Textbook Notes (290,000)

CA (170,000)

UTSC (20,000)

Statistics (100)

STAB22H3 (100)

Ken Butler (10)

Chapter

This

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TESTING HYPOTHESES ABOUT PROPORTIONS

[2]

(Ex-IGNOTS)

- huge pieces of metal that are used as structural parts for cars and planes

- problem: if they crack while they are manufactured, they must be remade, or

recycled, but recycling costs too much $

- before changes were made to manufacturing, only 80% free of cracks

- after changes, 400 ignots were sent for manufacturing and out of which 83% free of

cracks

- has the cracking rate really reduced, or was this by chance?

p531

[1]

(Ex-IGNOTS)

- treat 400 ignots as random sample

- recall: each random sample has diff. prop. of cracked ignots (b/c there is

variation from one sample to another)

- so we want to know:

- is this 17% due to sampling variability, or is it strong enough evidence that the

true cracking rate is now really below 20%?

[2]

(Ex-IGNOTS)

- the above qn, and ex's below are answered by testing

hypotheses

about models:

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- ex. has the PM's approval rating changed since the last yr?

- ex. has teenager smoking been reduced in past 3 yrs?

- ex. is global T decr'ing?

HYPOTHESES

[1]

Hypotheses = working models that are adopted temporarily

- ie. used temporarily

(Ex-IGNOTS)

- to test whether changes made to manufacturing process really did improve cracking

rate, assume that:

- it made no difference, & so any sort of improvement is really just random

fluctuation (sampling error)

= null hypothesis in this context

- states that prop. of cracks really is still 20%

- ie. p = 0.20

NULL HYPOTHESIS - assumption that there is no real difference between the

groups/treatments in comparison, and that if there is any sort, it is merely due to

random fluctuation (Sampling error)

[3]

NULL HYPOTHESIS

- denoted as H0

- specfies popn model parameter of interest

- proposes val. for that paramter

- typically written in this form:

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

parameter

=

hypothesized value

- specific hypothesized val. for parameter, which is used to compare against

observed statistic val.

[4]

NULL HYPOTHESIS (Ex-INGOTS)

H0 :

p

= 0.20

- what val. it takes on is typically obvious from Who and What of data

[5]

ALTERNATIVE HYPOTHESIS

- denoted as HA

- contains val's of parameter that we consider plausible IF we reject null hypothesis

ALTERNATIVE HYPOTHESIS (Ex-INGOTS)

- H0 is that:

p

= 0.20

- HA is p < 0.20

- we are interested in reducing the cracking rate

- this is sensible alternative other than making

p

equal 0.20

[6]

- what would make us think that cracking rate really went lower than 20%?

- if we observed cracking rate was significantly lower than 20%, then this is

likely convincing

- ex. only 3/400 ingots crack (0.75% rate)

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