An education researcher would like to test whether 2nd graders retain or lose knowledge during the summer when they are presumably not in school. She asks nine 2nd graders to take a comprehension exam at the end of the school year (May), and then asks those same students to come back after the summer (late August) to retake a different but equivalent exam, to see if their level of comprehension has changed. Using the data below, test this hypothesis using an alpha level of .05.
May August
90 100
65 80
78 92
50 60
89 90
92 98
75 70
90 96
65 87
a) What is the appropriate test? Is it a one or two tailed test?
b) State the null hypothesis (in words and using means).
c) State the alternative hypothesis (in words and using means).
d) Find the critical value.
e) Calculate the obtained value by hand. What does your decision mean?

Answers

Answer 1

Answer:

See step by step explanation

Step-by-step explanation:

From the problem statement, we understand that we need to investigate if 2nd graders RETAIN OR LOSE knowledge comparing information concerning two different months, therefore we are going to find out if the information gives us enough evidence of a difference in the two groups

a) The test should be a two tail-test

Sample sizes are small ( n₁ = n₂  = 9 ) which means we have to use  t-student test

b   and    c) Test Hypothesis:

For Null Hypothesis H₀,  we establish that the two means are equal, which in this case means that the two samples´ means are equal. And as Hypothesis alternative Hₐ that the H₀ is not true,  or that the samples mean are different.

Null Hypothesis     H₀             x₁  -  x₂   = 0   or    x₁  =  x₂

Alternative Hypothesis  Hₐ    x₁  -  x₂   ≠  0   or   x₁  ≠  x₂

d) Significance level α  = 0,05   then   α/2  = 0,025

then t(c)  with  α/2  =  0,025  and degree of freedom  

df =  n₁  +  n₂  - 2      df =  9 + 9 -2     df = 16

From t s-tudent table we find     t(c) =  2,12

e) Calculating:

x₁   and  σ₁

x₂  and  σ₂

σₓ  = [ ( n₁ - 1 )* σ₁² + ( n₂  - 1 )*σ₂² ]/ n₁ + n₂ - 2

Using a calculator:

x₁  =  77,11        σ₁  = 13,86

x₂  = 85,89      σ₂  = 12,74

σₓ  = [ ( 8*(13,86)² + 8*( 12,74 )² ] / 16

σₓ  =  (8* 192,1) + 8* ( 162,31) / 16

σₓ  = (1536,8 + 1298,48 ) / 16

σₓ  =  177,205

t(s) = ( x₁ - x₂ ) /√ σₓ²/ n₁  + σₓ²/ n₂

t(s) = ( 77,11 - 85,89 )/ (177,205)²/n₁ + (177,205)²/n₂

t(s) = - 8,78 / √3489,07 + 3489,07

t(s) = -8,78 / 83,54

t(s) =  - 0,11

Comparing  t(s) and  t(c)

|t(s)| < |t(c)|      

0,11 <  2,12

t(s) is in the acceptance region. We accept H₀

       


Related Questions

Find the indicated limit, if it exists.

See file below.

Answers

Answer:

c

Step-by-step explanation:

The limit exists because it's continuous since they equal each other

when x approaches zero.

Substitute both expressions with x=0 and both of them will equal 2, so the limit should be 2.

Help me fellow idiots (jk)

Answers

Answer:

[tex] \frac{4}{5} [/tex]

what is the distance of the points (-7,-4) and (-2,-4)

Answers

The answer would be (5,0)

Answer:

Step-by-step explanation:

The formula for calculating the distance between two points is:

d

=

(

x

2

x

1

)

2

+

(

y

2

y

1

)

2

Substituting the values from the points in the problem gives:

d

=

(

4

4

)

2

+

(

17

2

)

2

d

=

(

4

+

4

)

2

+

(

17

2

)

2

d

=

8

2

+

15

2

d

=

64

+

225

d

=

289

d

=

17

Can someone please help me on this I’ll give brainliest

Answers

Answer

b

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

whole numbers are higher than 10, nutural numbers are like 1 2 3 4 5 while integers are like fractions

look at the picture above

Answers

Answer:

