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Tems11 [23]
3 years ago
9

An article in an educational journal discussing a non-conventional high school reading program reports a 95% confidence interval

of (520 , 560) for the average score on the reading portion of the SAT. The study was based on a random sample of 20 students and it was assumed that SAT scores would be approximately normally distributed. Determine the margin of error associated with this confidence interval.
Mathematics
1 answer:
Maksim231197 [3]3 years ago
6 0

Answer:

The margin of error associated with this confidence interval is 20

Step-by-step explanation:

A confidence interval has two bounds, a lower bound and an upper bound. The interval is symmetric, which means that the margin of error is the difference between these two bounds(upper - lower), divided by 2.

In this problem, we have that:

Lower bound: 520

Upper bound: 560

Determine the margin of error associated with this confidence interval.

(560 - 520)/2 = 20

The margin of error associated with this confidence interval is 20

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The accompanying data contains the depth​ (in kilometers) and​ magnitude, measured using the Richter​ Scale, of all earthquakes
Sunny_sXe [5.5K]

Answer:

Depth:

μ =20.2025 km

M = 15.625 km

Range = 47.15 km

σ ≈ 15.92 km

Q₁ = 5.7375 km

Q₃ =  34.6675 km

Magnitude:

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

Step-by-step explanation:

The given data are;

Depth {}                                 Magnitude

0.76 {}                                    0.84

4.93 {}                                    0.47

8.16 {}                                     0.35

33.58 {}                                  1.32

21.2 {}                                     1.61

35.03 {}                                  4.57

10.05 {}                                   5.52

47.91 {}                                    1.99

For the Depth, we have;

The mean, μ = (0.76+4.93+8.16+33.58+21.2+35.03+10.05+47.91)/8 =20.2025 km

The median, M = The (n + 1)/2th term after arranging the term in increasing order as follows;

0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 , the median is therefore;

(8 + 1)/2th term or the 4.5th term which is 10.05 + (21.2 - 10.05)/2 = 15.625 km

The Range = The highest - The lowest value = 47.91 - 0.76 = 47.15 km

The Standard deviation of, σ, is given as follows;

\sigma =\sqrt{\dfrac{\sum \left (x_i-\mu  \right )^{2} }{N}}

Where;

x_i = The individual data point = (0.76, 4.93, 8.16, 10.05, 21.2, 33.58, 35.03, 47.91 )

N = The total number of data point = 8

Substituting, (using Microsoft Excel) we get;

\sigma =\sqrt{\dfrac{\sum \left (x_i-20.2025  \right )^{2} }{8}} \approx 15.92 \ km

Q₁ = The first quartile = The (n + 1)/4th =  term arranged in increasing order

Q₁ = The (8 + 1)/4th term = The 2.25th term = 4.93 + (8.16 - 4.93)×0.25) = 5.7375 km

Q₃ = The first quartile = The 3×(n + 1)/4th =  term arranged in increasing order

Q₃ = The 3×(8 + 1)/4th term = The 6.75th term = 33.58 + 3×(35.03 - 33.58)×0.25) = 34.6675 km

For the magnitude, we have, using the same formulas and procedures as above;

μ = 2.08375

M = 1.465

Range, R = 5.17

σ = 1.801485 ≈ 1.8

Q₁ = 0.5625

Q₃ = 3.925

4 0
3 years ago
13
il63 [147K]

The required value after simplification of the s = -16/3. None of these are correct.

Given that,
To simplify [\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2   and to find the value of s in x^s.

<h3>What is simplification?</h3>

The process in mathematics to operate and interpret the function to make the function simple or more understandable is called simplifying and the process is called simplification.

Simplification,

=[\frac{x^{2/3}x^{-1/2}}{x\sqrt{x^3}\sqrt[3]{x}}]^2\\= \frac{x^{4/3}x^{-1}}{x^2x^3*{x}^{2/3}}\\= \frac{x^{1/3}}{x^{17/3}}\\=x^{-16/3}
Comparing with x^S
s = -16/3


Thus, the required value of the s = -16/3. None of these are correct.

Learn more about simplification here: brainly.com/question/12501526

#SPJ1

4 0
1 year ago
What is the area of the shaded triangle inside the square . Round to the nearest square inch .
Anna11 [10]
16*16=256
256/2=128
=128
8 0
3 years ago
Read 2 more answers
What is the square root of 100.
ankoles [38]

Answer:

10 is the answer

Step-by-step explanation:

thank me layer

4 0
2 years ago
Read 2 more answers
Please help!!!!!
Naya [18.7K]
Your answer is 80. A triangle’s angles add up to 180 degrees. Therefore, you need to subtract 30 and 70 from 180 to find your answer: 180-(30+70)=80 or 180-70-30=80
5 0
3 years ago
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