriate test statistic?
a. taf
b. 2
c. 1-2 21 n
d. täf 2 t1

Answers

Answer 1

Answer:

[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]

Step-by-step explanation:

H0: µ1 – µ2 = 0

HA: µ1 – µ2 ≠ 0

We have given,

The population variances are not known and cannot be assumed equal.

The test statistic for the test is

[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]

Where,

[tex]\bar x_1[/tex] = sample meaan of population 1

[tex]\bar x_2[/tex] = sample mean of population 2

[tex]n_1[/tex] = sample size of population 1

[tex]n_2[/tex] = sample size of population 2

Therefore, this is the test

[tex]t=\frac{\bar x_1- \bar x_2}{\sqrt{\frac{s_1^2}{n_1} +\frac{s_2^2}{n_2} } }[/tex]


Related Questions

A mother decides to teach her son about a letter each day of the week. She will choose a letter from the name of the day. For example, on Saturday she might teach about the letter S or the letter U, but not the letter M.


1. What letters are possible to teach using this method? (There are 15.)







2. What are 4 letters that can't be taught using this method?








3. On TUESDAY, the mother writes the word on a piece of paper and cuts it up so that each letter is on a separate piece of paper. She mixes up the papers and picks one. What is the probability that she will choose the piece of paper with the letter Y? Explain your reasoning.

Answers

Answer: 1. A,D,E,F,H,M,N,O,R,S,T,U,W,Y

2.  B,C,G,J,K,L

3. the probability would be 7

Step-by-step explanation: i tried my best ig

A computer company produced this graph to show how many computers it expects to sell based on
how much the company spends on Internet advertising. The company expects to sell 40 million
computers, spending $5 million on Internet advertising. Which set of units and scales are appropriate
for the two axes?
Horizontal axis: Number of Computers (in millions):
Vertical axis: Advertising Dollars (in millions)
Horizontal axis: Advertising Dollars (in millions):
Vertical axis: Number of Computers (in tens of
millions)
Horizontal axis: Advertising Dollars (in millions);
Vertical axis: Number of Computers (in millions)
1 2
3
4
5
6
Horizontal axis: Number of Computers (in millions):
Vertical axis: Advertising Dollars (in tens of millions)

Answers

Answer:

The first one

Horizontal axis: Number of computers (in millions):

Vertical axis: Advertising Dollars (in millions):

Step-by-step explanation:

Since we have given that

Number of computers expected to sell = 40  millions

Cost price of internet advertising = $5 million

According to the graph, we can see that

40 millions is the y-coordinate and $5 million is the x-coordinate.

so, Horizontal axis - y- axis is the "Number of computers".

Vertical axis - x- axis is the "Advertising cost "

The set of units and scales are appropriate for the two axes

Horizontal axis: Number of computers (in millions):

Vertical axis: Advertising Dollars (in millions):

What is Graph?

The graph is simply a structured representation of the data. It aids in our comprehension of the data. The numerical information gathered through observation is referred to as data.

In a line graph, the information or data is represented as a series of markers, or dots, and is then connected to one another by a straight line.

Given:

Number of computers expected to sell = 40  millions

Cost price of internet advertising = $5 million

From to the graph, we can see that

40 millions is the y-coordinate and $5 million is the x-coordinate.

So, Horizontal axis - y- axis shows the "Number of computers".

and, Vertical axis - x- axis shows the "Advertising cost ".

Learn more about Graph here:

https://brainly.com/question/17267403

#SPJ2

The quarterback Tom Brady completes 60% of his passes. To simulate the outcome of a single pass we use the digits 0, 1, 2, 3, 4, and 5 to represent the outcome "the pass is completed" and the digits 6, 7, 8, and 9 to represent the outcome "the pass is not completed." To be confident that our simulation is accurate, one needs to :

A. Repeat the simulation several more times
B. Assign new digits to represent outcomes
C. Take the average of the results of Line 134 and Line 101

Answers

Answer:

A. Repeat the simulation several more times

Step-by-step explanation:

The purpose of the simulation model is to represent the effectivity of the passes.

