Introduction to Inference Confidence Intervals Issue of accuracy Remember: all 3 conditions must be met (randomization, normality, independence) Margin.

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Presentation transcript:

Introduction to Inference Confidence Intervals

Issue of accuracy Remember: all 3 conditions must be met (randomization, normality, independence) Margin of error is nonresistant to outliers. When formula is based on z-scores: need  and an approximately normal sampling distribution Formula modifications exist if certain assumptions are not met…like if we don’t know…

Confidence Intervals without z* Formula: Draw a random sample of size n from a large population with unknown  and . Z-interval One-sample t-interval

t distribution continued The t distribution takes into account the differences in variation due to sample size. The t distribution has n – 1 degrees of freedom.

Reading a t chart What is the t* for a 70% confidence interval that has 5 degrees of freedom? t* = What is the t* for a 90% confidence interval from a sample of 15 observations? t* = What critical value t* would you use for a 99% confidence interval from a sample of 20? t* = 2.861

André is a waiter in San Francisco. The Internal Revenue Service is doing an audit on his tax return this year. In particular, the IRS wants to know the average amount André gets for a tip. Tips in San Francisco are fairly normally distributed. In an effort to satisfy the IRS, André took a random sample of eight credit card receipts, each of which indicated his tip. The sample mean is $12.35 with a standard deviation of $2.25. Find a 90% confidence interval for the population mean of tips received by André. Find a 90% confidence interval for the population mean of tips received by André. Given random sample. df = 7 We are 90% confident that the true mean tip amount lies between $10.84 and $ sample t-interval Given tips are fairly normally distributed. Safe to infer population at least 80 tips for independence.