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.

Name: In a large survey it is found that 40% of schoolteachers are smokers.
Uploaded: 2022-12-08T14:54:05.000Z
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Description: In a large survey it is found that 40% of schoolteachers are smokers. Small random samples aretaken of teachers of various subjects and it is found that of 20 teachers of statistics, four aresmokers, whereas there are eleven smokers in a sample of 2