The proportion of successful passes is 60%.

As we have 10 digits available, 6 (digits from 0 to 5) are used for the outcome "the pass is completed" and 4 (digits 6, 7, 8, and 9) to represent the outcome "the pass is not completed". This is correct, as it represents a probability of 60% of having a successful pass.

But to have a representative distribution of the possible and probable results, the simulation have to run enough times to have a stable distribution of the results.

what is the area of the figure below

Answers

Answer:

58

Step-by-step explanation:

Answer: 58 in.^2

Step-by-step explanation:

Write the following number in standard decimal form.
six thousand five hundred thirty-four ten-thousandths

Answers

Answer: 6.534 x 10^(-1)

Step-by-step explanation:

Six thousand five hundred and thirty four ten thousandth

6534/10000

Convert to decimal

6534/10000=0.6534

Then convert to standard form

0.6534=6.534 x 10^(-1)

Which description matches finding the volume of the solid ?

Answers

Square prism + Triangular prism. Hope it helps.

the sum of three consecutive even numbers is 114 what's the smallest of these numbers​

Answers

Answer:

36

Step-by-step explanation:

consecutive even numbers are 2,4, 6...

Let the smallest of the 3 numbers be x.

2nd number= x+2

3rd number

=x+2+2

= x+4

sum of the 3 numbers= x +x+2 +x+4

114= 3x+6

3x= 114 -6 (-3 on both sides)

3x= 108 (simplify)

x= 108 ÷3

x= 36

Thus, the smallest number is 36.

Let's check!

36+38+40= 114 ✓


Temperature (x) 65 70 75 80 85 90 95 100 105
Number of ice cream cones sold per hour (y) 8 10 11 13 12 16 19 22 23
Note: Critical Value for n = 9 is 0.666

Calculate the linear correlation coefficient r, for temperature (x) and the number of ice cream cones sold per hour (y). (round to 3 decimal place)
Is there a linear relation between the two variables x, and y? Why? If yes, indicate if the relationship is positive or negative. (Hint: Compare the absolute value of r and critical value)
Construct the least-squares regression line for temperature (x) and the number of ice cream cones sold per hour (y) and interpret its slope. (round to 3 decimal place)
Predict the number of ice cream cones sold per hour when the temperature is 80 and calculate the residual for x = 80º. (round to nearest whole number)
Would it be reasonable to use the least-squares regression line to predict the number of ice cream cones sold when it is 50 degrees? Explain your answer.

Answers

Answer:

Step-by-step explanation:

Hello!

You have to calculate the linear correlation coefficient (r) between the variables

X₁: temperature

X₂: Number of ice cream cones sold per hour.

The formula to calculate the coefficient of linear correlation between the two variables is the following:

[tex]r= \frac{sumX_1X_2-\frac{(sumX_1)(sumX_2)}{n} }{\sqrt{[sumX_1^2-\frac{(sumX_1)^2}{n} ][sumX_2^2\frac{(sumX_2)^2}{n} ]} }[/tex]

∑X₁= 765; ∑X₁²= 66525 ∑X₂= 134 ∑X₂²= 2228 ∑X₁X₂= 11965 n=9

[tex]r= \frac{11965-\frac{765*134}{9} }{\sqrt{[66525-\frac{(765)^2}{9} ][2228-\frac{(134)^2}{9} ]} }[/tex]

r= 0.97

To test if there is a positive linear association between both variables the statistical hypotheses are:

H₀: ρ ≤ 0

H₁: ρ > 0

critical value 0.666

r= 0.97

The decision is to reject the null hypothesis, there is a positive linear correlation between the temperature and the number of ice cream cones sold per hour.

