the main purpose of inferential statistics is to a) adjust analyses to improve validity. b) account for variability within a population. c) decide whether the standard deviation is skewed by outliers. d) estimate a characteristic of a population based on a sample.

Answer:

3x - 15 + 5x + 9 = 180

8x - 6 = 180

8x = 186

x = 23.25

So angle ABC measures 3(23.25) - 15 = 54.75°, and angle LMN measures

5(23.25) + 9 = 125.25°.

B is correct.

The calculated list price of the computer is $480

From the question, we have the following parameters that can be used in our computation:

Total price = $513

Sales tax = 6.875%

using the above as a guide, we have the following:

Total price = List price * (1 + tax)

Substitute the known values in the above equation, so, we have the following representation

List price * (1 + 6.875%)  = 513

Evaluate

List price  = 480

Hence, the List price  = 480

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So the vector form of the quadratic function y = x² + 4x + 3 is: y = (x + 2)² - 1.

To change from standard form to vertex form, we need to complete the square.

First, we group the x-terms together and factor out any common coefficient of x², giving:

y = x² + 4x + 3

y = 1(x² + 4x) + 3

Next, we need to add and subtract a constant inside the parentheses to complete the square. To determine this constant, we take half of the coefficient of x (4) and square it:

(4/2)² = 4

So we add and subtract 4 inside the parentheses:

y = 1(x² + 4x + 4 - 4) + 3

Now we can factor the quadratic expression inside the parentheses as a perfect square:

y = 1[(x + 2)² - 4] + 3

Simplifying and rearranging terms, we get:

y = (x + 2)² - 1

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Answer:  A

Step-by-step explanation:

Draw a line going out in 3rd quadrant.

your opposite side from angle is5 using pythagorean

and it's positive because it's in the +5 y direction

so sin x = 5/13

The area of ΔRST is 2767 square inches.

We have,

r = 94 inches, s = 78 inches and ∠T=49

We will use the formula

Area= 1/2 a b sin C

So, area of ΔRST

= 1/2 r s sin <T

= 1/2 (94) (78) sin (49)

= 3666 sin(49)

= 2766.7653

= 2767 square inches

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Based on the given data, it seems that both the polysilicon doping level and anneal temperature can affect the base current.

To visually interpret the data, we can create a scatter plot with the polysilicon doping level on the x-axis and the base current on the y-axis, with different colors or symbols representing the different anneal temperatures. We can also create a similar plot with the anneal temperature on the x-axis and the base current on the y-axis, with different colors or symbols representing the different polysilicon doping levels.

To analyze the model, we can examine the residuals to see if they are randomly distributed around zero, indicating that the model is a good fit for the data. If the residuals show a pattern, it may suggest that the model is not a good fit.

Assuming a linear model, we can estimate the parameters using regression analysis. The model could be of the form:

Base current = β0 + β1(doping level) + β2(anneal temperature) + ε

where β0 is the intercept, β1 is the coefficient for doping level, β2 is the coefficient for anneal temperature, and ε is the error term.

Once we have estimated the parameters, we can plot the response surface to see how the base current changes as a function of both the doping level and annealing temperature. This will give us a better understanding of the relationship between these variables and the response variable.

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The change in Emile's height based on old and new height is 0.9 cm or 9/10 cm.

The change in Emile's height can be calculated using the subtraction. The formula to be used for it is -

Change in height = New height - Old height

Firstly changing the height to fraction.

Old height = [tex]3 \frac{7}{10} [/tex]

Old height = ((10×3)+7)/10

Old height = 37/10 cm

New height = [tex]4 \frac{3}{5} [/tex]

New height = ((5×4)+3)/5

New height = 23/5 cm

Keep the values in formula to find the value of change in height

Change in height = 23/5 - 37/10

Change = 23×2 - 37/10

Change = 46 - 37/10

Change = 0.9 cm

Hence, the change in height is 0.9 cm.

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The complete question is -

In seventh grade, Emile grew

3 7/10cm, and in eighth grade, he grew 4 3/5cm. How much did his height increase during these two years?

