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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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