The regression line is

^Y= a + bX

where

a: represents the estimation of the y-intercept

b: represents the estimation of the slope

[tex]b= \frac{sumXY-\frac{sumXsumY}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

b= 0.38

a= Y[bar]-bX[bar]

a= -17.69

The estimated regression line for the number of ice cream cones and the temperature is ^Y= -17.69 + 0.38Xi

To estimate the number of ice cream cones sold when the temperature is 80º you have to replace the value of X in the estimated regression line:

^Y= -17.69 + 0.38*80= 12.71

It is expected that they will sell 12.71 ≅ 13 ice cream cones when the temperature is 80º

You can use the estimation of the regression line to predict values within the range of definition of the independent variable, in this case from 65º to 105º of temperature, because it is within those values that you can be sure they have a linear association. Below or above you are not certain that their association is linear, it may be, for example exponential, or there may be no association between them.

Example: If the temperature is comfortable or cold, it is more likely that people won't buy ice creams, so for those values it will be no linear association  between them.

I hope this helps!

Consider this quadratic equation
X^2+2x+7=21

Answers

Answer:

x = sqrt(15) - 1 or x = -1 - sqrt(15)

Step-by-step explanation:

Solve for x:

x^2 + 2 x + 7 = 21

Subtract 7 from both sides:

x^2 + 2 x = 14

Add 1 to both sides:

x^2 + 2 x + 1 = 15

Write the left hand side as a square:

(x + 1)^2 = 15

Take the square root of both sides:

x + 1 = sqrt(15) or x + 1 = -sqrt(15)

Subtract 1 from both sides:

x = sqrt(15) - 1 or x + 1 = -sqrt(15)

Subtract 1 from both sides:

Answer: x = sqrt(15) - 1 or x = -1 - sqrt(15)

A 25 lb. bag Balkfoods Small Red Beans cost $52.92. What is the unit price
per Ib?

Answers

Answer:

$2.1 per pound

Step-by-step explanation:

price/pounds

52.92 / 25 = 2.1

Find the area of each face of the triangular prism and the total surface area.
Drag each tile to its matching measurement. Each number may be used once or not at all.

Answers

9514 1404 393

Answer:

24160120200528

Step-by-step explanation:

The area of each triangular face is given by the formula ...

  A = 1/2bh

The triangular faces have a base of b=8 cm, and a height of h=6 cm. Their area is ...

  A = 1/2(8 cm)(6 cm) = 24 cm²

__

Each of the rectangular faces has a length of 20 cm. The width depends on which face is of interest. In each case, the area is given by ...

  A = LW

Bottom face: A = (20 cm)(8 cm) = 160 cm²

Back face: A = (20 cm)(6 cm) = 120 cm²

Sloped face: A = (20 cm)(10 cm) = 200 cm²

__

The total area is the sum of the areas of all of the faces and bases. There are two triangular bases, so the total area is ...

  (2×24 + 160 +120 +200) cm² = 528 cm²

Help !!! I got -15 & it’s wrong !

Answers

Answer:

-11

Step-by-step explanation:

I substitute x in ( put parenthesis around x so it makes it clear)

-9-6-18+9+4+9

simplify

-33+22

-11

Answer: -11

Step-by-step explanation:

That polynomial simplifies to -2x^2-x+4

If we plug in -3 for x, we get -2(-3)^2-(-3)+4 and thats -11

write an equation of a line that is parellel to x=8 and that passes through the point -3,-2

Answers

Since the line is parallel to x = 8, the slope doesn't change.

In this case, the slope is undefined so nothing changes.

All we need to do is find the x-coordinate in (-3, -2). The x-coordinate is -3.

So, the equation will be x = -3

Best of Luck!

