(a) Let x = (x,...,xn) contain an observed random sample on a random variable X with...

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(a) Let x = (x₁,...,xn) contain an observed random sample on a random variable X with prob- ability density function f(x; 0) specified up to an unknown vector of parameters . The random sample is denoted by X = (X₁, ..., Xn)T. Suppose a null hypothesis Ho: 0 = 0 versus an alternative hypothesis H₁00 is to be rejected if the observed value T(x) of the test statistic T(X) is sufficiently large in magnitude. (i) Give a definition of the P-value of a test in general. [1 mark] (ii) Give a definition via a mathematical expression for the P-value of the test proposed here. [1 mark] (a) Let x = (x₁,...,xn) contain an observed random sample on a random variable X with prob- ability density function f(x; 0) specified up to an unknown vector of parameters . The random sample is denoted by X = (X₁, ..., Xn)T. Suppose a null hypothesis Ho: 0 = 0 versus an alternative hypothesis H₁00 is to be rejected if the observed value T(x) of the test statistic T(X) is sufficiently large in magnitude. (i) Give a definition of the P-value of a test in general. [1 mark] (ii) Give a definition via a mathematical expression for the P-value of the test proposed here. [1 mark]