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Sources of hypothesis?
Identification of a null and alternative hypothesis is used in statistical hypothesis testing. I've included two links which will show you how to formulate these hypothesis. The source of the null hypothesis is considered the "status quo" or what would be assumed without data. Perhaps, you buy 20 light bulbs which average 2500 hours of service, and 14 of these burn out after 2400 hours of service. Your null hypothesis is that the light bulbs will last 2500 hours or more, while the null hypothesis is that they will burn out on the average in less than 2500 hours. Hypothesis in application of the scientific method is entirely another matter. Please see related links.
Why is the level of significance always small?
The significance level is always small because significance levels tell you if you can reject the null-hypothesis or if you cannot reject the null-hypothesis in a hypothesis test. The thought behind this is that if your p-value, or the probability of getting a value at least as extreme as the one observed, is smaller than the significance level, then the null hypothesis can be rejected. If the significance level was larger, then statisticians would reject the accuracy of hypotheses without proper reason.
What happens if a hypothesis is tested and shown to be false?
We do not make a clear separation between "proven true" and "proven false" in hypothesis testing. Hypothesis testing in statistical analysis is used to help to make conclusions based on collected data. We always have two hypothesis and must chose between them. The first step is to decide on the null and alternative hypothesis. We also must provide an alpha value, also called a level of significance. Our null hypothesis, or status quo hypothesis is what we might conclude without any data. For example, we believe that Coke and Pepsi tastes the same. Then we do a survey, and many more people prefer Pepsi. So our alternative hypothesis is people prefer Pepsi over Coke. But our sample size is very small, so we are concerned about being wrong. From our data and level of significance, we find that we can not reject the null hypothesis, so we must conclude that Coke and Pepsi taste the same. The options in hypothesis testing are: Null hypothesis rejected, so we accept the alternative or Null hypothesis not rejected, so we accept the null hypothesis. In the taste test, we could always do a larger survey to see if the results change. Please see related links.
What role does the Central Limit Theorem play in evaluation of the confidence level or hypothesis testing?
Without getting into the mathematical details, the Central Limit Theorem states that if you take a lot of samples from a certain probability distribution, the distribution of their sum (and therefore their mean) will be approximately normal, even if the original distribution was not normal. Furthermore, it gives you the standard deviation of the mean distribution: it's σn1/2. When testing a statistical hypothesis or calculating a confidence interval, we generally take the mean of a certain number of samples from a population, and assume that this mean is a value from a normal distribution. The Central Limit Theorem tells us that this assumption is approximately correct, for large samples, and tells us the standard deviation to use.
What are the applications of dispersion without deviation?
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