{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Slides-09 - ECON1203/ECON2292 Business and Economic...

This preview shows pages 1–9. Sign up to view the full content.

Click to edit Master subtitle style ECON1203/ECON2292 Business and Economic Statistics Week 9

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

View Full Document
22 Week 9 topics l Calculating probability of type 2 errors l Power of test l Hypothesis testing & confidence intervals for the mean when population variance is unknown l t distribution l Sampling distribution of sampling proportion l Hypothesis testing & confidence intervals for the population proportion l Key references l Keller 11.3-11.4, 12.1, 9.2 pp 309-14, 12.3
33 Type I errors in hypothesis testing l Type I errors occur when we reject a true null hypothesis l Denote P (Type I error) = α P (Reject H 0| H 0 true) = α l Analyst specifies α l Typical values chosen for α in applications are 0.10, 0.05 or 0.01 l Value of α is called the significance level of the test

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

View Full Document
Type II errors in hypothesis testing l Type II errors occur when we don’t reject a false null hypothesis l Denote P (Type II error) = β l For given α there will be a range of β values (depending on the true alternative) l Can be calculated for all values under alternative P (Do not reject H 0 | H 0 not correct) = β l Changing α for given fixed alternative changes β l There is a tradeoff between the 2 types of errors 44
55 Calculating probability of Type II errors l Recall McDonalds example l H 0: μ = 0.25, H 1: μ < 0.25 l With n = 25, α = 0.05, σ = 0.05 previously found a decision rule (DR) of rejecting H 0 if sample mean < 0.2336 l Suppose that McDonald’s only puts 0.24 pounds in their quarter pounder. Will we detect this?

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

View Full Document
66 Power of a test l Defined as the probability of correctly rejecting a false null hypothesis l P (Do not reject H 0| H 0 not correct) = β l P (Reject H 0| H 0 not correct) = Power = 1- β l Keller p. 370, (Fig. 11.10) l H 0: μ = 170; H 1: μ > 170 l n = 400, α = 0.01, σ = 65 l DR: reject H 0 if sample mean > 177.57 l Power if μ = 180?
77 Power of a test… l What happens to power if increase α to 0.05? l What happens to power if increase n to 1000?

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

View Full Document
Power of a test...
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 27

Slides-09 - ECON1203/ECON2292 Business and Economic...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online