Confidence Intervals

Study Guide Exam :)

What is a Confidence Interval?

Range of values from sample data, that is likely to contain the true value of an unknown parameter

Point Estimate

A single statistic used to estimate an unknown population parameter.

Examples of a Point Estimate

• MEAN number of facebook friends among people under 35 is 220.

• 67% of the under-35 population use a facebook account.

Interval Estimate

A range of values within which the population parameter is likely to fall

Examples of Interval Estimate 

• people UNDER 35 have between 200 & 240 facebook friends 

• 60-75% of under-35 population uses a facebook account 

Primary Purpose of Confidence Intervals 

Provide a range within which the true population parameter is likely to lie 

What is Sample Size? 

The smaller sample size, the wider the confidence interval (smaller samples have larger margins of error) 

Relationship between sample size and Confidence Intervals 

Larger Sample Size → More Precision → narrower confidence interval 

Smaller Sample Size → more uncertainty → wider confidence interval 

When a confidence interval contains zero….

NOT ENOUGH EVIDENCE to conclude the effect is statistically significant at the given confidence level

Represents NO effect of difference

Margin of Error (MoE) 

an ESTIMATE that indicates how far the sample estimate may be from the true population value

Should Margin of Error be interpreted?

YES!

• Small margin of error means greater precision

• Larger margin of error means more uncertainty

What is a z-test?

Used to compare a sample mean to a known population mean when the population SD is known and the sample size is large.n

Uses standard normal (z) distribution

What is a single sample t-test?

Used to compare a sample mean to a known population mean when the population SD is unknown and the sample size is small.

Uses students t-distribution to account for extra uncertainty.