Paul McCartney and John Lennon, the two ex-Beatles, were infamously known for their constant arguments over each other’s compositions. John had expressed his strong dislike towards Paul’s composition “Ob-La-Di, Ob-La-Da” on several occasions, stating that it was a classic representation of Paul’s “granny song-writing style”. Paul, however, was extremely defensive about his own creation, claiming that 80% of their fans actually enjoyed this piece of work. George and Ringo were suspicious about Paul’s presumption. They decided to take a random sample of 100 people who have listened to their album and asked them whether they like “Ob-La-Di, Ob-La-Da”. They found out that 72 people they surveyed gave positive feedback on this song. A hypothesis test is to be carried out to test George and Ringo’s suspicionx. 

 

(a) Identify the population of interest. 

(b) State the null and alternative hypotheses. 

(c) Determine any conditions that must be valid to carry out the test.  

(d) Compute the test statistic. 

(e) Find the exact value or provide a range of values for the P-value. Sketch your model and shade the corresponding region (a sketch by hand is fine). 

(f) Do you think Paul is right about his presumption based on your hypothesis test using a 5% significance level? 

(g) Based on your conclusion above, what type of error are you at risk of making? Explain your answer in the context of this question.