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Univariate Inferences about a MeanPowerPoint Presentation

Univariate Inferences about a Mean

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### Univariate Inferences about a Mean

Shyh-Kang Jeng

Department of Electrical Engineering/

Graduate Institute of Communication/

Graduate Institute of Networking and Multimedia

Scenarios

To test if the following statements are plausible

A clam by a cram school that their course can increase the IQ of your children

A diuretic is effective

An MP3 compressor is with higher quality

A claim by a lady that she can distinguish whether the milk is added before making milk tea

Rejection or Acceptance of Null Hypothesis

Student’s t-Statistics

Student’s t-distribution

Student’s t-distribution

Student’s t-distribution

Origin of the Name “Student”

- Pseudonym of William Gossett at Guinness Brewery in Dublin around the turn of the 20th Century
- Gossett use pseudonym because all Guinness Brewery employees were forbidden to publish
- Too bad Guinness doesn’t run universities

Selection of a

- Often chosen as 0.05, 0.01, or 0.1
- Actually, Fisher said in 1956:
- No scientific worker has a fixed level of significance at which year to year, and in all circumstances, he rejects hypotheses; he rather gives his mind to each particular case in the light of his evidence and hid ideas

Statistical Significance vs. Practical Significance

- The cram school claims that its course will increase the IQ of your child statistically significant at the 0.05 level
- Assume that 100 students took the courses were tested, and the population standard deviation is 15
- The actual IQ improvement to be statistically significant at 0.05 level is simply

More Specific Hypotheses

- Null hypothesis
- Alternative hypothesis

Power

- The probability of concluding that the sample came from the H1distribution (i.e., concluding there is a significant difference), when it really did from the H1distribution (there is a difference)

Effective Sizes

- How many samples are required to validate the following claim of the cram school:
- Our course will raise IQ levels of your child by 5 points

- statistically significant at 0.05 level, and the type II error is 0.1
- Normal IQ mean is 100, with standard deviation 15
- Sample standard deviation is assumed to be 15, too

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