The answer should be written as a proper mixed number and should be simplified, if possible

During these two years, Emile's height increased by 0.9 cm or 9/10 cm.

We will calculate the change in Emile's height using Subtraction. The formula that we will use is:

Change in height = Eighth-grade height - Seventh-grade height

Firstly, we will convert the height to a fraction.

Seventh-grade height = ((10×3)+7)/10

Seventh-grade height = 37/10 cm

Now,

Eighth-grade height = ((5×4)+3)/5

Eighth-grade height = 23/5 cm

Now, find the change in height by substituting the values in the formula.

Change in height = Eighth-grade height - seventh-grade height

                             =   23/5 - 37/10

Change in height = 23×2 - 37/10

Change = 46 - 37/10

Change = 0.9 cm

Therefore, the increase in height during these two years is 0.9 cm or 9/10 cm.

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From the triangle, the values of α  , β and Ф are 97⁰, 45⁰ and 38⁰

Recall that the sum of angles of a straight line is 180 degrees and the sum of angles of a triangle is 180 degrees also.

using the given properties of a triangle and angles,

We have that Y + β - 180  ( sum of angles on a straight line)

where β = 135 degrees

Y = 180-135

Y = 45⁰

Also, using the same properties,

α + <EAC = 180 (sum of <s of a straight line)

α + 83 = 180

α = 97⁰

Ф = 180 - (97 + 45)

Ф = 180 -  142

Ф = 38⁰

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The diameter of the cone part of the funnel to the nearest tenth is approximately 21.9 cm.

The volume of a cone is given by the formula V = (1/3)πr^2h

where

We know that the total volume of the funnel is 159π cm^3, and the height of the cone part of the funnel is 12 cm. Therefore, we can write:

V = (1/3)πr^2h

159π = (1/3)πr^2(12)

477 = 4r^2

r^2 = 477/4

r = √(477/4) ≈ 10.93

The diameter of the cone is twice the radius, so:

d = 2r ≈ 21.86

Therefore, the diameter of the cone part of the funnel to the nearest tenth is approximately 21.9 cm.

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Answer:

The Correct answer is

57°

To determine the distribution of total revenue for the professional football team using the given information and assumptions, you would need to conduct a simulation in Excel with 50 trials.

1. First, create a data table with columns for Seating Zone, Seats Available, Ticket Price, Mean Demand, and Standard Deviation.
2. Fill in the given data for each seating zone in the appropriate columns.
3. Create columns for simulated demand and revenue for each seating zone.
4. Use the NORMINV function in Excel to generate the simulated demand based on the mean demand and standard deviation. For example, in the First Level Sideline zone, the formula would be: =NORMINV(RAND(), 14500, 750).
5. Calculate the revenue for each seating zone by multiplying the simulated demand by the ticket price, making sure not to exceed the seats available.
6. Sum the revenue from all seating zones to get the total revenue for each trial.
7. Repeat steps 4-6 for 50 trials.
8. Finally, create a histogram of the total revenue data to visualize and summarize the results.

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True. The determinant of an n x n matrix can be defined as a sum of multiples of determinants of (n-1) x (n-1) submatrices, which are called the minors of the matrix.

The determinant of an n x n matrix can be defined as a sum of multiples of determinants of (n-1) x (n-1) submatrices, which are called the minors of the matrix.

More specifically, let A be an n x n matrix with entries a_ij. The determinant of A, denoted by det(A), can be defined recursively as follows:

- If n = 1, then det(A) = a_11.
- If n > 1, then det(A) = sum((-1)^(i+j) * a_ij * det(A_ij)), where the sum is taken over the first row or first column of A. Here, A_ij denotes the (n-1) x (n-1) submatrix obtained by deleting the i-th row and j-th column of A.

This recursive definition shows that the determinant of an n x n matrix can be expressed as a sum of (n-1) x (n-1) determinants of submatrices, with appropriate signs and coefficients. This is known as the cofactor expansion of the determinant along the first row or first column of the matrix.

