Question

olo wo T 30 seconds Oombine Sally enumel samo tostogo b do Housugog SOS VOYAH Erns AGENTA 2. An FM rock station claims that 85% of all its listeners are college students. A statistician decides to test this claim against the suspicion that the percentage is too high. A random sample of 2000 listeners is selected from the population of all listeners and it is determined that 1655 are college students. Perform a hypothesis test to answer the question: Do the sample results support the statistician's claim at a = 1%?

Answer 1

207 P= Population proportion of listeners who are college students na sample size = 2000, P = Sample proportion = 1655 = 0.8275 x=0.01 Ho: P = 0.85 Hi : P < 0.85 (ie actual propostion is lower than clain) I since , n is large, from large sample theory for sample propostion, we can use Normal distribution ie hoN(P, P(IP)). (6 mean = P . estimate = b = 0.8275 Standard error (Plie, estimate = (0.8275*(1-0.8275) = 0.00845 III Reject Ho il p-value < 0.01=(2) (1) sample result = h = 0.8275 under Mo, Under to - b -P ~ N(01) co Jeli-e Zo - 0.8275 -0.85 – 2.818 a test statistic 2000 0.85 0.15 2000 P-value = P(a <-2.818) = 0.00242 (0) P-value < 2 = 0.01 =) We reject Ho Yes, statistician reject the rock station's claim at &=0.01 . We conclude proportion of listeners who are college students are less than 85%