Multiply (2m+3)(m^2-2m+2)
A) 2m^3-m^2-8m+3
B) 2m^3-m^2-10m+3
C)2m^3-m^2-4m+3
D)2m^37m^2-4m+2

Answers

Answer:

Step-by-step explanation:

The first step is to distribute the 2m and 3 to ([tex]m^2-2m+2[/tex]), like so:

[tex](2m+3)(m^2-2m+2)[/tex]

[tex]2m^3-4m^2+4m+3m^2-6m+6[/tex]

Then, add like terms:

[tex]2m^3 -m^2 -2m + 6[/tex]

Mark wants a new car that costs $30000. He only has $500 in his savings account and $300 in his checking account. Which financing option should he chose

Answers

Answer: He should choose the savings account because he can earn more interest and the money in his savings account is more than the money in his checking account.

Step-by-step explanation:

BRAINLIEST for anyone who gets this correct! Factor the expression below.
16x^2 + 40x+ 25
A. (2x+5)(8x+5)
В. (4х+5)(8х+3)
C. (4x - 5)(4x-5)
D. (2x - 5)(8x-5)​

Answers

(4x+5)2

Expand the polynomial using the FOIL method.

16x^2−40x+25

c(4x - 5)(4x-5)

Farmer Smith Jr is putting together fruit baskets. He has 240 oranges and 150 grapefruits. What is the largest number of baskets he can put together so that he can have the same number of oranges in each basket and the same number of grapefruits in each basket?

Answers

Answer:

why does it say college even tho this is a question on my homework

Step-by-step explanation:

and i'm in 7th grade.

given that the quadratic equation (k^2-1)x^2-2kx+3k+1=0 has equal roots show that 3K^3-3K-1=0

Answers

Step-by-step explanation:

The roots are equal, so the discriminant equals 0.

b² − 4ac = 0

(2k)² − 4 (k²−1) (3k+1) = 0

4k² − 4 (3k³ + k² − 3k − 1) = 0

k² − (3k³ + k² − 3k − 1) = 0

k² = 3k³ + k² − 3k − 1

0 = 3k³ − 3k − 1

h(t)= -20 + 11t
h(11) =

Answers

Answer:

h(11) = -20 + 11(11)

h(11) = -20 + 121

h(11) = 101

Step-by-step explanation:

replace t by 11

do multiplication

add them together

Answer:

h(t) =−20+11t  h(11)= 101

Step-by-step explanation:

Ann desires to grow tall sunflower plants. She wonders how the amount of water she provides the sunflowers will affect their growth. One spring Ann planted 25 sunflower plants, making sure each one had the same soil, amount of space, and exposure to sunlight. The first one received one ounce of water per day. The second one received 2 ounces of water per day, and so on.
To determine the ideal amount of water needed, she consistently watered her sunflowers this way and at the end of the summer recorded the height of each sunflower (in cm). Then she performed a regression analysis on the data.

She conducts a significance test to determine if there is convincing evidence of a positive linear relationship between the amount of water her sunflower plants received and how tall they grew. What is the correct test statistic and conclusion? Assume all conditions for inference are met.
(A)
t=2.68\textit{t}=2.68
t=2.68. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(B)
t=2.68\textit{t}=2.68
t=2.68.There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(C)
t=5.10\textit{t}=5.10
t=5.10. There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(D)
t=5.10\textit{t}=5.10
t=5.10.There is not convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.
(E)
t=5.875\textit{t}=5.875
t=5.875.There is convincing evidence of a positive linear relationship between the amount of water and height of a sunflower.

Answers

Answer: a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The appropriate test is a t-test for slope. The test statistic is t = 2.68 and the p-value is 0.005. Because the p-value, 0.005, is less than α=0.05 we have convincing evidence that there is a positive linear relationship between the amount of water received and how tall the sunflower plants grew.

Nora wants to put new glass in her window

If her window measures 34 inches by 48 inch

What is the area of the glass that she will need

Answers

Answer:

1632 inches squared

Step-by-step explanation:

Hi!

So the formula for area is length times width.

So you would multiply the length by the width which is 34 times 48 to get the area which is 1632 in squared.

Hope this helps!

Which statement describes a cause of screwed data

Answers

a sample that excludes subjects that are not part of the population being measured.

