Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 38 randomly selected people who train in groups, and finds that they run a mean of 49.5 miles per week. Assume that the population standard deviation for group runners is known to be 1.1 miles per week. She also interviews a random sample of 33 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 2.6 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2.

Required:
Draw a conclusion and interpret the decision.

Answers

Answer 1

Answer:

conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.

Step-by-step explanation:

H0 : μ1 = μ2

H0 : μ1 ≠ μ2

The test statistic :

(x1 - x2) / √(s1²/n1) + (s2²/n2)

(49.5 - 48.5) / √(1.1²/38) + (2.6²/33)

1 / √0.2366905

Test statistic = 2.055

Using the Pvalue from Tstatistic calculator :

df = (smaller sample - 1) = 33 - 1 = 32

Pvalue from Test score calculator = 0.048

Pvalue > α ; Fail to reject the null ;

Hence, conclude that there is no significant evidence to support the claim that difference exists between the mean number of miles run by the two groups.


Related Questions

A sample of 14 cans of Brand I diet soda gave the mean number of calories of 23 per can with a standard deviation of 3 calories. Another sample of 16 cans of Brand II diet soda gave the mean number of calories of 25 per can with a standard deviation of 4 calories. At the 1% significance level, can you conclude that the mean number of calories per can are different for these two brands of diet soda? Assume that the calories per can of diet soda are normally distributed for each of the two brands and that the standard deviations for the two population are equal.

Answers

Answer:

ठथठलछंशू फथजलट एक ओज पनि हो र स्वार्थी यसलाई मैले कसरी भुल्न सक्थेँ र त्यहाँको बडेमाको बिल्डिङ भित्र म. म जिन्दगी एक यात्रा तय गर्न गर्ने हो र त्यहाँको बडेमाको बिल्डिङ बनाउनलाई मुख्य समाचार पृष्ठ सभकेँ रिफ्रेश कए देखू। म भने त्यो भने हेर्न

a skier travels 4 seconds and cover 72 meters. how long will it take the skier to travel 360 meters?

Answers

It should take 20 seconds for the skier to travel 360 meters.

Please help me faster if know please?!!!!

Answers

.83

25 bus riding sophomores / 30 sophomores

PLZ HELP NO LINK PPPPLLLLLLLLLZZZZ

Answers

Answer:

its A

Step-by-step explanation:

Answer:

uhk3rbfghsfbhufevhjb

Step-by-step explanation:

give me brainlest

Only answer if you’re sure :) need the whole answer! Will give Brainly

Answers

Answer:

Step-by-step explanation:

y = -1x + 1

y = -x + 1

I'm sure  :P

Answer:

y=-1x+1

Step-by-step explanation:

the slope is 1/1 and line is declining hence the negative

i need help on this for math class dont mind how i answered a

Answers

Step-by-step explanation:

I think its c cus its more relatable .

Answer:

c would be the answer.

when you answer the equation x - 15= 60

you would add 15 to 60 to get 75. That is the only answer that would make sense.

Population Growth

Using the graph, find the value of y when x = 7.

a. y = 7 c. y = 2.71
b. y = 6.1 d. y = 4.42

Please select the best answer from choices provided

Answers

Answer:

D. y = 4.42

Step-by-step explanation:

I calculated it logically

What is the slope of the line that is perpendicular to the line y = -2x + 5?
slope =

Answers

Answer:

The perpendicular line is vertical and the slope is undefined.

Step-by-step explanation:

Slope : - 2
Y intercept : ( 0,5 )

Solve: 63z2+61z=−6. Multiple answers

Answers

z = -1/9 , -6/7

Have a nice day!

help me plzzzzzzzzz
solve for x

Answers

Answer:

[tex]7) \frac{x+20}{x}=\frac{46}{30}[/tex]

[tex]30(x+20)=46x[/tex]

[tex]30x+600=46x[/tex]

[tex]46x-30x=600[/tex]

[tex]16x=600[/tex]

[tex]x=75/2[/tex]

[tex]x=37.5[/tex]

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

[tex]8) \frac{10}{3x+1} =\frac{22}{7x-1}[/tex]

[tex]10(7x-1)=22(3x+1)[/tex]

[tex]70x-10=66x+22[/tex]

[tex]70x-66x=22+10[/tex]

[tex]4x=32[/tex]

[tex]x=\frac{32}{4}[/tex]

[tex]x=8[/tex]

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

hope it helps...

have a great day!!

