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
icon
Related questions
Question

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.

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman