Problem 7. A random sample of 21 third-grade students was selected to test whether directed reading activities in the classroom help elementary school students improve aspects of their reading ability. After an eight-week period, students took a Degree of Reading Power (DRP) test which measures the aspects of reading ability. The reading scores were 24, 43, 58, 71, 43, 49, 61, 44, 67, 49, 53, 56, 59, 52, 62, 54, 57, 33, 46, 43, and 57. It is plausible to assume that the sample data are from a normal population. The sample mean score is 51.48 and the sample standard deviation of the scores is 11 (http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html). Q1. Construct a 90% confidence interval for the population mean score of reading ability and write a brief interpretation of your confidence interval in terms of the context. Q2. What assumption was made on the distribution of the population scores of reading ability when the confidence interval in Q1 was constructed? Q3. Without constructing the 95% confidence interval, what can you say about the 95% confidence interval compared to the 90% one in Q1 in terms of the interval length? Write a sentence to justify your answer. Q4. Do the data support the claim that the population mean reading score is higher than 45 at a significance level of 0.01? Answer the question by the following steps. a) Formulate null and alternative hypotheses in terms of the population parameter as well as the context of this application; Formulate null and alternative hypotheses in terms of the population parameter as well as the context of this application;
Problem 7. A random sample of 21 third-grade students was selected to test whether directed reading activities in the classroom help elementary school students improve aspects of their reading ability. After an eight-week period, students took a Degree of Reading Power (DRP) test which measures the aspects of reading ability. The reading scores were 24, 43, 58, 71, 43, 49, 61, 44, 67, 49, 53, 56, 59, 52, 62, 54, 57, 33, 46, 43, and 57. It is plausible to assume that the sample data are from a normal population. The sample mean score is 51.48 and the sample standard deviation of the scores is 11 (http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html). Q1. Construct a 90% confidence interval for the population mean score of reading ability and write a brief interpretation of your confidence interval in terms of the context. Q2. What assumption was made on the distribution of the population scores of reading ability when the confidence interval in Q1 was constructed? Q3. Without constructing the 95% confidence interval, what can you say about the 95% confidence interval compared to the 90% one in Q1 in terms of the interval length? Write a sentence to justify your answer. Q4. Do the data support the claim that the population mean reading score is higher than 45 at a significance level of 0.01? Answer the question by the following steps. a) Formulate null and alternative hypotheses in terms of the population parameter as well as the context of this application; Formulate null and alternative hypotheses in terms of the population parameter as well as the context of this application;
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:Problem 7. A random sample of 21 third-grade students was selected to test whether
directed reading activities in the classroom help elementary school students improve
aspects of their reading ability. After an eight-week period, students took a Degree of
Reading Power (DRP) test which measures the aspects of reading ability. The reading
scores were 24, 43, 58, 71, 43, 49, 61, 44, 67, 49, 53, 56, 59, 52, 62, 54, 57, 33, 46, 43,
and 57. It is plausible to assume that the sample data are from a normal population. The
sample mean score is 51.48 and the sample standard deviation of the scores is 11
(http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html).
Q1.
Construct a 90% confidence interval for the population mean score of
reading ability and write a brief interpretation of your confidence interval in terms of the
context.
Q2.
What assumption was made on the distribution of the population scores of
reading ability when the confidence interval in Q1 was constructed?
Transcribed Image Text:Q3.
Without constructing the 95% confidence interval, what can you say about
the 95% confidence interval compared to the 90% one in Q1 in terms of the interval
length? Write a sentence to justify your answer.
Q4. Do the data support the claim that the population mean reading score is higher than
45 at a significance level of 0.01? Answer the question by the following steps.
a)
Formulate null and alternative hypotheses in terms of the population
parameter as well as the context of this application;
Formulate null and alternative hypotheses in terms of the population
parameter as well as the context of this application;
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