Sample Size Margin of Error and Confidence Intervals

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Sample Size, Margin of Error, and Confidence Intervals Unit 5 - Statistics - Day

Sample Size, Margin of Error, and Confidence Intervals Unit 5 - Statistics - Day 5

Sample Size ➔ The number of people to be surveyed, or items to be

Sample Size ➔ The number of people to be surveyed, or items to be reviewed, etc. ➔ Depends on many factors: ◆ Cost, deadlines, acceptable level of precision, variability within the population of interest, sampling method, etc.

How accurate are your numbers? ➔ Looking at the mean obtained from a sample

How accurate are your numbers? ➔ Looking at the mean obtained from a sample would not be as accurate as the mean for the population. ➔ How can we make sure our numbers include the true population mean? CONFIDENCE INTERVALS

Level of Precision (MOE) ➔ Determine Margin of Error (MOE). . . how precise

Level of Precision (MOE) ➔ Determine Margin of Error (MOE). . . how precise do you need to be in your study? ➔ Determine Confidence Level. . . what percent of the time will your results be true? ➔ Example: You could design a study to ensure that your results from a sample do not differ from the true population by more than 10% (MOE) 95% of the time (confidence level).

MOE Formula

MOE Formula

% Confidence z* Value 80 1. 28 90 1. 645 95 1. 96 98

% Confidence z* Value 80 1. 28 90 1. 645 95 1. 96 98 2. 33 99 2. 58

Example The president of a large university wishes to estimate the average of the

Example The president of a large university wishes to estimate the average of the students presently enrolled. From past studies, the standard deviation is known to be 2 years. A sample of 50 students is selected and the mean is found to be 23. 2 years. Find the 95% confidence interval of the population mean.

Example The president of a large university wishes to estimate the average of the

Example The president of a large university wishes to estimate the average of the students presently enrolled. From past studies, the standard deviation is known to be 2 years. A sample of 50 students is selected and the mean is found to be 23. 2 years. Find the 95% confidence interval of the population mean. 1. Calculate the Margin of Error (use 1. 96 for z*) 2. Create the Confidence Interval MOE = +/- 0. 55 23. 2 - 0. 55 < pop mean < 23. 2 + 0. 55 22. 65 < pop mean < 23. 75

Example A certain medication is known to increase the pulse rate of its users.

Example A certain medication is known to increase the pulse rate of its users. The standard deviation of the pulse rate is known to be 5 beats per minute. A sample of 30 users had an average pulse rate of 104 beats per minute. Find the 99% confidence interval of the true mean. 104 +/- 2. 36 or 101. 64 < pop mean < 106. 36

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