Explain the following (i) what a statistical hypothesis is, (ii) an estimator and an estimate (iii) Type I and Type II errors

Here are the explanations for question 4:

a) (i) A statistical hypothesis is a statement or claim about a population parameter that is subject to verification using sample data. It typically includes a null hypothesis ($H_0$) and an alternative hypothesis ($H_1$). (ii) An estimator is a statistic (a function of the sample data) used to estimate an unknown population parameter. An estimate is the specific numerical value obtained by applying the estimator to a particular sample. (iii) Type I and Type II errors are potential mistakes made when performing hypothesis testing: • A Type I error occurs when a true null hypothesis is incorrectly rejected (a false positive). Its probability is denoted by $\alpha$. • A Type II error occurs when a false null hypothesis is incorrectly failed to be rejected (a false negative). Its probability is denoted by $\beta$.

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