Given two independent random samples with the following results: n1=8x‾1=186s1=33 n2=7x‾2=171s2=23 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed. Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Answers

Answer 1

Answer:

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And the confidence interval is given by:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 186[/tex] the sample mean for the first sample

[tex] \bar X_2 = 171[/tex] the sample mean for the second sample

[tex]s_1 =33[/tex] the sample deviation for the first sample

[tex]s_2 =23[/tex] the sample deviation for the second sample

[tex]n_1 = 8[/tex] the sample size for the first group

[tex]n_2 = 7[/tex] the sample size for the second group

The confidence interval for the true difference is given by:

[tex] (\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}[/tex]

We can find the degrees of freedom are given:

[tex] df = n_1 +n_2 -2 =8+7-2= 13[/tex]

The confidence level is given by 90% so then the significance would be [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2=0.05[/tex] we can find the critical value with the degrees of freedom given and we got:

[tex] t_{\alpha/2}= \pm 1.77[/tex]

The point of estimate for the true difference would be:

[tex] 186-171= 15[/tex]

And replacing into the formula for the confidence interval we got:

[tex] (186-171) -1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= -10.753[/tex]

[tex] (186-171) +1.77 \sqrt{\frac{33^2}{8} +\frac{23^2}{7}}= 40.753[/tex]


Related Questions

graph x2 - y2 = 16 what are the lines of symetry

Answers

Answer:

it has 4 lines of symetery the x - axis,the y-axis,y=x,and y ''Cx every line through the center is a line of symetry

Step-by-step explanation:

Of the 250 students at Moreland middle school, 80% ride the bus to school. Monica wants to know the number of students that ride the bus.

Answers

Answer:

200; 80% of 250 is 200

Answer:

Step-by-step explanation:

200

6. A golfer is standing at the tee,
looking up to the green on a hill. If the
tee is 36 yards lower than the green
and the angle of elevation from the tee
to the hole is 12º, find the distance from
the tee to the hole.​

Answers

Answer:

173.15 yards is the distance from tee to hole.

Step-by-step explanation:

Please refer to the image attached.

Let A is the position of tee and where the golfer is standing.

C is the position of hole.

CB is the vertical distance between greens and tee.

Angle of elevation, [tex]\angle BAC = 12^\circ[/tex]

To find: side AC.

Using trigonometric functions, we know that value of sine is:

[tex]sin\theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}[/tex]

Here [tex]\theta = \angle BAC = 12^\circ[/tex]

Perpendicular is side CB.

Hypotenuse is side AC.

[tex]sin12^\circ = \dfrac{\text{CB}}{\text{AC}}\\\Rightarrow \text{CB} = \dfrac{36}{sin12^\circ}\\\Rightarrow \text{CB} = 173.15\ yards[/tex]

Hence, 173.15 yards is the distance from tee to hole.

Tate is paid $17.35 per hour with time and a half overtime. What will his gross pay period in which he worked 35 hours one week and 44 hours next week for a total 79 hours?

Answers

Answer:

The new rule has a higher salary level for exemption from overtime, at $684 a week. This means that lower-pay exempt employees may qualify for overtime.

Step-by-step explanation: this is your answer plz rate e the most brainlest


which is equivalent to sin^-1 ( sqrt 3/2 )? Give your answer
Give your answer in radians.

Answers

Answer: pi/3

Step-by-step explanation:

correct on edge 2020

The equivalent value of trigonometric relation sin⁻¹ ( √3/2 ) = π/3

What are trigonometric relations?

