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In a large survey it is found that 40% of schoolteachers are smokers. Small random samples are taken of teachers of various subjects and it is found that of 20 teachers of statistics, four are smokers, whereas there are eleven smokers in a sample of 25 history teachers. (a) Suppose that 40% of all statistics teachers smoke. Calculate, approximately, the probability that 4 or fewer are smokers in a random sample of 20 such teachers. (b) Find an approximate 95% confidence interval for the overall proportion of statistics teachers who smoke, using the information from the sample described above. (c) Without doing formal tests of hypotheses, use the results of (a) and (b) to discuss whether the proportion of smokers among statistics teachers is likely to be the same as that for all teachers. (d) Find an approximate 95% confidence interval for the difference between the proportions of smokers among history teachers and among statistics teachers.

In a large survey it is found that 40% of schoolteachers are smokers. Small random samples are taken of teachers of various subjects and it is found that of 20 teachers of statistics, four are smokers, whereas there are eleven smokers in a sample of 25 history teachers. (a) Suppose that 40% of all statistics teachers smoke. Calculate, approximately, the probability that 4 or fewer are smokers in a random sample of 20 such teachers. (b) Find an approximate 95% confidence interval for the overall proportion of statistics teachers who smoke, using the information from the sample described above. (c) Without doing formal tests of hypotheses, use the results of (a) and (b) to discuss whether the proportion of smokers among statistics teachers is likely to be the same as that for all teachers. (d) Find an approximate 95% confidence interval for the difference between the proportions of smokers among history teachers and among statistics teachers.

MATLAB: An Introduction with Applications
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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In a large survey it is found that 40% of schoolteachers are smokers. Small random samples are taken of teachers of various subjects and it is found that of 20 teachers of statistics, four are smokers, whereas there are eleven smokers in a sample of 25 history teachers. (a) Suppose that 40% of all statistics teachers smoke. Calculate, approximately, the probability that 4 or fewer are smokers in a random sample of 20 such teachers. (b) Find an approximate 95% confidence interval for the overall proportion of statistics teachers who smoke, using the information from the sample described above. (c) Without doing formal tests of hypotheses, use the results of (a) and (b) to discuss whether the proportion of smokers among statistics teachers is likely to be the same as that for all teachers. (d) Find an approximate 95% confidence interval for the difference between the proportions of smokers among history teachers and among statistics teachers.
Transcribed Image Text:In a large survey it is found that 40% of schoolteachers are smokers. Small random samples are taken of teachers of various subjects and it is found that of 20 teachers of statistics, four are smokers, whereas there are eleven smokers in a sample of 25 history teachers. (a) Suppose that 40% of all statistics teachers smoke. Calculate, approximately, the probability that 4 or fewer are smokers in a random sample of 20 such teachers. (b) Find an approximate 95% confidence interval for the overall proportion of statistics teachers who smoke, using the information from the sample described above. (c) Without doing formal tests of hypotheses, use the results of (a) and (b) to discuss whether the proportion of smokers among statistics teachers is likely to be the same as that for all teachers. (d) Find an approximate 95% confidence interval for the difference between the proportions of smokers among history teachers and among statistics teachers.
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