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Statistics: Margin of Error, Sample Sizes and Confidence Intervals

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Question: Give an estimate of the sample size needed to obtain the specified margin of error for a 95% confidence interval.

Margin of error = 0.01, standard deviation = 0.25

Scenario: Researchers want to determine the mean number of hours students spend watching TV. A margin of error of 0.25 hour is desired. Past studies suggest a population standard deviation of 1.7 hours is reasonable. Estimate the minimum sample size required to estimate the population mean.

Scenario: Based on a sample of 62 homes, the data offered gives the mean weight in pounds and the standard deviation for paper, glass & plastic. For each category, estimate the mean weight for the entire population of homes. Give the 95% confidence interval.

Sample Mean Sample Standard Deviation
Paper 9.42 4.12
Glass 3.75 3.11
Plastic 1.91 1.07

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Give an estimate of the sample size needed to obtain the specified margin of error for a 95% confidence interval;

Margin or error = 0.01, standard deviation = 0.25

Solution: The z-score for a 95% confidence interval is 1.96, namely, z=1.96. The margin is given by

So, we have

So, the sample size needed is 2401.

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Researchers want to determine the mean number of hours students spend watching TV. A margin of error of 0.25 hour is desired. Past studies suggest a population standard deviation of 1.7 hours ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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