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Marat540 [252]
3 years ago
9

For each of the following​ situations, indicate what the general impact on the Type II error probability will​ be:

Mathematics
1 answer:
Paraphin [41]3 years ago
3 0

Answer:

Step-by-step explanation:

Hello!

The type II error is committed when you fail to reject a false null hypothesis.

The probability associated with this type of error is symbolized as β.

a. The alpha level is increased.

α and β are two probabilities that are closely related in such a way that if alpha is decreased, beta automatically increases and vice versa when the sample size n is predetermined.

If you increase α then the probability of committing type II error (β) decreases.

b. The "true" population mean is moved farther from the hypothesized population mean.

If the true population mean is moved away from its hypothesized value, then the probabilities of "keeping" a false null hypothesis are bigger.

c. The alpha level is decreased.

This is the inverse situation from a. If you decrease α then, β is automatically increased.

d. The sample size is increased.

If the sample size "n" is left free, it can be shown that by increasing the sample size, both α and β decrease. In practice, α is fixed and β is calculated with several possible sizes of n. Finally choosing as sample size the one that minimizes or gives a reasonable value of β.

I hope it helps!

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Hello, Brainly community!
ioda

Answer:

(B)  \displaystyle \frac{W(3.1) - W(2.9)}{0.2}

General Formulas and Concepts:

<u>Calculus</u>

Limits

Derivatives

  • The definition of a derivative is the slope of the tangent line.

Derivative Notation

Instantaneous Rates

  • Tangent Line: \displaystyle f'(x) = \frac{f(b) - f(a)}{b - a}

Step-by-step explanation:

Since we are trying to find a <em>rate</em> at which W(t) changes, we must find the <em>derivative</em> at <em>t</em> = 3.

We are given 2 close answer choices that would have the same <em>numerical</em> answer but different <em>meanings</em>:

  1. (A)  \displaystyle  \lim_{t \to 3} W(t)
  2. (B)  \displaystyle \frac{W(3.1) - W(2.9)}{0.2}

If we look at answer choice (A), we see that our units would simply just be volume. It would not have the units of a rate of change. Yes, it may be the closest numerically correct answer, but it does not tell us the <em>rate</em> at which the volume would be changing and it is not a derivative.

If we look at answer choice (B), we see that our units would be cm³/s, and that is most certainly a rate of change. Answer choice (B) is also a <em>derivative</em> at <em>t</em> = 3, and a derivative tells us what <em>rate</em> something is changing.

∴ Answer choice (B) will give us the best estimate for the value of the instantaneous rate of change of W(t) when <em>t</em> = 3.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

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