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The coordinates of the image of the dilation of the quadrilateral MNOP are;

M = (0, 4)       M' = (0, 3)

N = (1, 2)        N' = (2, -1)

O = (0, 0)       O' = (0, -5)

P = (-1, 2)        P' = (-2, -1)

The drawing of the figure with the vertices labeled, created with MS Excel is attached

A dilation transformation is one in which a geometric figure is resized to become smaller or larger.

The coordinates of the dilation of a point about the point (0, 5) can be found by first translating the quadrilateral MNOP with regards to the point (0, 5), such that the center is located at the origin as follows;

The coordinates of MNOP are; M(0, 4), N(1, 2), O(0, 0), and P(-1, 2)

The  coordinates of the image following the translation are;

M' = M - (0, 5) = (0, -1)

N' = N - (0, 5) = (1, -3)

O' = O - (0, 5) = (0, -5)

P' = P - (0, 5) = (-1, -3)

The translated points are then dilated as follows;

The coordinates of the image following the dilation are;

M'' = 2 × M' = (0, -2)

N'' = 2 × N' = (2, -6)

O'' = 2 × O' = (0, -10

P'' = 2 × P' = (-2, -6)

The above image are translated to their initial position to get;

M''' = M'' + (0, 5) = (0, 3)

N''' = N'' + (0, 5) = (2, -1)

O''' = O'' + (0, 5) = (0, -5)

P''' = P'' + (0, 5) = (-2, -1)

Please find attached the diagram of the dilated image created with MS Excel

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a. The circumference of circle A and B are 131. 88 meters and 175. 84 meters

b. Yes, the the relationship between the radius and circumference the same for all circles. As the radius increases, the circumference also increases

The formula that is used to calculate the circumference of a circle is expressed as;

C = 2πr

It is so such that the parameters of the equation are;

From the information given, we have that;

For circle A

Circumference = 2× 3.14 × 21

Multiply the values

Circumference = 131. 88 meters

For circle B

Circumference = 2× 3.14 × 28

Multiply the values

Circumference = 175. 84 meters

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The required decrease in dollars was $1222 and the amount of money in Bob's account at the end of last year was $3978.

To find the decrease in dollars and the amount of money in Bob's account at the end of last year, we can use the following steps:

Calculate the amount of the decrease. We can do this by multiplying the original amount by the percentage decrease as a decimal:

Decrease = 0.235 x $5200 = $1222

So, the decrease in dollars is $1222.

Calculate the amount of money in Bob's account at the end of last year. We can do this by subtracting the decrease from the original amount:

Amount at end of last year = $5200 - $1222 = $3978

So, the amount of money in Bob's account at the end of last year was $3978.

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The he dimensions of the box are approximately 7 ft x 7 ft x 10 ft  are

Volume: x² * h = 490 ft³

Surface area: x² + 4 * x * h = 329 ft²

volume equation

substitute this expression for h into the surface area equation:

[tex]x^2 + 4 * x * (490 / x^2) = 329[/tex]

solve for x:

[tex]x^2 + 1960 / x = 329[/tex]

we can multiply both sides by x:

[tex]x^3 + 1960 = 329x[/tex]

This is a cubic equation:

[tex]x^3 - 329x + 1960 = 0[/tex]

The approximate solution for x using cubic equation  is:

x ≈ 7

h = 490 / (7^2)

h = 490 / 49

h = 10

So, the dimensions of the box are approximately 7 ft x 7 ft x 10 ft

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In order to determine if the golf instructional expert's claim is accurate, the LPGA would need to analyze the data collected from the random sample of 45 students.

Based on the given information, the new golf instructional expert claims that her students can hit their drivers an average of 300 yards. However, the LPGA is skeptical about this claim and believes that the students actually hit the ball less than that. To test this hypothesis, the LPGA took a random sample of 45 of her students.

By taking a random sample, the LPGA can estimate the average driving distance of all of the expert's students. If the sample's average is significantly less than 300 yards, then the LPGA's hypothesis would be supported. On the other hand, if the sample's average is close to 300 yards, then the new golf instructional expert's claim would be supported.

