3. 4.1 Specific logic and main steps of hypothesis testing
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5. the 95% confidence interval is ( 8.15, 10.15 ), the 99% confidence interval is ( 7.78, 10.51 ).
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8. Sample mean μ How to explain this difference? Two guesses
9. 4.1.1 Set up the statistical hypotheses null hypothesis alternative hypothesis
10. 4.1.2 Select statistics and calculate its current value
11. Symmetric around 0 -2.8345 0 2.8345 Fig.4.1 Demonstration for the current value of t and the P -value
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14. Current situation Extreme situation -2.8345 0 2.8345 0.01< p <0.02 Fig.4.1 Demonstration for the current value of t and the P -value
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20. Probability of detecting a predefined statistical significant difference. Making Type I or Type II errors often result in monetary and nonmonetary costs.
21. 4.2 The t Test for One Group of Data under Completely Randomized Design
30. Solution : t =2.69 ， 0.005< P <0.01 Conclusion: the mean of pulses for healthy males in the mountainous area is higher than that in the general population
31. P value P value One side -2.69 0 2.69 0.005< p <0.01 Fig.4.1 Demonstration for the current value of t and the P -value
37. P value One side -2.08 0 2.08 0.01< p <0.05 Fig.4.1 Demonstration for the current value of t and the P -value
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Editor's Notes
I will introduce the specific logic and main steps of HT through an example.
t value given alpha=0.05 and DF=19. Explain the meaning of the 95%CI.
There are two explanations to the difference between 9.15 and 10.50. One is sampling error, another is different population mean.
We have to make a choice between the two hypotheses. We cannot prove which one is correct. The best way is to find which hypothesis is more contradicted with the data and reject it. We have to collect evidence=probability. H0 is relatively simple and easily find the statistical distribution . So focus on the H0, reject or not reject.
Under the H0, we want to find the P of getting the current sample data and more extreme. For the mean of a normal distribution with unknown variance.
t distribution under H0. According to the P value, the current situation and even more extreme situation are not quite possible to appear. That is, a small P value indicates that the information does not support the H0.
An ignorable small probability alpha should be defined in advance such as alpha=0.05, so the current P value could be regarded as small or almost zero.
How to understand the meaning of “it does not mean that the difference is big or obvious”?
When we test a hypothesis, we have to make a choice, reject or not reject H0.( Be or not to be). We make decision based on the probability, not prove. So we may make mistake. There are two kind of mistakes we might make.
If we consider that the pulses of healthy males in the mountainous area would never be lower than that in general area on average, then one-side test should be used.
t distribution under H0. According to the P value, the current situation and even more extreme situation are not quite possible to appear. That is, a small P value indicates that the information does not support the H0.
1 ounce = 28.35 g; 115 oz = 6.5 jin ; 120 oz = 6.8 jin
t distribution under H0. According to the P value, the current situation and even more extreme situation are not quite possible to appear. That is, a small P value indicates that the information does not support the H0.
IF a type I error is made, then a special-care nursery will be recommended, with all the extra costs involved, when in fact it is not needed. If a type II error is made, a special-care nursery will not be needed, when in fact it is needed. The nonmonetary cost of this decision is that low-birthweight babies may not survive without the unique equipment in a special-care nursery.
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