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2 years ago

16. A large-sample 95 percent confidence interval for the proportion of credit

Mathematics

1 answer:

borishaifa [10]2 years ago

3 0

Answer:

(B) 0.057

Step-by-step explanation:

The 95% confidence interval is (0.028, 0.086). The formula for the confidence interval is μ ± e where μ is the mean and e is the margin of error.

Therefore the confidence interval is (μ - e , μ + e).

That is μ - e = 0.028 and μ + e = 0.086

To get the point estimate which is the mean, we sum the two proportions and divide it by two.

Therefore point estimate (μ) = (0.028 + 0.086) / 2 = 0.057

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Which definite integral approximation formula is this: the integral from a to b of f(x)dx ≈ (b-a)/n * [<img src="https://tex.z-d

Stella [2.4K]

The answer is most likely A.

The integration interval [a, b] is split up into n subintervals of equal length (so each subinterval has width (b - a)/n, same as the coefficient of the sum of y terms) and approximated by the area of n rectangles with base (b - a)/n and height y.

n subintervals require n + 1 points, with

x₀ = a

x₁ = a + (b - a)/n

x₂ = a + 2(b - a)/n

and so on up to the last point x = b. The right endpoints are x₁, x₂, … etc. and the height of each rectangle are the corresponding y 's at these endpoints. Then you get the formula as given in the photo.

• "Average rate of change" isn't really relevant here. The AROC of a function G(x) continuous* over an interval [a, b] is equal to the slope of the secant line through x = a and x = b, i.e. the value of the difference quotient

(G(b) - G(a) ) / (b - a)

If G(x) happens to be the antiderivative of a function g(x), then this is the same as the average value of g(x) on the same interval,

$g_{\rm ave}=\dfrac{G(b)-G(a)}{b-a}=\dfrac1{b-a}\displaystyle\int_a^b g(x)\,\mathrm dx$

(* I'm actually not totally sure that continuity is necessary for the AROC to exist; I've asked this question before without getting a particularly satisfying answer.)

• "Trapezoidal rule" doesn't apply here. Split up [a, b] into n subintervals of equal width (b - a)/n. Over the first subinterval, the area of a trapezoid with "bases" y₀ and y₁ and "height" (b - a)/n is

(y₀ + y₁) (b - a)/n

but y₀ is clearly missing in the sum, and also the next term in the sum would be

(y₁ + y₂) (b - a)/n

the sum of these two areas would reduce to

(b - a)/n = (y₀ + 2 y₁ + y₂)

which would mean all the terms in-between would need to be doubled as well to get

$\displaystyle\int_a^b f(x)\,\mathrm dx\approx\frac{b-a}n\left(y_0+2y_1+2y_2+\cdots+2y_{n-1}+y_n\right)$

7 0

2 years ago

When is the additive relationship used? Select all that apply.

Mrac [35]

Answer:

your answer is for sure D but I think C is also the answer

Step-by-step explanation:

Additive relationship are two quantities can be expressed as related to each other through addition. It can be written as y = x + a, where y is related to x through the addition of a constant, a. The value for a may be positive or negative.

7 0

3 years ago

Read 2 more answers

A machine at a food-distribution factory fills boxes of rice. The distribution of the weights of filled boxes of rice has

12345 [234]

Answer:

22,7%

Step-by-step explanation:

I can help you with this statistical reasoning assignments and quiz check me on ig or twit at essaywriter04

5 0

3 years ago

A car manufacturer estimates that 25% of the new cars sold in one city have defective engine