a) The New York Times in 1989 reported that on average the people who boarded the Titanic they paid $43 and a standard deviation of $51. you as a student statistic wants to prove this statement. To do this, take a random sample of 32 people and with a significance level of 5%, propose a hypothesis test and Conclude about the NY time statement with the p-value.

b) State the statistical assumptions that you need to carry out the test of hypotheses, and justify whether these assumptions are satisfied.