Question 19

The forecast club Marvellous always makes its miraculous predictions about the raults of significant European soccer matdt 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 'THUE' and 'FALSE'. The total soc researched were performed and the results are shown as follows. Assume that all the n5earches were conducted independently in the ve places. Places Question [a]. For analysing the prediction rults of the researches conducted in Australia, examine whether the true probability of \"TRUE\" is larger than 0.61. Demonstrate your hypothesa and utilise a significance IEvel of 5.1356. Question lb}. 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 2.556. Question lcl. Assume there is a type II error in the researdt in Australia shown in Question la} at a significance level of 5.05:. and the tme probability of \"TRUE" is I165, what is the probability of the type II error? Question [d]. The researchers also wanted to gure out whether there exist some negative interferences of places on the performance of octopus for the fairness of the prediction. Test whether the rults of prediction and the places are independent. Demonstrate your hypotheses and analyse by using a significance level of 596. Question [e]. Determine the soc. confidence interval for the true probability of 'THLIE" 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 hypolhes and analyse by utilising a significance level of 10%. Question lg}. 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%