12

Step-by-step explanation:

Area of a triangle = [tex]A=\frac{bh}{2}[/tex]

Where b = base and h = height

The shown triangle has a base length of 3 cm and a height of 8 cm

Using these dimensions we plug in the values into the formula

[tex]A=\frac{3*8}{2} \\3*8=24\\\frac{24}{2} =12\\A=12[/tex]

Hence, the area of the triangle is 12 square centimeters

Answer:

12 centimeters^2

Step-by-step explanation:

We find the area of a triangle by multiplying the base and width of the triangle before dividing by 2

Why because if u put 2 triangles together you get a rectangle

3*8=24

24/2=12


Which of the a-values satisfy the following inequality?
7 + a < 11
Choose all answers that apply:
A: a=3
B: a=4
C: a=5

Answers

Answer:

A = 3

I hope it's helps you

One-third of 1/2 cake =_____ cake.

Answers

Answer:

1/6

Step-by-step explanation:

1/3 x 1/2 = 1/6

1/6

1/3*1/2=(1*1)/(3*2)=1/6

Olivia has 150 caramel apples to sell. Each caramel apple is covered with one topping.
• 2/3 of the caramel apples are covered with peanuts.
• 1/5 are covered with chocolate chips.
• 1/10 are covered with coconuts.
How many caramel apples are covered with sprinkles?

Answers

5

Step-by-step explanation:

add the fractions. you have to find the common denominator, 100/150+30/150+15/150= 145 so 5

1/30 of 150=5

The caramel apples that are covered with sprinkles are 5.

What is arithmetic operation?

Arithmetic operation is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.

Now it is given that,

Olivia has 150 caramel apples.

Each caramel apple is covered with one topping.

• 2/3 of the caramel apples are covered with peanuts.

• 1/5 are covered with chocolate chips.

• 1/10 are covered with coconuts.

The rest are covered with sprinkles.

Let 'n' be the number of caramel apples are covered with sprinkles.

Thus,we can write

(2/3)*150 + (1/5)*150 + (1/10)*150 + n = 150

100 + 30 + 15 + n = 150

145 + n = 150

⇒ n = 150 - 145

⇒ n = 5

Thus, the caramel apples that are covered with sprinkles are 5.

To learn more about arithmetic operation :

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The complete question is,

Olivia has 150 caramel apples to sell. Each caramel apple is covered with one topping.

• 2/3 of the caramel apples are covered with peanuts.

• 1/5 are covered with chocolate chips.

• 1/10 are covered with coconuts.

The rest are covered with sprinkles.

How many caramel apples are covered with sprinkles?

Raincoats regularly priced at $24 were on sale for 33% off.
a. What is 33% of $24?
b. What is 33 % less than $24?

Answers

I'm pretty sure the answer for Question a is $7.92. And for be it's 16

A. $7.92

B. 16

The following data are from an experiment designed to investigate the perception of corporate ethical values among individuals who are in marketing. Three groups are considered: management, research and advertising (higher scores indicate higher ethical values).
Marketing Managers 8 7 6 7 8 6
Marketing Research 10 10 9 9 10 9
Advertising 5 6 5 4 5 5
1. Compute the values identified below (to 1 decimal, if necessary).
a. Sum of Squares, Treatment?
b. Sum of Squares, Error?
c. Mean Squares, Treatment?
d. Mean Squares, Error?
2. Use Alpha= .05 to test for a significant difference in perception among the three groups.
3. Calculate the value of the test statistic (to 2 decimals)?
4. The p-value is?
5. What is your conclusion?
6. Using Alpha= .05, determine where differences between the mean perception scores occur.
7. Calculate Fisher's LSD value (to 2 decimals)?
8. Test whether there is a significant difference between the means for:________.
marketing managers (1),
marketing research specialists (2),
and advertising specialists (3).
Difference Absolute Value Conclusion for (1)-(2)?
Difference Absolute Value Conclusion for (1)-(3)?
Difference Absolute Value Conclusion for (2)-(3)?