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the trigonometric relation be represented as A

Now , the value of A is

sin⁻¹ ( √3/2 ) = θ

Now , the value of θ is calculated by

In a triangle , sin θ = opposite / hypotenuse

So , sin θ = √3/2

The value of θ = 60°

So , the measure of 60° in radians is θ = π/3

Hence , the value of θ from the trigonometric relation is π/3

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Find the middle term of the expansion of (x+y)^8 a40x^2y^2 b70x^2y^2

Answers

Answer:

the middle term = 70x⁴y⁴

Step-by-step explanation:

Given;

(x+y)⁸

This expression can be expanded as follows, using Paschal triangle;

                                                 1      1

                                               1    2     1

                                             1     3      3      1

                                         1     4       6      4     1

                                    1       5     10    10       5    1

                            1           6      15     20     15     6        1

                    1            7         21      35     35      21     7          1

        1                 8          28        56     70     56    28       8         1

At level 8, the middle coefficient is 70

Also the power of x and y will be equal in the middle term = A(xⁿ yⁿ)

A = 70 ,

n +n = 8

n = 4

Thus, the middle term = 70x⁴y⁴

1.(1 0) You measure the distance, l, a projectile travels several times using the same apparatus and find the following values (cm): 5.11, 4.89, 5.04, 4.94, 4.93, 5.06 and 5.09. Assuming that the errors are random: a) What is the mean value forl? b) What is the standard deviation for this data set? c) What is the uncertainty associated with your best estimate forl? d) How should one report the result of this measurement along with the uncertainty at the 95 % confidence level? e) If you desire to reduce the statistical uncertainty associated with the reported result using the same apparatus to be only 0.01 cm, how many measurements must be made?

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached image below to see the step by step explanation to the question above.

apply the distributive property to factor out the gcf of 35+14

Answers

Answer:

  7(5 +2)

Step-by-step explanation:

From our knowledge of times tables, we know that ...

  35 = 5·7

  14 = 2·7

so the greatest common factor of 35 and 14 is 7. Factoring that out, we have ...

  35 +14 = 7(5 +2)

Graph-3x2 + 12y2 = 84. What are the domain and range?

Answers

Domain (infinity,infinity)

Range (infinity,[tex]\sqrt{7}[/tex])

Finding the work done in stretching or compressing a spring.

Hooke's Law for Springs.
According to Hooke's law, the force required to compress or stretch a spring from an equilibrium position is given by F(x)=kx, for some constant k. The value of k (measured in force units per unit length) depends on the physical characteristics of the spring. The constant k is called the spring constant and is always positive.

In this problem we assume that the force applied doesn't distort the metal in the spring.

A 2 m spring requires 11 J to stretch to 2.4 m. Find the force function, F(x), for the spring described.

Answers

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images below to see the step by step explanation to the question above.

If you flipped a fair coin 18 times about how many times would you expect heads to appear?

Answers

Answer:

9 times

Step-by-step explanation:

hope this helps

Answer:

9

Step-by-step explanation:

Mathematically, 9, although reality wise, you could flip the coin and get heads every time, or the opposite.

I think you mean mathematically though, so yes, it would be 9.

A girl and a puppy are 850 feet apart when they start running towards each other. The girl runs at a speed of 8 feet per second, and the puppy runs at a speed of 7 feet per second. How soon will they meet?

Answers

Answer:

The correct answer is 56.6666666667 second's

Answer:

56 2/3

Step-by-step explanation:

In a comparison of the body fat percentage of four different ethnic groups, the body fat percentage was measured for 200 African-Americans, 160 Whites, 220 Hispanics, and 310 Others. Because a comparison of average body fat percentage between these groups is desired, an ANOVA test was conducted, which resulted in p-value of 0.11. What conclusion can you make if level of significance is 0.05?

Answers

Answer:

There is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

Step-by-step explanation:

The Analysis of Variance (ANOVA) test is used to determine whether there is any significant difference between the mean of various independent groups.

In this case an ANOVA test is being performed to determine whether the fat percentage of four different ethnic groups are different or not.

The hypothesis can be defined as:

H₀: The fat percentage of four different ethnic groups are same, i.e. μ₁ = μ₂ = μ₃ = μ.

Hₐ: The fat percentage of at least one of the four ethnic groups is different, i.e. at least one μ[tex]_{i}[/tex] is different.

The significance level of the test is, α = 0.05.

The decision rule is:

If the p-value of the test is less than the significance level, then the null hypothesis will be rejected.And if the p-value of the test is not less than the significance level, then the null hypothesis will not be rejected.

