{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

06.testing

# 06.testing - Lecture 6 Review of Statistics(Last Part...

This preview shows pages 1–7. Sign up to view the full content.

Lecture 6: Review of Statistics (Last Part) Hypothesis Testing and Interval Estimation BUEC 333 Summer 2009 Simon Woodcock

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The Importance of Sampling Distributions Why all the fuss about sampling distributions? Because they are fundamental to hypothesis testing . Remember that our goal is to learn about the population distribution. In practice, we are interested in things like the population mean, population variance, some population conditional mean, etc. We estimate these quantities in a random sample taken from the population. This is done with sample estimators like the sample mean, the sample variance, or some sample conditional mean. Knowing the sampling distribution of our sample estimator (e.g., the sampling distribution of the sample mean), gives us a way to assess whether particular values of population quantities (e.g., the population mean) are likely or unlikely. E.g., suppose we calculate a sample mean of 5. If the true population mean is 6, is 5 a “likely” or “unlikely” occurrence?
Hypothesis Testing We use hypothesis tests to evaluate claims like: the population mean is 5 the population variance is 16 some population conditional mean is 3 When we know the sampling distribution of a sample statistic, we can evaluate whether its observed value in the sample is “likely” when the above claim is true . We formalize this with two hypotheses. For now, we’ll focus on the case of hypotheses about the population mean, but we can generalize the approach to any population quantity.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Null and alternative hypotheses Suppose we’re interested in evaluating a specific claim about the population mean. For instance: “the population mean is 5” “the population mean is positive” We call the claim that we want to evaluate the null hypothesis , and denote it H 0 . H 0 : μ = 5 H 0 : μ > 0 We compare the null hypothesis to the alternative hypothesis , which holds when the null is false . We will denote it H 1 . H 1 : μ ≠ 5 (a “two-sided” alternative hypothesis) H 1 : μ ≤ 0 (a “one-sided” alternative hypothesis)
How tests about the population mean work Step 1: Specify the null and alternative hypotheses. Step 2a: Compute the sample mean and variance Step 2b: Use the estimates to construct a new statistic, called a test statistic , that has a known sampling distribution when the null hypothesis is true (“under the null”) the sampling distribution of the test statistic depends on the sampling distribution of the sample mean and variance Step 3: Evaluate whether the calculated value of the test statistic is “likely” when the null hypothesis is true. We reject the null hypothesis if the value of the test statistic is “unlikely” We do not reject the null hypothesis if the value of the test statistic is “likely” (Note: we never “accept” the null hypothesis)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: the t-test Suppose we have a random sample of n observations from a N(μ,σ 2 ) distribution.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 20

06.testing - Lecture 6 Review of Statistics(Last Part...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online