We can do this but need a modication to make it work

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: glu (UMich) Interval Estimation 7 / 16 Interval Estimation of Population Mean Case 2: Normally distributed population, σ unknown We keep talking about unknown population parameters: µ is unknown, we are building an interval estimate for it. How realistic is that σ is known. Not really: we almost never know what σ is. So what do we do? We can use s , sample standard deviation, instead. We can do this, but need a modification to make it work. It turns out the sampling distribution of x is not normal if you use s instead of σ . ¯ Sampling Distribution of x with unknown σ ¯ If x is the sample mean of a sample drawn from a population with N (µ, σ 2 ) distribution, ¯ then t= x −µ ¯ √ s/ n has a Student’s t distribution with n-1 degrees of freedom Utku Suleymanoglu (UMich) Interval Estimation 8 / 16 Interval Estimation of Population Mean Student’s t-distribution is another continuous probability distribution. It looks a lot like the standard normal distribution with symmetricity and mean at zero. It has a single parameter, called its degrees of freedom. As df increases, it converges to N (0, 1). We will rely on another table to calculate probabilities for it. Utku Suleymanoglu (UMich) Interval Estimation 9 / 16 Interval Estimation of Population Mean Utku Suleymanoglu (UMich) Interval Estimation 10 / 16 Interval Estimation of Population Mean CI for µ, Case 2: Normal Population, σ unknown If population has a normal distribution and σ is unknown, but sample standard deviation,s , is known, a 100(1 − α)% confidence interval for µ can be constructed via: √ x ±...
View Full Document

Ask a homework question - tutors are online