Answers

Answer:

Part 1

a. Sum of Squares, Treatment= 61

b. Sum of Squares, Error= 7.5

c. Mean Squares, Treatment = 30.5

d. Mean Squares, Error= 0.5

2. the F value lies in the rejection region > 3.6823

3. The value of the test statistic = 61

4. The p-value is < 0.00001

5. Conclusion

Since p-value < α, H0 is rejected.

6. Between x`2 and x`3

7. Fisher's Least Significant Difference value almost 0.869

8.There is a significant difference between the means

Step-by-step explanation:

Summary of Data

                          Treatments

                       1             2             3                 Total

n                      6             6             6                   18

∑x                   42          57           30                  129

Mean              7            9.5           5                  7.167

∑x2              298         543        152                    993

Sd.D       0.8944     0.5477     0.6325           2.0073

ANOVA Table

Source                                  SS              df                  MS

Between-treatments           61              2                   30.5       F = 61

Error                                     7.5           15                     0.5

Total                                     6             8.5                     17

a. Sum of Squares, Treatment= 61

b. Sum of Squares, Error= 7.5

c. Mean Squares, Treatment = 30.5

d. Mean Squares, Error= 0.5

2. Using alpha= 0.05 the F value lies in the rejection region i.e F > 3.6823

x1` -x2`= 7-9.5= -2.5 Not significant as difference <3.68

x1`- x3`= 7-5= 2 Not significant as difference <3.68

x2` -x3`= 9.5-5= 4.5 Significant as difference > 3.68

3. The value of the F test statistic = 61

4. The p-value is < 0.00001

5. Conclusion

Since p-value < α, H0 is rejected.

6. Using alpha= .05, differences occurs between x2` and x3` as their difference is greater than 3.68

7. Fisher's Least Significant Difference value almost 0.869

Least Significant Difference= t( 0.025,15) √2s²/r s²= 0.50 r= 6 =n1=n2=n3

Least Significant Difference= 2.13 √ 2*0.50/ 6

=0.869

8.There is a significant difference between the means

x1` -x2`= 7-9.5= -2.5 Significant as difference > Least Significant Difference

x1`- x3`= 7-5= 2 Significant as difference > Least Significant Difference

x2` -x3`= 9.5-5= 4.5 Significant as difference > Least Significant Difference

A small university is concerned with monitoring its electricity usage in its Student Center. Specifically, its officials want to know if the amount of electricity used differs by day of the week. They collected data for nearly a year, and the relevant summary statistics are provided. Note that electricity usage is measured in kilowatt hours. Day of Week n x bar s Sunday 45 86.48 34.89 Monday 45 109.29 27.37 Tuesday 45 110.96 28.64 Wednesday 44 115.03 31.68 Thursday 44 114.97 33.26 Friday 45 108.58 32.22 Saturday 45 87.07 38.56 Overall 313 104.56 34.25 Computer output from the analysis is provided: One-way ANOVA: Electricity versus Day of Week Source DF SS MS F P Day of Week 6 41646 6941 6.55 0.000 Error 306 324428 1060 Total 312 366073 What is the decision on the hypothesis test and why

Answers

Answer:

Since p-value > ∝, H0 is accepted

Step-by-step explanation:

Calculating gives the following results.

ANOVA Table

Source DF               Sum             Mean      F Statistic P-value

                                 of Square           Square

Groups     6         191.61                      31.935        0.020          0.999

(b/w groups)

Error

(within 14          21736.08                1552.577

groups)                                                                                                    

Total  20          21927.69 1096.385                                          

1. H0 hypothesis

Since p-value > ∝, H0 is accepted.

Hence the averages of all groups considered to be equal.

Or the difference between the averages of all groups is not big enough to reject H0.