A 14-foot ladder is leaning against the side of a house.The angle the ladder makes with the ground is 50 degrees. How far is the base of the ladder from the house to the nearest tenth of a foot

Answers

Answer:

9 ft

Step-by-step explanation:

You can use cosine to solve this, which is adjacent over hypotenuse. The ladder forms a triangle with the house, and the side you need to solve for is adjacent to the angle. You can set up the equation:

cos(50)=x/14

Then you multiply 14 by cos(50) and get almost 9 ft (rounding to the nearest tenth of a foot).

Is a temperature of 0.67 degrees a positive number or a negative number.

Answers

Answer:

It is a positive number.

Step-by-step explanation:

Numbers that are above 0 are considered positive and numbers below 0 are considered negative.

~Anna

a(b+c) =a.b+a.c, where a, b, and c are real numbers. Use the distributive property to simplify the expression 8(3+4)=24+ ?

Answers

Answer: 32

Step-by-step explanation:

All you have to do is is multiply 8 by the numbers in the parentheses. So you multiply 8 by 3, which equals 24. Then multiply 8 by 4, which is 32. Hope this helps! :)

Answer:

The answer is 32 and the next one is C, 24x+32.

Step-by-step explanation:

Can someone help me with this

Answers

Answer:

(y-b) /x = m

Step-by-step explanation:

y = mx+b

Subtract b from each side

y -b = mx+b-b

y-b = mx

Divide each side by x

(y-b) /x = mx/x

(y-b) /x = m

The area of a circle is 286 cm2. Use the π button on your calculator for π in your calculations.
8a
If its radius is r cm, find r, correct to 2 decimal places.
Be careful not to round your answer until the very end.

Answers

Answer:

9.54 cm

Explanation:

area = πr^2

286 cm^2= πr^2

=>πr^2= 286 cm^2

=>r^2= 286÷π

=>r= √286÷π

: 9.54. m

circumference=2πr

=> circumference=2×π×9.54

=60 cm

The function Fx) = log5 xis increasing.

Answers

Answer:

Yes

Step-by-step explanation:

If F(x)= log base 5 of x, then yes, it is increasing.

Answer: True

Step-by-step explanation: Got it correct on a-p-e-x

The product of two consecutive natural numbers is 19 greater than their sum. Find thee numbers.

Answers

Answer:

The numbers are suppose to be natural numbers that is positive integers form 1 upward. So the numbers will be 5 and 6.  

Step-by-step explanation:

The product of 2 consecutive natural numbers is 19 greater than their sum . We need to understand important terms in this question like consecutive and natural numbers.

Consecutive numbers are numbers that follows each other continuously from smallest to largest.  Natural numbers are numbers that includes all the positive numbers from 1 to infinity example 1, 2, 3, 4............infinity.

Let the consecutive number be a and a+1.

The product of this 2 numbers are when you multiply them. Therefore,

a(a + 1) = a² + a

The sum of the 2 numbers are their addition. Therefore,

a + (a + 1) = 2a + 1

The product is 19 greater than the sum. This means the product of this numbers minus the sum of this numbers is equals to 19.

a² + a - (2a + 1) = 19

a²+ a - 2a - 1 = 19

a²- a - 20 = 0

Find the numbers that can be multiplied to get -20 and added together to get -1. The numbers are 4 and -5

a² + 4a - 5a - 20  = 0

a(a + 4) - 5(a + 4) = 0

(a + 4)(a - 5) = 0

a = - 4 and a = 5

The numbers are suppose to be natural numbers that is positive integers from 1 upward. So the numbers will be 5 and 6.  

To prove it

5 × 6 = 30(products)

5 + 6 = 11(sum)

30 - 11 = 19


Drag the item from the item bank to its corresponding match.

Match the prism or cylinder with its volume.

Answers

Answer:

i cant help you because i cant see the things on the picture if u get a better picture i can help

Step-by-step explanation:

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