Confidence intervals and point estimate problems

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SUMMARY

The discussion focuses on solving two statistical problems involving confidence intervals and point estimates. The first problem requires calculating the sample size used in a study with a 99% confidence interval of 152 to 158 and a standard deviation of 10, which is determined to be 36. The second problem involves finding the point estimate of the proportion of students who responded "no opinion" from a sample of 300 students, where 15 expressed no opinion, resulting in a point estimate of 0.05.

PREREQUISITES
  • Understanding of confidence intervals and their calculations
  • Knowledge of point estimates and proportions
  • Familiarity with standard deviation and its role in sample size determination
  • Basic statistical concepts and terminology
NEXT STEPS
  • Study the calculation of sample sizes for confidence intervals in statistics
  • Learn about point estimates and how to calculate proportions from survey data
  • Explore the concept of standard error and its application in confidence intervals
  • Review statistical software tools like R or Python for performing statistical analyses
USEFUL FOR

Students, educators, and professionals in statistics, data analysis, or research who need to understand confidence intervals and point estimates in practical applications.

colle
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I am lost on how to do these two problems and can't find info on how to solve them anywhere. If anyone can get me on the right track as to how to start, that would be amazing!

1. A 99% confidence interval for a population mean was reported to be 152 to 158. If the standard deviation is 10, what sample size was used in this study?

2. A survey for a sample of 300 students resulted in 175 yes responses, 110 no responses, and 15 no opinions. What is the point estimate of the proportion in the population who respond "no opinion"?
 
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colle said:
I am lost on how to do these two problems and can't find info on how to solve them anywhere. If anyone can get me on the right track as to how to start, that would be amazing!

1. A 99% confidence interval for a population mean was reported to be 152 to 158. If the standard deviation is 10, what sample size was used in this study?

As reported in...

http://mathhelpboards.com/questions-other-sites-52/unsolved-statistics-questions-other-sites-part-ii-1566-post12072.html#post12072

... is [approximately] $ \text{erfc}\ (x) = .01$ for $x \sim 1.8$ so that is $\displaystyle \frac{10}{\sqrt{n}} = \frac{5}{3} \implies n=36$... Kind regards $\chi$ $\sigma$
 

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