62 students in a certain statistics class are asked which is their favourite colour among Red, Orange, Blue, and Green. The results are as follows: o <-c(red = 10, orange 16, yellow 24, green= 12) . State a sensible null hypothesis • State the observed values and the expected values under your null. • Calculate the Pearson's chi-square statistic sum ((o-e) "2/e) and show your working; state what its approximate null distribution is . State the precise definition of p-value and explain what "more extreme" means in this context. • Calculate the pvalue using pchisq() and your result from above, and interpret. • Excellence question: using random simulation, or otherwise, estimate the probability that all four colours have different numbers of students.
