4. A coin is thrown until a head occur and the number X of tosses recorded. After repeating the experiment 256 times, we obtained the following results: X 1 2 3 4 5 6 7 8 f 136 60 34 12 9 1 3 1 Test the hypothesis, at 0.05 level of significance, that the observed distribution of X may be fitted by the binomial distribution B (x; 1/), x =1, 2, 3, ..., 8. 5. A company wishes to purchase one of five different machines A, B. C. D and E. In an experiment designed to determine whether there is a performance difference between the machines, five experienced operators each work on the machines for equal times, the table shows the number of units produced by each machine. Test the hypothesis that there is no difference between the machines at 5% level of significance. A 68 72 77 42 53 B 72 53 63 53 48 C 60 82 64 75 72 D 48 61 57 64 50 E 64 65 70 68 53 6. A car rental agency, which uses 5 different brands of tyres in the process of deciding the brand of tyre to purchase as standard equipment for its fleet, finds that each of 5 tyres of each brand last the following number of kilometers (in thousands). Test at 5% level of significance. Test the hypothesis that the five tyre brands have almost the same average lives, A B C D E 36 46 35 45 4 37 39 42 36 39 42 35 37 39 37 38 37 43 35 35 47 43 38 32 38