What must the values of x and y be so that the two houses are similar?

Answers

your answer on the page is c

Find the measure angles

No links for answers

Answers

Answer:

Angle L = 44

Angle M = 93

Angle O = 88

Angle P =  74

Step-by-step explanation:

First find your x, all angles will equal 360 when put together

360=61+x+(2x+5)+(x+30)+(2x)

360 = 61 + 5 +30 + x + 2x + x + 2x

360 - 96 = 6x

264 = 6x

264 / 6 = x

44 = x

Now place 44 in place of all x

Angle L:

x = 44

Angle M

(2x+5) = 2*44 + 5 = 93

Angle O

2x = 2*44 = 88

Angle P

(x+30) = 44 + 30 = 74

If m∠A = 29°, m∠B = 84°, and c = 14, what are the measures of the remaining sides and angle?

Answers

Answer:

m∠C = 67°, a = 7.37, b = 15.13

Step-by-step explanation:

There are 180° in a triangle. We know two angles in the triangle, so we can calculate the third angle.

Since this is not a right triangle, we will use the Law of Sines.

SinA/a = SinB/b = SinC/c

see image.

The gray figure below is the image of the black figure after a dilation. Which represents the dilation?

A (x,y) -> (2x, 2y)
B (x,y) -> (3x, 3y)
C (x,y) -> (0.5x, 0.5y)
D (x,y) -> (x+4, y+5)

Answers

The answer is A (x,y) -> (2x, 2y) it is representing the dilation.

What is dilation?

Dilation is a medical procedure that involves widening a part of the body, such as the cervix or esophagus, by stretching and enlarging it. This can be done for a variety of reasons, including to allow for the passage of a baby during childbirth or to facilitate the insertion of a medical instrument or device. Dilation is usually done using dilators, which are cylindrical tools with a tapered end that can be inserted into the body and then gradually increased in size.

Dilation is a geometric transformation that enlarges or reduces the size of a shape by a factor. In this case, the shape is enlarged, with the resulting shape being twice the size of the original black figure. This is represented by the equation A (x,y) -> (2x, 2y), where the x and y coordinates of each point in the figure are multiplied by two.

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In a village, the cases of a particular infectious
disease have been exponentially decreasing at
a rate of 95% per year since the people started
receiving the vaccine. If there were 200 cases
in the village to start with, predict the number
of cases after 2 years.
First, complete the equation:
Remaining Amount = 200(1-0.95)²

Answers

The number remaining in the village is 30.

How many people remain?

We have to note that the case in which the population of the community is being reduced because of the fact that the community is being ravaged by disease is a case of a decrease in the population and is a problem of exponential decrease.

Then we would have that;

N =Noe^-rt

N = Number at time t

No = Initial number

r = spread rate

t = time taken

Then;

N = 200e^-0.95 * 2

N = 30

Thus, they would have only 30 people left.

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what is the area shaded in the region?

Answers

Answer:

Option C

The Area Of Shaded Region is 50.2 cm²

Step-by-step explanation:

For A given Circle,

For Small (Non-Shaded) Circle:

Diameter (d) = 6 cm

Radius = d ÷ 2 = 6/2 = 3 cm

For Area of Small (Non-Shaded) Circle

Formula:

A = πr²

A = 3.14 × (3)² cm

A = 3.14 × 9 cm

A = 28.26 cm²

For Area of Big (Shaded) Circle:

Diameter (d) = 10 cm

Radius = d ÷ 2 = 10/2 = 5 cm

For Area of Small (Non-Shaded) Circle

Formula:

A = πr²

A = 3.14 × (5)² cm

A = 3.14 × 25 cm

A = 78.5 cm²

For The Area Of Shaded Region

Area of Big Circle - Area of Small Circle

78.5 cm² - 28.26 cm² = 50.24 cm²

Thus, The Area Of Shaded Region is

50.2 cm²

-TheUnknownScientist

Answer:

3rd option

50cm2

Step-by-step explanation:

50cm2

explanation is given above

A circle of radius 8 cm is cut into 6 parts
of equal size, as shown in the diagram.
Calculate the area of each part, giving
your answer correct to 2 decimal places.

