Question 19

The forecast club Marvellous always makes its miraculous predictions about the results of significant European soccer matches by utilising its octopus. The club conducted researches on the accuracy of the prediction of soccer matches using octopus at different places in the world including USA, France, Italy, Australia and Japan. The prediction results include 'TRUE' and 'FALSE'. The total 300 researched were performed and the results are shown as follows. Assume that all the researches were conducted independently in the five places. Places USA France Italy Australia Japan TRUE 33 28 36 26 32 FALSE 29 31 27 30 28 Question (a). For analysing the prediction results of the researches conducted in Australia, examine whether the true probability of "TRUE" is larger than 0.61. Demonstrate your hypotheses and utilise a significance level of 5.0%. Question (b). Test whether the true probability of "TRUE" in Italy is larger than that in USA. Demonstrate your Demonstrate your hypotheses and utilise a significance level of 2.5%. Question (c). Assume there is a type II error in the research in Australia shown in Question (a) at a significance level of 5.0% and the true probability of "TRUE" is 0.65, what is the probability of the type II error? Question (d). The researchers also wanted to figure out whether there exist some negative interferences of places on the performance of octopus for the fairness of the prediction. Test whether the results of prediction and the places are independent. Demonstrate your hypotheses and analyse by using a significance level of 5%. Question (e). Determine the 90% confidence interval for the true probability of 'TRUE" of the prediction results as shown in Question (d). Question (f). The researchers considered whether there exist some preferences of octopus for the places and believed that the octopus is twice likely to prefer USA to Australia, and twice likely to prefer Italy to Japan. Test the researchers' claim by demonstrating your hypotheses and analyse by utilising a significance level of 10%. Question (g). Test whether the places of France and Australia interact to contribute to the prediction results of octopus. Demonstrate your hypothesis and utilize a a significance level of 5%