## P- value Distribution when Ho is true

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When the null hypothesis (Ho) is true, the distribution of the p-value follows a uniform distribution between 0 and 1. This means that if the null hypothesis is true, the observed data is equally likely to fall in any part of the distribution.

For example, if we conduct a hypothesis test where the null hypothesis states that the population mean is equal to a certain value, and we collect a sample that yields a p-value of 0.05, we can interpret this to mean that if the null hypothesis is true, we would expect to obtain a p-value of 0.05 or smaller in 5% of all samples due to chance variation.

Therefore, when the null hypothesis is true, the p-value distribution provides a measure of the likelihood of obtaining the observed data or more extreme values, assuming the null hypothesis is true. It is important to note that p-values do not directly provide evidence for the truth or falsity of the null hypothesis but only provide information about the probability of observing the obtained results by chance variation if the null hypothesis is true.

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