# Statistics: Margin of Error, Sample Sizes and Confidence Intervals

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 ...

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