2. P-value

P-value equals 0.999. This means that if we would reject H0, the chance of type1 error (rejecting a correct H0) would be too high i.e  (99.99%)

The bigger  p-value  supports H0.

3. The statistics

The test statistic F equals 0.020, which lies in the accepted range: [-∞ : 2.8477]

What is the following simplified product? Assume x>0.
218x3 3.V10x4 – x15x?
0 244² √5% - 44² √10x
24x35x - 4x3 10X
24x3 75-4x310x
O 24x35x +4x® /10x

Answers

Answer:

[tex]24x ^{3} \sqrt{5 - 4x ^{3} } \sqrt{10x} [/tex]

Some students reported how many pets they had. The dot plot shows the data collected: A dot plot is titled Students Pets and labeled Number of Pets. The values on the horizontal line are 0, 1, 2, 3, and 4. There are 5 dots above 0, 4 dots above 1, 3 dots above 2, 2 dot above 3, and 1 dot above 4. What do the dots above the number 3 indicate? There are exactly 2 students with 3 pets. There are exactly 3 students with 2 pets. There are exactly 2 students with more than 3 pets. There are exactly 3 students with more than 2 pets.

Answers

Answer:

A dot plot is similar to histogram wherein they show the frequency of data. In this kind of plot, instead of bars, dots are stacked on their corresponding bin. The bins here are the number of pets, while the dots are the students. So, the 2 dots above number 3 signifies that, there are two students with three pets. The answer is A.

Step-by-step explanation:

to find the sum of all the odd integers from to 49 inclurive

Answers

Answer:

625 is the sum of first 49 odd numbers.

Step-by-step explanation:

Add the all odd numbers between 1 - 49.

1+3+5+7+9+11+ 13+ 15+17+ 19+21+23+25+ 27+29+31+33+35+37+39+41+43+45+ 47+ 49 = 625

Hope it is helpful....

Write the anwser in the simplest form.​

Answers

Answer:

6/9

Step-by-step explanation:

really sorry if I'm wrong good luck!

Julie can type 250words in 5 minutes. How long does she take to type 900words

Answers

Answer:

18 minutes

Step-by-step explanation:

900/250 is 3.6

3.6 * 5 = 18

Answer:

18 minutes

Step-by-step explanation:

Hi! Okay, let's get started!

Let's find her rate per minute first = 250/50 = 50 words per minute

Now, we need to find the time for 900 words, so we do 900/50, which gives you 18, or 18 minutes!

Hope that helps! :)

Find an expression which represents the sum of (8x+10y)

Answers

Answer:

Not sure of what your asking....

Step-by-step explanation:

equivalent to: 2(4x+5y)

Answer:

2(4x+5y)

Step-by-step explanation:

the sum of 8x+10y is 8x+10y

i guess you could make it even more complicated if you want

ln(8x)=ln(1/(10y))

ln(8x/(1/(10y)))

or you can just keep it simple

8x+10y = 2(4x+5y)

A tent that sells for 250 is on sails for 20% discount what's the sale price of the tent

Answers

Step-by-step explanation:

Original price- $250

Discount 20% x   20

                       -----------

                        5000

Equals amount taken off $5000

Subtract original price        -250

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

                 Sale Price          4750

Hope this helps! If this is not the answer please tell me!

find the value of x and the value of y ?​

Answers

Answer:

B)  x = 7,  y = 4[tex]\sqrt{2}[/tex]

Step-by-step explanation:

you can find the value of 'y' first by connecting the bases with another altitute measuring 4 units

you now have an isosceles triangle where each leg is 4 which makes the hypotenuse equal to 4[tex]\sqrt{2}[/tex]

to find 'x', it is the sum of 3 and 4

Solve

FIND THE SIMPLE INTEREST WHEN PRINCIPAL= $300, rate = 8%
Time= 4 years





WILL GIVE BRAINLIST


X
X

X
X
X
X
X
X
X
X
X

Answers

Answer:

I = p× r× t

300×8×4

pinicipal × rate × time

That is the formula

the answer is 300×8×4= 9600

The median number of parks cleaned by 101010 service workers in a certain year is 444. The range of the number of parks cleaned by those service workers that year is 777.
Determine if the following statement is true, is false, or does not contain enough information.
If the greatest number of parks cleaned is 101010, then the fewest parks cleaned is 333.
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
True

(Choice B)
B
False

(Choice C)
C
Not enough informationvv

Answers

Answer:

The answer is A

Step-by-step explanation:

I got it wrong and it showed that it’s A

Round to the nearest tenth if necessary.

