Stating hypothesis

In statistical hypothesis testing, two hypotheses are compared. These are called the null hypothesis and the alternative hypothesis . The null hypothesis is the hypothesis that states that there is no relation between the phenomena whose relation is under investigation, or at least not of the form given by the alternative hypothesis. The alternative hypothesis, as the name suggests, is the alternative to the null hypothesis: it states that there is some kind of relation. The alternative hypothesis may take several forms, depending on the nature of the hypothesized relation; in particular, it can be two-sided (for example: there is some effect, in a yet unknown direction) or one-sided (the direction of the hypothesized relation, positive or negative, is fixed in advance). [23]

However, if the mean of sample is not likely to be significantly greater than 2% (and remain at say around %), then we CANNOT reject the null hypothesis. The challenge comes on how to decide on such close range cases. To make a conclusion from selected samples and results, a level of significance is to be determined, which enables a conclusion to be made about the null hypothesis. The alternative hypothesis enables establishing the level of significance or the "critical value” concept for deciding on such close range cases. As per the standard definition , “A critical value is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis”. In the above example, if we have defined the critical value as %, and the calculated mean comes to %, then we reject the null hypothesis. A critical value establishes a clear demarcation about acceptance or rejection.

The difference in the means is the "signal" and the amount of variation or range is a way to measure "noise". The greater the signal, the more likely there is a shift in the mean. The lower the noise, the easier it is to see the shift in the mean. The t-Statistic is a formal way to quantify this ratio of signal to noise. The actual equation used in the t-Test is below and uses a more formal way to define noise (instead of just the range). The theory behind this is beyond the scope of this article but the intent is the same. The larger the signal and lower the noise the greater the chance the mean has truly changed and the larger t will become.

Stating hypothesis

stating hypothesis

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