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# Univariate Inferences about a Mean - PowerPoint PPT Presentation

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

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### Univariate Inferences about a Mean

Shyh-Kang Jeng

Department of Electrical Engineering/

Graduate Institute of Networking and Multimedia

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

Developed by Fisher, Pearson, Neyman, etc.

Two-sided

One-sided

Student’s t-Statistics

Student’s t-distribution

Student’s t-distribution

Student’s t-distribution

• 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

• 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

• Null hypothesis

• Alternative hypothesis

• 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)

• 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