The p-value of the ANOVA test is computed as, p-value = 0.11.

p-value = 0.11 > α = 0.05.

The null hypothesis was failed to be rejected.

Hence, it can be concluded that there is not enough evidence to support the claim that the fat percentage of at least one of the four ethnic groups is different.

A line has the equation 3x–4y–12=0.

Is the point (2, −1) on the graph?

Answers

Answer:

The point (2, -1 ) is not on the graph of the line.

Step-by-step explanation:

3x–4y–12=0

3*2 - 4*(-1) - 12= 0

6 + 4 - 12 =0

10 - 12 = 0

- 2 = 0 , false, so the point (2, -1 ) is not on the graph of the line.

A large company that produces a "fat-burner" pill claims an average loss of 20 pounds in the first month. A consumer advocacy group believes that this claim is actually just "hype" intended to sell more of the compound. The advocacy group would like to obtain statistical evidence about this issue and takes a random sample of 100 consumers who responded that they had purchased the pill but didn't know what the survey was about. They find that these 100 people lost an average of 18 pounds with a standard deviation of 7.5 pounds. What are the null and alternative hypothesis in this situation

Answers

The null and alternative hypothesis for the tests are:

H0: μ = 20

Ha: μ < 20

Given data:

In this situation, the null and alternative hypotheses can be formulated as follows:

Null Hypothesis (H0): The average weight loss of consumers who take the "fat-burner" pill is equal to 20 pounds.

Alternative Hypothesis (Ha): The average weight loss of consumers who take the "fat-burner" pill is less than 20 pounds.

In symbolic notation:

H0: μ = 20

Ha: μ < 20

where μ represents the population mean weight loss of consumers who take the "fat-burner" pill.

The null hypothesis assumes that the claim made by the company is accurate and that the average weight loss is indeed 20 pounds. The alternative hypothesis challenges this claim and suggests that the actual average weight loss may be less than 20 pounds, implying that the "hype" around the pill's effectiveness might be exaggerated.

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Need help ASAP! Simplify the expression so there is only one positive power for the base, -5. (The questions/answers are in the group chat.)


A.

B.

C.

D.

Answers

The correct answer is C. -5^5.

Answer: C

Step-by-step explanation:

-5^7 ➗ -5^2

(-5)^(7-2)

-5^5

A number increased by 11 is equal to twice the number decreased by 12

Answers

Answer: 10

Step-by-step explanation:

What is the GCF of 45 and 72?

Answers

Answer:

The common factors of 45 and 72 are 9, 3, 1

Step-by-step explanation:

Answer:

The GCF of these two numbers is nine.

Step-by-step explanation:

They share three common factors: 1, 3 and 9. The greatest out of all of those is 9. Hope this helps!

Please help ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.

Answers

Answer:

D

Step-by-step explanation:

Answer:C and D

Step-by-step explanation:

7x^2-42x=0

First find the highest common factor of 7x^2 and 42x

7x^2=7 x X x X

42x=2 x 3 x 7 x X

Highest common factor is 7x

7x(x-6)=0

7x=0. or x-6=0

x=0. or x=6

Giving brainliest for CORRECT awnser.

Answers

Answer:

x < 18 - 10

x < 8

Step-by-step explanation:

Answer:

8 > x

Step-by-step explanation:

-10 > x- 18

Isolate the variable, x. Note the inequality sign, treat it like an equal sign; what you do to one side, you do to the other. Add 18 to both sides:

-10 (+ 18) > x - 18 (+18)

-10 + 18 > x

Simplify. Combine like terms:

(-10 + 18) > x

18 - 10 > x

8 > x

8 > x is your answer.

~

Please help me with my work for math

Answers

Answer:

AAA

Stp-by-step explanation:

If a punnet of strawberries wrighs 100g, how many punnets would weigh 1 kg

Answers

Step-by-step explanation:

1kg = 1000g so

10 x 100 = 1000

So 100 punnets of strawberries weigh 1 kg

Describe a free market economy

Answers

DescriptionA market economy is an economic system in which the decisions regarding investment, production and distribution are guided by the price signals created by the forces of supply and demand.