Answers

To find the area of each part of the circle, we first need to find the total area of the circle. The formula for the area of a circle is A = πr^2, where A is the area, r is the radius, and π (pi) is a constant approximately equal to 3.14. Plugging in the given values, we find that the total area of the circle is:

A = π * 8^2 = 3.14 * 64 = 201.12 cm^2

Since the circle is divided into 6 equal parts, the area of each part is equal to the total area of the circle divided by 6:

Area of each part = 201.12 cm^2 / 6 = 33.52 cm^2

Rounded to 2 decimal places, the area of each part is 33.52 cm^2.

Answer:  To calculate the area of each part of the circle, we need to first find the total area of the circle and then divide it by the number of parts.

The formula for the area of a circle is A = πr², where A is the area, r is the radius, and π is approximately equal to 3.14.

In this case, the radius of the circle is 8 cm, so the area of the circle is A = π * 8² = 3.14 * 64 = 200.96 cm².

Since the circle is divided into 6 parts of equal size, the area of each part is equal to the total area of the circle divided by the number of parts. Therefore, the area of each part is 200.96 cm² / 6 = 33.49 cm².

Rounded to 2 decimal places, the area of each part is 33.49 cm² ≈ 33.50 cm².

Step-by-step explanation:

Plz help me!!!!! 3. &4 only!!!

Answers

Answer:

Step-by-step explanation:

3.

Note that

[tex]L_1 : 4x-y=10 \\ L_2: -2x+4y=16[/tex]

aren't parralel lines. So they are intersected in one point.

Answer: Number of solutions is ONE. The system is soluble

4.

Similarly to 3. Number of solutions is ONE. The system is soluble

15 trading cards he wants to give to 5 friends. Each friend gets same number of trading cards

Answers

Answer:

Each friend gets 3 cards

Step-by-step explanation:

Divide 15 by 5 since he is splitting 15 cards with 5 friends.

:D

A study was conducted to see if students from public high schools were more likely to attend public colleges compared to students from private high schools. Of a random sample of 100 students from public high schools, 60 were planning to attend a public college. Of a random sample of 100 students from private high schools, 50 of them planned to attend a public college. The 90% confidence interval for the difference between the proportion of students planning to attend public college between students at public versus private high schools is (-0.0152, 0.2152). Select the correct interpretation of this confidence interval.
a. Reject the null hypothesis
b. Fail to reject the alternative hypothesis
c. Accept the null hypothesis
d. Fail to reject the null hypothesis

Answers

Answer:

B

Step-by-step explanation:

We are 90% confident the proportion of students planning to attend public colleges who attended public high schools is between 0.0152 lower than to 0.2152 higher than the proportion of students planning to attend public colleges who attended private high schools.

Find each angle measure to the nearest degree
1) Find m.
5
S
R
5.7
T
please help, show work if possible :)

Answers

Answer:

RS=26.49 m;

ST =14.08 m;

m<R =28°

Step-by-step explanation:

what is the value of x in the equation shown below x^3+1=9

Answers

Answer:

x = 2

Step-by-step explanation:

x^3 + 1 = 9

x^3 = 8

[tex]\sqrt[3]{x^3}[/tex] = [tex]\sqrt[3]{8}[/tex]

x = 2

A, B, C, or D?
and an explanation

Answers

the answer would be d

Answer:

A

Step-by-step explanation:

3
Use the drawing tool(s) to form the correct answer on the provided graph.
The function f(x) is shown on the provided graph.
Graph the result of the following transformation on f(x).
Drawing Tools
Select
Line
Click on a tool to begin drawing
-10
-8
f(z) + 6
-6
4
-2
10-
8-
6
Delete
Undo
Reset
10 i need help with this

Answers

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

what is transformation ?

