The Trial Urban District Assessment (TUDA) measures educational progress within participating large urban districts. TUDA gives a reading test scored from 0 to 500. A score of 208 is a "basic" reading level for fourth‑graders. Suppose scores on the TUDA reading test for fourth‑graders in your district follow a Normal distribution with standard deviation ?=40. In 2019 the mean score for fourth‑graders in your district was 219. You plan to give the reading test to a random sample of 25 fourth‑graders in your district this year to test whether the mean score ? for all fourth‑graders in your district is still above the basic level. You will therefore test ?0:?=208 ??:?>208 If the true mean score is again 219, on average, students are performing above the basic level. You learn that the power of your test at the 5% significance level against the alternative ?=219 is 0.394. Explain in simple language what "power"=0.394" means. - ?0 will not be rejected 0.394%0.394% of the time. - ?0 will be correctly rejected 39.4%39.4% of the time. - ?0 will be correctly rejected 60.6%60.6% of the time. - ?0 will not be rejected 39.4%39.4% of the time. Explain why the test you plan will not adequately protect you against incorrectly

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The Trial Urban District Assessment (TUDA) measures educational progress within participating large urban districts. TUDA gives a reading test scored from 0 to 500. A score of 208 is a "basic" reading level for fourth‑graders. Suppose scores on the TUDA reading test for fourth‑graders in your district follow a Normal distribution with standard deviation ?=40. In 2019 the mean score for fourth‑graders in your district was 219. You plan to give the reading test to a random sample of 25 fourth‑graders in your district this year to test whether the mean score ? for all fourth‑graders in your district is still above the basic level. You will therefore test ?0:?=208 ??:?>208 If the true mean score is again 219, on average, students are performing above the basic level. You learn that the power of your test at the 5% significance level against the alternative ?=219 is 0.394.

Explain in simple language what "power"=0.394" means.

- ?0 will not be rejected 0.394%0.394% of the time.

- ?0 will be correctly rejected 39.4%39.4% of the time.

- ?0 will be correctly rejected 60.6%60.6% of the time.

- ?0 will not be rejected 39.4%39.4% of the time.

Explain why the test you plan will not adequately protect you against incorrectly deciding that average reading scores in your district are not above basic level.

- If ?=219, 60.6% of the time under repeated sampling, ?0 will not be rejected, even though it should be.

- If ?=219, 39.4% of the time under repeated sampling, ?0 will be rejected, even though it should not be.

- If ?=219, 39.4% of the time under repeated sampling, ?0 will not be rejected, even though it should be.

- If ?=219, 60.6% of the time under repeated sampling, ?0 will be rejected, even though it should not be.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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