Answers

A is 2
B is 4 ft
C is 6 ft

Amy goes to a pumpkin patch and picks out a pumpkin that weighs 3,550 grams. If 1 gram = 0.0352 ounces, how many ounces does the pumpkin weigh?
A) 124.56 ounces
B) 124.96 ounces
C) 125.56 ounces
D) 125.96 ounces

Answers

9514 1404 393

Answer:

  B) 124.96 ounces

Step-by-step explanation:

To find ounces, multiply the number of grams by the number of ounces in each gram.

  3550 × 0.0352 = 124.96 . . . ounces

If f (x ) = -4x – 11, what is f (5)?

Answers

Answer:

-31

Step-by-step explanation:

We are given with a function f(x) = - 4x - 11 , and we need to find f(5) . For which , we just have to put x = 5 in f(x) . So , by putting x = 5 , we have

[tex]{:\implies \quad \sf f(5)=-(4\times 5)-11}[/tex]

[tex]{:\implies \quad \sf f(5)=-20-11}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{f(5)=-31}}}[/tex]

A 3 foot wide painting should be centered on 13 foot wide wall how many feet should be on each side of the painting

Answers

Answer:

5 feet of wall should be on each side of the painting.

Step-by-step explanation:

Given that a 3 foot wide painting should be centered on 13 foot wide wall, to determine how many feet should be on each side of the painting, the following calculations must be performed:

(13 - 3) / 2 = X

10/2 = X

5 = X

Therefore, 5 feet of wall should be on each side of the painting.

26) Which of these equations is parallel to -3x - y = 1?
A) y
12 x – 5
3
B) y = 3x + 4
C) y
= -3x
1
D) y = x + 1

Answers

Answer:

y=-3x

Step-by-step explanation:

use the point slope formula to find the line parallel to -3x-y=1

Answer:

B) y = 3x+4

Step-by-step explanation:

A parallel line should include the same the same slope for it to be parallel

Help me please whats 93 divided by 29 to the power of 3 and multiplied by 283

Answers

Answer:

1.07913403584

Step-by-step explanation:

hope it helps you!!

branliest plssssss

Answer:

641,894,091

Step-by-step explanation:

There were 24 students in Mrs. Weibel’s class last year and now she has 27 students. What is the percent increase in students from last year to this year? Express your answer to the nearest tenth.

Answers

Answer:

12.5%

Step-by-step explanation:

change/original amount * 100= percentage change

3/24 * 100 = 12.5

Write the power (-8)^2 in repeated multiplication form. Then find the value of the power

Answers

Answer:

(-8)x(-8)=64

Step-by-step explanation:

(-8)²

(-8)x(-8)=64

The repeated multiplication of (-8)² is -8 x (-8).

What are Exponent and Power?

Exponents and powers can be used to represent extremely big or extremely small numbers in a more straightforward fashion.

For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 34, where 4 is the exponent and 3 is the base.

We know that exponents and power used to express powers.

like if we have 5³ then 5 is multiplied to itself 3 times.

Here we have (-8)² then we can write

(-8)²

= -8 x -8

= 8 x 8

= 64.

Learn more about Exponent and power here:

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SOLVE


HOW MUCH
COMISSION
WILL AN AGGENT
MAKE ON THE SALE OF A $111,500 HOUSE IF SHE RECEIVES 1.5% OF THE SELLING PRICE



WILL
GIVE
BRIANLIST

Answers

Answer:

$1672.5

Step-by-step explanation:

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