Four various modifications that can be made to a point, line, or geometric object are referred to as transformations collectively. You must be able to identify which changes have been made and that each alteration has been made. The following guidelines for function translation and transformation: The function is shifted up by b units by F (x) + b. F (x) b causes the function to move downward. The expression f (x + b) causes the function to be moved left b units. Translation, reflection, rotation, and dilation are the four different types of transformations. Transform, reflect, or rotate the geometric shapes that are displayed on a coordinate plane. The transformation, often known as f: X X, is the name given to a function, f, that maps to itself.

given

-1 on the left x-axis and 4 on the right y-axis

Start at -2 on the y-axis, move up the y-axis six times, and you should arrive at 4. However, you must identify the first line in order to complete the puzzle.

Start at -2 on the y-axis, count up until it is on a corner of the graph, then move 4 up on the y-axis and once to the right, making the fraction 4/1.

Since you should be at 4, apply the formula rise/run 4/1 to ascend 6 on the y-axis.

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Can someone help me out. Paying big points

Answers

Answer:

1) the quadrants go counter clockwise, Quadrant I is the upper right square, Quadrant II is the upper left square, Quadrant III is the lower left square, and Quadrant IV is the lower right square.

2) Quadrant II

3) Quadrant IV

4) Quadrant III

5) Quadrant I

6) Both would be on the horizontal axis

7) Both would be on the vertical axis

Step-by-step explanation:

Hope this helped!

write 363 in the base-four system

Answers

Answer:

  363 = 11223₄

Step-by-step explanation:

You want 363 written in base 4.

Base conversion

We can convert to base 4 by looking at the remainders from repeated division by 4:

  363 ÷ 4 = 90 r 3

  90 ÷ 4 = 22 r 2

  22 ÷ 4 = 5 r 2

  5 ÷ 4 = 1 r 1

  1 ÷ 4 = 0 r 1

Writing the remainders in reverse order gives the base-4 number:

  363 = 11223₄

A walkway forms one diagonal of a square playground. The walkway is 32 m long. How long is each side?

Answers

Answer:30.45751052, or 30.5

Step-by-step explanation:

since you know that the playground is a square, a diagonal would cut the square into 2 45-45-90 triangles, now that you know that information, there is a really easy way to solve the problem, the way i did it was i used the law of sines, which states that side a/sin(angle A)=side b/sin(angle B). so 32/sin(90)=30.7943... substitute that into the equation and you get 30.7943... =side b/sin(angle B). since you know that angle B =45 degrees take the sin of that and multiply it by 30.7943 to get the answer.

any help please — Put the fractions 12,38 and 34 in order from smallest to largest. Find the value of 113+256.

Answers

The value of 113+256 is determined by the above fractional formulae. Is 369

Why are fractional equations difficult to solve?

An exact number that shows a percentage of a total is called a fraction. You may figure it out by dividing a sum by the quantity of parts. As an example, the number 12 represents one-half of a whole number or an object. Simple subtraction of the smaller numerator from the larger numerator will yield the solution to the problem. To solve, for instance, 6/8 - 2/8, just take 2 out of the answer. The answer, which can be abbreviated to "4/8," is 12, or 12.

Making a fraction simpler by reducing or simplifying it is our goal. In order to do this, we divide the denominator and numerator by the largest integer that can be divided into both integers precisely. That is to say,

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Can someone help plz

Answers

Answer:

I never did this sort of stuff so correct me if I am wrong but I think it's 25

Step-by-step explanation:

Only question b

b) Write down the output y in terms of x

Input = x > +7 > x5 > Output = y

Answers

Therefore ,As a result, y = 5x + 35 is the equation that gives the answer to the given algebra issue.

Algebra: What Is It?

Algebra is used to analyze mathematical symbols, and logic is used to manipulate those symbols. The PEMDAS rule stands for the following operations: parenthesis, exponent, multiplication, division, addition, and subtraction. This rule is applied to solve the equation properly and accurately.

Here,

In this case, the equation for y in terms of x will be as follows:

y = 5(x + 7)

If you make the equation simpler, you get

y = 5(x + 7)

y = 5x + 35

y will have the linear equation y = 5x + 35 in terms of x.

Therefore , As a result, y = 5x + 35 is the equation that gives the answer to the given algebraic issue.

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