Statistics - Class 16 (Confidence Intervals)

Point Estimate

a single value that is our best estimate for the parameter of interest

Confidence Interval

• a plausible range of values for the population slope (β1) using the point estimate

• the entire interval must be less than or greater than a value

• wide interval = not very informative

Margin of Error

• aka: wiggle room in the estimate

• this reflects how accurate the sample statistic is as an estimate for the parameter

Common Form of a Confidence Interval

Statistic + / - Margin of Error

Standard Error

We expect the point estimate to be about ______ away from the population slope.

Critical Value

• t*

• a _____ that controls how sure we are that the population parameter (β1) is inside the interval

• a _____ for the density curve with n - 2 degrees of freedom to obtains the desired confidence level

Plausible Confidence Interval

• an interval that is narrow enough that we can actually use the interval in an informative way

• doesn’t consider every possibility

Confidence Level

• the percent of samples that we could draw from the population which, if we created a confidence interval on those samples, would contain β1

• aka: the most extreme samples we could get

  • we are never 100% confident

Confidence Level Interpretation

“___% of those intervals would contain the true population slope (β1).”

qt ( )

• a function (code)

• calculates the t-score with a specified area to its left

Confidence Interval Interpretation

“We are ____% confident that if the number of [ X ] increases by 1 [ X unit ], the number of [ Y ] increases between [ min. value ] and [ max. value ], on average.”

Hypothesis Tests

• Confidence Intervals and _____ almost always agree as long as the two methods use equivalent levels of significance/confidence

  • A two-sided hypothesis with a significance level of ⍺ is equivalent to a confidence interval with:

    • CL = 1 - ⍺