According to Center for Disease Control and Prevention (http://www.cdc.gov/), the length 3-week old Ameri- can boys is normally distributed with the mean of 53.39 cm and the standard deviation is about 1.927 cm. A local hospital went through this year's 3-week check-up records. They found, 22 boys had their 3-week check-up in their facility, their mean length was 54.44 cm, and the standard deviation was about 2.26 cm. 1.1. Based upon this record, find the 98% confidence interval of the expected mean length of the 3-week old boys born from this hospital. 1.2. Do these statistics indicate that the 3-week old boys checked up by this hospital tend to be longer than the national average? Set up your hypotheses and test them with the significance level of a = 0.01. 1.3. Estimate the ß value, the conditional probability for the type II error, under a new hypothesis that the true mean length of the 3-week old boys in the vicinity of the hospital is indeed about 54.44 cm, and the true standard deviation is indeed about 2.26cm. 1.4. Find the minimal sample size to ensure the probability for type Il error is capped at B = 0.15, under the new hypothesis introduced in the previous problem.
According to Center for Disease Control and Prevention (http://www.cdc.gov/), the length 3-week old Ameri- can boys is normally distributed with the mean of 53.39 cm and the standard deviation is about 1.927 cm. A local hospital went through this year's 3-week check-up records. They found, 22 boys had their 3-week check-up in their facility, their mean length was 54.44 cm, and the standard deviation was about 2.26 cm. 1.1. Based upon this record, find the 98% confidence interval of the expected mean length of the 3-week old boys born from this hospital. 1.2. Do these statistics indicate that the 3-week old boys checked up by this hospital tend to be longer than the national average? Set up your hypotheses and test them with the significance level of a = 0.01. 1.3. Estimate the ß value, the conditional probability for the type II error, under a new hypothesis that the true mean length of the 3-week old boys in the vicinity of the hospital is indeed about 54.44 cm, and the true standard deviation is indeed about 2.26cm. 1.4. Find the minimal sample size to ensure the probability for type Il error is capped at B = 0.15, under the new hypothesis introduced in the previous problem.
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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Transcribed Image Text:According to Center for Disease Control and Prevention (http://www.cdc.gov/), the length 3-week old Ameri-
can boys is normally distributed with the mean of 53.39 cm and the standard deviation is about 1.927 cm. A
local hospital went through this year's 3-week check-up records. They found, 22 boys had their 3-week
check-up in their facility, their mean length was 54.44 cm, and the standard deviation was about 2.26 cm.
1.1. Based upon this record, find the 98% confidence interval of the expected mean length of the 3-week old
boys born from this hospital.
1.2. Do these statistics indicate that the 3-week old boys checked up by this hospital tend to be longer than the
national average? Set up your hypotheses and test them with the significance level of a = 0.01.
1.3. Estimate the ß value, the conditional probability for the type II error, under a new hypothesis that the true
mean length of the 3-week old boys in the vicinity of the hospital is indeed about 54.44 cm, and the true standard
deviation is indeed about 2.26cm.
1.4. Find the minimal sample size to ensure the probability for type Il error is capped at B = 0.15, under the new
hypothesis introduced in the previous problem.
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