3. Let Y; ~ N(r;ß,o²) be independent, i = 1,...,n, where (r1,..., In) and o² > 0 arc known rcal numbers, ß is an unknown parameter. (a) Write down the log-likclihood log L(ß). (b) Find the MLE for ß.

1. Find the exact numerical (a) sinh(log3), tanh(2log5). (c) value of cach expression. (b) cosh (-log 2),

6.) Use the acidity model give by pH = - log [H•]. where acidity (pH) is a measure of the hydrogen ion concentration [H] (measured in moles of hydrogen per liter) of a solution. a) Find the pH if [H] = 2.3 x 10-s, (Round to the nearest tenth.) am od ne 810S or 2105 moni VM b99weldmuT to (ahnsauony n) nouelugog sri b) Compute [H] for a solution in which the pH = 4.9. (Round to eight decimal places.)W La

How do you know when a hypothesis test is left-tailed, right-tailed or two-tailed? How is this related to the alternative hypothesis?