Being confident make one's self more reassured. Briefly, explanations below are for two sided confidence levels/intervals in order to simplify the idea. Saying " two sided " gives initial impression that there is something like two limits, yeah they are: upper and lower limits where the confidence interval lies in between. Example: Let's look at the population of a specific mobile phone model. Suppose we are now interested in the ' weight ' property. We found that weight property follows a normal distribution with mean value of 120 grams and a standard deviation of 1.4 grams. Weight ~ Normal (Mu, Sigma) = Normal (120, 1.4) This understanding means that majority of mobiles tested will weigh very closely to 120 grams. Yes, there should be fluctuations above and below the mean value but surely that still relatively close to mean value. Suppose a question: do you expect weights like: 121, 119.5, 122.1, 118.9? Answer: Yes , I surely expect such ...
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A general hypothesis is defined as following (eg a hypothesis on the population mean): H0: Mu = Mu0 H1: Mu != Mu0 OK, apart from we have a two or one sided hypothesis, after performing the checking and statistical tests: our conclusion should be one of the following: Rejecting the null hypothesis (H0). Failing to reject the null hypothesis (H0). The following statements for conclusions are not accurate : Accepting the null hypothesis (H0). Accepting the alternative hypothesis (H1). But why? When we fail to reject H0, it does not mean we accept H0 as a fact because we still could not prove it as a fact. But what happened is that we failed to prove it to be false. This goes like following: we have suspected new factors may affected the population mean, then we have taken all possible evidences and checking, but all checking failed to prove our suspects. As well, rejecting H0 does not mean accepting H1 as a fact....
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