Over the lockdown period both John and Jane were getting very bored, so they looked at their old university books and decided to consider some of the questions they were asked to calculate during their seminars Jane asks John to calculate the numbers of the questions below and explain to their mother, who is an artist what these numbers mean Assume you are John and answer Janes questions a) Given the following sample data * = 15.s? = 270 n = 150 Where x bar is the sample mean, s squared is the sample variance and n is the sample size. Test the Null Hypothesis that the true mean is equal to 12, against a two sided alternative. Use the 5% significance level. b) The IQ (the intelligence quotient) of the whole population is Normally distributed with mean 100 and standard deviation 16 i What proportion of the population has an IQ above 1302 ii. What proportion of the population has IQ between 90 and 110? ili. In the past, about 10% of the population went to university Now the population is about 30% What was the IQ of the "marginal" student in I the past? What is it now? (30 marks)