Chapter 23 The t-distribution, Confidence Intervals, and Significance Testing for Quantitative Data.

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Presentation transcript:

Chapter 23 The t-distribution, Confidence Intervals, and Significance Testing for Quantitative Data

Inference for the Mean of a Population when  is Unknown

Inference for the Mean of a Population when  is Unknown

Inference for the Mean of a Population when  is Unknown The density curves (notice it’s plural) of the t-distributions are symmetric about 0 and bell-shaped. The spread is larger than that of a normal dist. due to the extra variability. As the degrees of freedom increase (i.e. the sample size, n-1), the t- dist. curves approach the standard normal curve.

Inference for the Mean of a Population when  is Unknown Conditions: Data represents a SRS of population Sample size < 10% of Population size Or items sampled are independent of each other And….

Inference for the Mean of a Population when  is Unknown Conditions: Sample size guidelines n < 15: Use t-procedures if the data is close to normal. If severe skewness or outliers are present, do not use t. 15 ≤ n < 30 : The t-procedures can be used except in the presence of outliers n  30 : The t-procedures can be used even for clearly skewed distributions when the sample is large by CLT.

Inference for the Mean of a Population when  is Unknown

Inference for the Mean of a Population when  is Unknown Two key phrases when making statements: Phrase 1: Interprets a single confidence interval: We are #% confident that the true (or population) mean of ____(context) lies in the interval ……

Inference for the Mean of a Population when  is Unknown Two key phrases when making statements: Phrase 2: Interprets the confidence level: Saying that we are “#% confident” means that with this data, if many intervals were constructed in this manner, we would expect approximately #% of them to contain the true (or population) mean of ____(context).