Understanding the Significance of p-values in Hypothesis Testing

A low p value = reject the null hypothesis/keep the null hypothesis

A low p-value typically indicates that there is strong evidence against the null hypothesis

A low p-value typically indicates that there is strong evidence against the null hypothesis. In hypothesis testing, the null hypothesis represents the default or baseline assumption, while the alternative hypothesis is the claim or hypothesis being tested.

The p-value is a measure of the strength of the evidence against the null hypothesis. It represents the probability of obtaining the observed data or more extreme results if the null hypothesis is true. Therefore, a low p-value suggests that the observed data is unlikely to occur by chance under the assumption that the null hypothesis is true.

When the p-value is small (usually less than a predetermined significance level, often 0.05), we reject the null hypothesis. This means that we have sufficient evidence to support the alternative hypothesis and that the observed data is more likely to be attributed to the alternative hypothesis rather than random chance.

On the other hand, if the p-value is not small (larger than the significance level), we fail to reject the null hypothesis. This does not mean that the null hypothesis is proven true, but rather there is not enough evidence to support the alternative hypothesis.

It is important to note that rejecting the null hypothesis does not guarantee that the alternative hypothesis is true. It simply suggests that the observed data is more consistent with the alternative hypothesis than with the null hypothesis. Hypothesis testing helps us make decisions based on the available evidence, but it cannot provide definitive proof.

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