It is important to note that the average driving distance of a random sample may not necessarily represent the average driving distance of all of the expert's students. However, taking a random sample is a reliable way to estimate the population's average with a certain level of confidence.

To address your question, let's break it down into steps:

1. A golf instructional expert claims that her students can hit their drivers an average of 300 yards.
2. The LPGA believes this claim is inaccurate and thinks the students' actual average distance is less than 300 yards.
3. To test the claim, the LPGA takes a random sample of 45 students from the golf instructional expert's students.

In order to determine if the golf instructional expert's claim is accurate, the LPGA would need to analyze the data collected from the random sample of 45 students. They would calculate the average distance these students can hit their drivers and compare it to the claimed 300-yard average. If the actual average distance is significantly less than 300 yards, the LPGA would have evidence to dispute the golf instructional expert's claim.

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Complete Question:

A new golf instructional expert is on the scene. She claims that her students can hit their drivers an average of 300 yards. The LPGA does not think that this is accurate and that the students actually hit the ball less than that. The LPGA took a random sample of 45 of her students. Assume an error level of 5%. What is the null hypothesis?

First models could be used to find the distance, in miles, run by each of the 3 runners.

We have,

A relay race with a total distance of 1/2 mile is run by a team of 3 runners.

So, Distance Covered by each runner is

= (1/3) (1/2)  

= 1/16

So, (1/2) x (1/3) = 1/6

(1/2) ÷ 3 = 1/6

So, the correct model  1/2 mile is divided in 3 equal parts are the correct options.

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A student club is designing a trebuchet to launch a pumpkin into projectile motion. The trajectory of the launched pumpkin is predicted to be parabolic, and can be described by the equation y(x). This means that as the pumpkin moves through the air, its path will follow a parabolic shape, which is common in projectile motion scenarios.

Based on the student club's design, they predict that the trajectory of the launched pumpkin will follow a parabolic path. This means that the height of the pumpkin (y) will depend on its horizontal distance from the launch point (x). The equation that describes this relationship is known as the "trajectory equation" or "equation of motion."

The general form of the trajectory equation for projectile motion is:

y(x) = ax^2 + bx + c

where a, b, and c are constants that depend on the initial velocity, angle of launch, and other factors.

To determine the specific values of a, b, and c for the student club's trebuchet, they will need to conduct experiments or simulations to measure the pumpkin's height at different horizontal distances. They can then use this data to fit the trajectory equation to the observed data points.

Once they have the trajectory equation, they can use it to make predictions about the pumpkin's flight path and adjust their design accordingly. For example, if the pumpkin is not landing where they want it to, they can tweak the launch angle, velocity, or other factors to get a better result.

Based on your question, a student club is designing a trebuchet to launch a pumpkin into projectile motion. The trajectory of the launched pumpkin is predicted to be parabolic, and can be described by the equation y(x). This means that as the pumpkin moves through the air, its path will follow a parabolic shape, which is common in projectile motion scenarios.

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The first four ordered pairs using both sequences are (4, 14), (8, 9), (10, 20), and (11, 15).

To find the ordered pairs using both rules, we simply apply both rules to each starting value.

Starting with 4:
- Applying the first rule gives us 8, which we then apply the second rule to and get 14. So the first ordered pair is (4, 14).
- Applying the second rule first gives us 6, which we then apply the first rule to and get 9. So the second ordered pair is (8, 9).

Starting with 10:
- Applying the first rule gives us 11, which we then apply the second rule to and get 20. So the third ordered pair is (10, 20).
- Applying the second rule first gives us 18, which we then apply the first rule to and get 15. So the fourth ordered pair is (11, 15).

Therefore, the first four ordered pairs using both sequences are (4, 14), (8, 9), (10, 20), and (11, 15).

