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

2. 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.

3. 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

4. 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).

5. MOE Formula

6. % Confidence
z* Value 80
1.28 90
1.645 95
1.96 98
2.33 99
2.58

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

8. Example MOE = +/- 0.55 23.2 - 0.55 < pop mean < 23.2 + 0.55
The president of a large university wishes to estimate the average age 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.
Calculate the Margin of Error (use 1.96 for z*)
MOE = +/- 0.55
< pop mean <
22.65 < pop mean < 23.75
2. Create the Confidence Interval

9. 104 +/- 2.36 or 101.64 < pop mean < 106.36
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
< pop mean <