Calculating Confidence Intervals for Means and Proportions in Statistics, Slides of Statistics

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Estimation

Point Estimation

1. Using a sample statistic to estimate a population parameter

Interval Estimation

1. Constructing an interval about a sample statistic

Mean plus or minus

Z (alpha) * (SD/square root of N)

This line above is the standard error of measurement (SEM)

Example of Interval Estimation

1. Dr. Violet wants to determine the average number of arrests that police officers make
2. She selects a sample of 58 police officers, and calculates M = 2.3 and SEM = 1.
3. She can be 68% confident that μ lies somewhere in the interval of 1.2 to 3.

Confidence Intervals and the Normal

Distribution

Confidence Intervals for Means From

Large Samples

1. N > 30

2. M  z * SEM

Confidence Intervals and the Mean for

Small Samples

1. N  30

2. M  t * SEM

Example of Small Sample Confidence

Interval

1. Dr. Daisy wants to know the average number of grades that juvenile delinquents fail
2. She selects a sample of 28, and finds M = 1.4 and SEM = 0.
3. She wants to be 99% confident
4. 1.4 ± 2.771(0.3)
5. She can be 99% confident that μ lies somewhere in the interval of 0.5687 to 2.

Degrees of Freedom

1. Assume that the sum of three numbers is 10

Two of the number are 5 and 3

Degrees of Freedom -- continued

4. What can the value of X 3 be?
   1. It must be 2
   2. It is not free to vary

Standard Error of the Proportion

n

p p

P

Estimating the Standard Error of the

Proportion

1. Conservative approach
   1. Set p =.

Confidence Intervals and Proportions for

Small Samples

1. N  30

2. p  t * SEP

Example of Small Sample Confidence Interval for a Proportion

• Dr. Felicia wants to determine what proportion of the general population is in favor of decriminalizing marijuana
• She selects a sample 26, and finds p = .34 and SEP =
• She wants to be 95% confident
• .34 ± 2.06(0.5)
• She can be 95% confident that P lies somewhere in the interval of 0.327 to 0.