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The surface area of the larger prism is 104 square inches

From the question, we have the following parameters that can be used in our computation:

The surface area is then calculated as

Area = 2(lw + wh + lh)

Where:

By substitution, we have the following equation

Area = 2 * (2 * 2 + 2 * 12 + 12 * 2)

Evaluate the sum and the products

Area = 104

Hence, the surface area is 104 square inches

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Answer:

-6/5

Step-by-step explanation:

The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the slope formula:

slope = (y2 - y1) / (x2 - x1)

Plugging in the given points, we get:slope = (14 - 8) / (-3 - 2) = 6 / (-5)

To write this in simplest form, we can divide the numerator and denominator by their greatest common factor, which is 1 in this case. So the slope in simplest form is:

slope = 6 / (-5) = -6/5

Using the rise/run notation, we can say that the slope of the line passing through the points (2, 8) and (-3, 14) is -6/5, or -6 over 5.

The rise is -6 (since we move down 6 units from y1 to y2), and the run is 5 (since we move 5 units to the left from x1 to x2).

Answer:

p = 12

Step-by-step explanation:

Make p an independent variable. First, combine like terms.

3/2p+3=21

Multiply everything by 2.

3p+6=42

Subtract 6 from both sides.

3p=42-6

3p=36

Divide both sides by 3.

p=36/3

p=12

According to the survey results, 53% of respondents reported having colleagues who are rude or disrespectful. This is a concerning finding, as workplace incivility can have negative effects on employee well-being, job satisfaction, and productivity.

It is important for organizations to address and prevent such behaviors through training, policies, and a culture of respect and accountability. It is also important for individuals to speak up and address rude or disrespectful behavior when it occurs, in a constructive and professional manner. By promoting civility and respect in the workplace, we can create a more positive and productive work environment for everyone.

According to the survey, 53% of respondents reported having colleagues who are rude or disrespectful. This percentage indicates that more than half of the surveyed individuals have experienced unprofessional behavior from their coworkers.

It is essential for everyone in a professional environment to treat their colleagues with respect and maintain a positive work environment.

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The probability of randomly NOT selecting a gear made by supplier B is 40%.

There are a total of 500 gears in the storage container, with 300 of them made by supplier B. The probability of randomly selecting a gear made by supplier B is therefore 300/500, or 60%.

The probability of NOT selecting a gear made by supplier B is 1 minus the probability of selecting a gear made by supplier B. So, the probability of randomly NOT selecting a gear made by supplier B is 1 - 0.6, or 0.4.

Therefore, the answer is 40%.

To find the probability of NOT selecting a gear made by supplier B, follow these steps:

1. Determine the total number of gears: There are 200 gears from supplier A and 300 gears from supplier B, so there are a total of 200 + 300 = 500 gears in the storage container.

2. Calculate the proportion of gears made by supplier A: Since there are 200 gears from supplier A out of a total of 500 gears, the proportion is 200/500.

3. Convert the proportion to a percentage: (200/500) * 100 = 40%

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The values of angle O in the triangle is 13.1 degrees

From the question, we have the following parameters that can be used in our computation:

o = 2.2 cm, n = 8.6 cm and ∠N=134

Using the law of sine, we have

o/sin(O) = n/sin(N)

substitute the known values in the above equation, so, we have the following representation

2.2/sin(O) = 8.6/sin(134)

So, we have

sin(O) = 2.2 * sin(134)/8.6

Evaluate and talke the arc sin

O = 13.1 degrees

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Answer:

10.6

Step-by-step explanation:

Trust; also im smart so like yeah.

The area of the diagram ABDC is 625cm2.

We are given that;

RQ is parallel to ST, which implies that ∆PRQ and ∆PST are similar by the AA criterion (angle-angle). We are also given that ST = 4 cm, RP = 10 cm, and PT = 5 cm;

Now,

we can use the fact that RP = 10 cm and PT = 5 cm to find PQ by using the Pythagorean theorem. PQ is the hypotenuse of the right triangle PRT, so we get:

PQ2 = RP2 + PT2 PQ2 = 102 + 52 PQ2 = 100 + 25 PQ2 = 125 PQ = √125 PQ ≈ 11.18 cm

Now we can use PQ and ST as corresponding sides to find the scale factor. We get:

Scale factor = PQ / ST Scale factor ≈ 11.18 / 4 Scale factor ≈ 2.795

ii. To find |RQ|, we can use the scale factor and multiply it by |ST|. We get:

|RQ| = Scale factor * |ST| |RQ| ≈ 2.795 * 4 |RQ| ≈ 11.18 cm

b. Find the area of ∆PST if the area of ∆PRQ is 80 cm2.

