Inferencial statistics a) Acme Toy Company prints baseball cards. The company claims that 30% of the cards are Rookies, 60% Veterans but not All-Stars, and 10% are Veteran All-Stars. Suppose a random sample of 100 cards has 50 Rookies, 45 Veterans, and 5 Veterans All-Stars. Table 1: Rookies Veterans Veteran All-Star Observed 50 45 5 Expected 30 60 10 i) Set-up a hypothesis test to test if this information is consistent with the Acme's company claim? Use a 0.05 level of significance. [8] Hint: Use chisquare goodness of fit test. ii) Suppose the random sample of 100 cards is said to have a standard deviation of 10.58 %, find a 90 % confidence interval for the population standard deviation. [4] b) An analysis of the tries, penalty goals and dropped goals scored by South Africa in rugby tests against the British Isles, New Zealand, Australia and France gave the following contingency table: Table 2: Tries Penalties Drops British Isles 70 31 6 New Zealand 44 38 11 Australia 79 31 7 France 43 32 3 The number of penalities scored against New Zealand and France seems unexpectedly high, and this leads you to want to test the hypothesis that the mode of scoring is dependent on the opponents. At 5% level of significance, can you carry out a test for association? [13] Hint: Use chisquare test for independence/association. NB: Make use of the chi-squared distribution table on "Appendix".