Seats at a local entertainment venue sell for $5 each in the lower level and $4 each in the upper level. If all the seats

Confidence Interval Mistakes and Misunderstandingsâ€”Suppose that 500 randomly selected recent graduates of a university were as

kvv77 [185]

Answer:

The correct 95% confidence interval is (8.4, 8.8).

Step-by-step explanation:

The information provided is:

$n=500\\\bar x=8.6\\\sigma=2.2$

(a)

The (1 - α)% confidence interval for population mean (μ) is:

$CI=\bar x\pm z_{\alpha/2}\times \frac{\sigma}{\sqrt{n}}$

The 95% confidence interval for the average satisfaction score is computed as:

8.6 ± 1.96 (2.2)

This confidence interval is incorrect.

Because the critical value is multiplied directly by the standard deviation.

The correct interval is:

$8.6\pm 1.96 (\frac{2.2}{\sqrt{500}})=8.6\pm 0.20=(8.4,\ 8.6)$

(b)

The (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true there is a 95% confidence that the true parameter value is contained in this interval.

The mistake is that the student concluded that the sample mean is contained in between the interval. This is incorrect because the population is predicted to be contained in the interval.

(c)

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

The 95% confidence interval for the mean rating, (8.4, 8.8) implies that the true mean satisfaction score is contained between 8.4 and 8.8 with probability 0.95 or 95%.

Thus, the students is not making any misinterpretation.

(d)

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

In this case the sample size is,

n = 500 > 30

Thus, a Normal distribution can be applied to approximate the distribution of the alumni ratings.

7 0

3 years ago

What is the horizontal asymptote of the function f(x)= -2x/x+1

daser333 [38]

Answer:

-2

Step-by-step explanation:

We have been given a function f(x)=\frac{-2x}{x+1} and we are asked to find the horizontal asymptote of our given function.

Recalling the rules for a horizontal asymptote:

1. If the numerator and denominator have equal degree, the horizontal asymptote will be the ratio of the leading coefficients.

2. If the polynomial of denominator has larger degree than the numerator, then the horizontal asymptote will be the x-axis or y=0.

3. If the polynomial of numerator has larger degree than denominator, then the function has no horizontal asymptote.

Here, the numerator and denominator are of the same degree. So the horizontal asymptote will be the ratio of the coefficients.

Horizontal asymptote = $-\frac{2}{1}$ = -2

8 0

3 years ago

Two students walk in the same direction along a straight path, at a constant speed - one at .90 m/s and the other at 1.90 m/s.a.

anyanavicka [17]

Answer:

a)The second student arrive 7 minutes and 36 seconds sooner

b)They have to walk 598,51 m

Step-by-step explanation:

Speed= Distance/Time

We are looking for time now

Time = Distance/Speed

First student

Time = 780 m/0.90 m/s=866,66 seconds

Second student

Time = 780 m/1.90 m/s=410,52 seconds

Difference=866,66-410,52= 456,14 seconds

In minutes

Difference= 456,14 seconds /60=7 minutes 36 seconds

Distance=Speed x Time

Speed¹ x Time¹ =Speed² x Time²

Time¹= Time² + 5.50 min

5.50 min =350 seconds

Time² =Speed¹ x Time¹ /Speed²

Time² =Speed¹ x (Time² + 350 seconds ) /Speed²

Time² =0.9 x (Time² + 350 seconds ) /1.9

Time² =0,4737 x (Time² + 350 seconds )

Time² =0,4737 Time² + 165,79 seconds

Time² - 0,4737 Time² = 165,79 seconds

0,5263 Time² = 165,79 seconds

Time² = 165,79 seconds/0,5263 =315,01 seconds

Distance=1,9 x 315,01 seconds = 598,51 m

5 0

3 years ago

Which of the following is a proportional relationship?

Solnce55 [7]

The two equations represent the proportional relationship.

y=3x and y=12x are proportional relation ship equations

proportion equations can be defined as

If we change x the y will change in the same proportion.

<h3>What is the proportional relationship?</h3>

Proportional relationships are relationships between two variables where their ratios are equivalent.

Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.

That constant is known as the constant of proportionality.

proportional relationship equation contain (0,0) points

If we put x=0

This will give us,y=0

If we put x=0, in y=12x

It will give y=0

put if we put x=0 in

y=3x it will give us y=0

hence these two equations represent the proportional relationship.

To learn more about the equation visit:

brainly.com/question/2972832

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6 0

2 years ago

Step 1: Choose ONE of the following triangles and complete the table below:

Archy [21]

The question is incomplete below you will find the missing part.

Step 1 : Choose ONE of the following triangles complete the table below:

1. Obtuse Scalene Triangle Translation to prove SSS Congruence

or

2. Isosceles Right Triangle Reflection to prove ASA Congruence

or

3. Equilateral Equiangular Triangle Rotation to prove SAS Congruence

Original Coordinate Point

Transformation Rule

Image Coordinate Points

A (1, 4) (x,y) -> (x+ ,y -) A’ ( , )

B ( 7,4) (x,y) -> (x+ ,y - ) B’ ( , )

C (8,9) (x,y) -> (x+ ,y -) C’ ( , )

The appropriate table is also shown below.

The triangles ABC and A'B'C' are congruent by SSS through Obtuse Scalene Triangle Translation because the corresponding sides are congruent

Two triangles are congruent if their size and shape are the same.

Now we have to transform the triangle,

The coordinates of the triangle ΔABC are given as:

A = (1, 4)

B = (7,4)

C = (8,9)

so the lengths of the sides of the triangle are given by

AB= √(7-1)²+(4-4)²= √6²= 6

BC= √(8-7)²+(9-4)²= √1²+5²= √1+25= √26

CA= √(8-1)²+(9-4)²= √7²+5²= √49+25= √74

In order to prove the SSS congruence, we have to transform the triangles under the following translation rule:

(x,y) -> (x -3, y +6)

in the above translation,

The triangle will be translated 3 units left

And then translated 6 units up.

So, we have the new coordination of the points of the translated triangle ΔA'B'C'

A' = (1-3, 4+6)

A' = (-2, 10)

B' = (7-3, 4+6)

B' = (4, 10)

C' = (8-3, 9+6)

C' = (5, 15)

Now

so the lengths of the sides of the triangle are given by

A'B'= √(4-(-2))²+(10-10)²= √6²= 6

B'C'= √(5-4)²+(15-10)²= √1²+5²= √1+25= √26

C'A'= √(-2-5)²+(10-15)²= √(-7)²+(-5)²= √49+25= √74

By comparing two triangles ΔABC and ΔA'B'C'

AB ≅ A'B'

BC ≅ B'C'

CA ≅ C'A'

Hence ΔABC ≅ A'B'C' (By S-S-S rule)

By the above transformation, the triangles ABC and A'B'C' are congruent by SSS because the corresponding sides are congruent as all the points are gone through the same transformation.

Learn more about the transformation

here: brainly.com/question/4289712

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6 0

2 years ago