To find the area of ∆PST, we can use the fact that the ratio of the areas of similar triangles is equal to the square of the scale factor. We get:

Area of ∆PST / Area of ∆PRQ = (Scale factor)2 Area of ∆PST / 80 = (2.795)2 Area of ∆PST / 80 = 7.812 Area of ∆PST = 7.812 * 80 Area of ∆PST ≈ 625 cm2

Therefore, by the area the answer will be 625cm2.

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The probability that the average number of cherries in 36 cherry puffs will be less than 5.5 is approximately 0.997.

(a) The population mean of X is:

E(X) = 4(.2) + 5(.4) + 6(.3) + 7(.1) = 4.9

The population variance of X is:

Var(X) = E(X^2) - [E(X)]^2

= 4^2(.2) + 5^2(.4) + 6^2(.3) + 7^2(.1) - (4.9)^2

= 1.49

(b) Since the distribution is discrete and the sample size is large (n = 36), we can use the Central Limit Theorem to approximate the distribution of the sample mean as normal. Therefore, the mean of the sample mean is equal to the population mean, which is 4.9, and the variance of the sample mean is given by:

Var(X) = Var(X)/n

= 1.49/36

≈ 0.0414

(c) To find the probability that the average number of cherries in 36 cherry puffs will be less than 5.5, we standardize the variable as follows:

Z = (X - μ) / (σ / √n)

where μ = 4.9, σ = √Var(X) = √0.0414 ≈ 0.2035, and X = 5.5

Z = (5.5 - 4.9) / (0.2035 / √36) = 2.95

Using a standard normal distribution table or calculator, the probability that Z is less than 2.95 is approximately 0.997. Therefore, the probability that the average number of cherries in 36 cherry puffs will be less than 5.5 is approximately 0.997.

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The only claim that would tend to be refuted by the 90% confidence interval of 135 to 160 is B) The population mean is 125.

The 90% confidence interval for the mean of a population being computed to be 135 to 160 means that if we were to take multiple samples from the population and compute the mean of each sample, 90% of the intervals we construct would contain the true population mean. Therefore, any claim that falls outside of this interval would tend to be refuted.

Let's consider the options.

A) The population mean is 145.
This claim falls within the 90% confidence interval of 135 to 160, so it is not refuted by the interval.

B) The population mean is 125.
This claim falls outside of the 90% confidence interval of 135 to 160, so it is refuted by the interval.

C) The population mean is 170.
This claim also falls outside of the 90% confidence interval of 135 to 160, so it is refuted by the interval.

D) The population mean is between 130 and 150.
This claim falls within the 90% confidence interval of 135 to 160, so it is not refuted by the interval.

Therefore, the only claim that would tend to be refuted by the 90% confidence interval of 135 to 160 is B) The population mean is 125.
A 90% confidence interval for the mean of a population, computed to be 135 to 160, provides a range in which we can be 90% confident that the true population mean lies. This confidence interval helps us make inferences about the population based on sample data. The given interval would tend to refute any claim that falls outside of this range.

For example, if someone claims that the population mean is either below 135 or above 160, this confidence interval would challenge that assertion. Since we are 90% confident that the true population mean falls between 135 and 160, it would be statistically unlikely for the actual mean to be outside of this range. In conclusion, any claim suggesting a population mean outside the 135 to 160 interval would be refuted by this 90% confidence interval.

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Complete question: For the problem, select the best response.

A 90% confidence interval for the mean of a population is computed to be 135 to 160. Which one of the following claims would the interval tend to refute?

A. The population mean is more than 110.

B. The population mean is less than 150.

C. The population mean is between 140 and 150.

D. The population mean is more than 140.

E. The population mean is less than than 125.