The mean weight of penguins last year was 15.4 kg. In a random sample of 35 penguins, the standard deviation of the weight is 2.5 kg. If the actual mean weight is as low as 15.1 kg, what is the probability of a type 2 error for a two-sided hypotheses test at the 0.05 significance level? If a hypothesis test were run and the null hypothesis is not rejected, would you trust the results (how powerful would the test be)? What can be done to have a more powerful test?