Answer:

soviet russia

Step-by-step explanation:

just kidding

The free market is an economic system based on supply and demand with little or no government control. ... Based on its political and legal rules, a country's free market economy may range between very large or entirely black market

Countries that have a market economy are Mexico, United States, United Kingdom, Germany, and Canada . These countries have a market economy because the prices of goods and services are set by supply and demand

Need help with Math question

Answers

Answer:

B; {x|x<-8}

Step-by-step explanation:

Need done ASAP please

Answers

Step-by-step explanation:

a. 81 ÷ 9 = 9

b. 40 ÷ 5 = 8

c. 21 ÷ 3 = 7

d. 54 ÷ 6 = 9

e. 42 ÷ 7 = 6

f. 63 ÷ 9 = 7

g. 36 ÷ 4 = 4

h. 45 ÷ 9 = 5

i. 39 ÷ 3 = 12

j. 24 ÷ 6 = 4

....................

Answers

Answer:

I would love to help you but all I see is dots

The Great Pyramid of Cheops is a square-based pyramid. The base has sides of 230m, and the height is 147m.

Using the same material, what would the height be if you gave the base sides of 240m?



Answer to nearest meter and explained solution please. ​

Answers

Answer:

height = 140.875m

Step-by-step explanation:

Volume of first pyramid= base * height /3 = 230*147/3= 11270

if the base is 240, volume is remain -> height = volume *3 /base

                                                                            = 11270*3/240 =140.875m


use the figure to help you explain the statement

The base(b) of a triangle is ----------inches

The height (h) of the triangle is--------inches

The area of a triangle is ------- Square inches

The area of the rectangle is ------ Square centimeters

help fassstttt

Answers

Step-by-step explanation:

base is 6 in

height is 4 in

to get the area of a triangle is 1/2base×height

being 1/2(6)(4)=12

to get the area of a rectangle is length×width being 9×8=72

By observing the given figure,

The base(b) of a triangle is 6 inches

The height(h)  of  a triangle is 4 inches

The area of the triangle is 12 square inches

The area of the rectangle is 72 square centimeter

What is Triangle?

A triangle is a polygon with three edges and three vertices

What is Rectangle?

A rectangle is a quadrilateral with four right angles

What is Area?

Area is the quantity that expresses the extent of a region on the plane or on a curved surface

From the given figure

The base(b) of a triangle is 6 inches

The height(h)  of  a triangle is 4 inches

The area of a triangle = [tex]\frac{1}{2}bh[/tex]

=[tex]\frac{1}{2}(6)(4)[/tex]

=12 square inches

Length of the rectangle = 8 centimeter

Width of the rectangle = 9 centimeter

Area of the rectangle = l × w = 9×8=72 square centimeter

Hence,

The base(b) of a triangle is 6 inches

The height(h)  of  a triangle is 4 inches

The area of the triangle is 12 square inches

The area of the rectangle is 72 square centimeter

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The perimeter of a rectangular is 20 centimeters the length is 6 centimeters what is the area of the rectangular

Answers

Answer:

24 centimeters

Step-by-step explanation:

Since the longer side is 6 then multiply it by 2 which is 12, now subtract it by 20 since that is its perimeter. then u divide 8 by 2 since theres 2 sides. now do 6 times 4 which is 24

The roots of a quadratic equation are 6 and 3/4. If one of the two factors of the equation is x – 6, what is the second factor?

A. 3x - 4
B. 3x + 4
C. 4x - 3
D. 4x + 3​

Answers

Answer:

  C.  4x - 3

Step-by-step explanation:

The factor could be (x -3/4). Apparently, you're expected to show the factor as 4 times this, or ...

  4x -3 . . . . . matches choice C

___

If r is a root, then (x -r) is a factor. As here, factors containing fractional roots can be multiplied by the denominator to make the coefficients be integers.

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