Problem 1 (20 pts). In a large university, John is running for the president of a student association. He guesses that currently 45% students are his supporters. A major debate is planned. John hopes to attract more supporters after the debate. He plans to take two simple random sample of size 100 each, one before the debate and one after the debate. He suspects that the debate may induce 10% of current non-supporters to change minds and support him, and he does not expect any of his supporters to change minds after the debate. How much better could a panel study be than a two independent samples study? Express your answer as a ratio of the anticipated 95% confidence interval width for the panel study compared to the corresponding anticipated width for the two independent sample study, assuming equal sample sizes. Report your final answer to two decimal places. You must show the key steps of your calculations and define notation used. Problem 1 (20 pts). In a large university, John is running for the president of a student association. He guesses that currently 45% students are his supporters. A major debate is planned. John hopes to attract more supporters after the debate. He plans to take two simple random sample of size 100 each, one before the debate and one after the debate. He suspects that the debate may induce 10% of current non-supporters to change minds and support him, and he does not expect any of his supporters to change minds after the debate. How much better could a panel study be than a two independent samples study? Express your answer as a ratio of the anticipated 95% confidence interval width for the panel study compared to the corresponding anticipated width for the two independent sample study, assuming equal sample sizes. Report your final answer to two decimal places. You must show the key steps of your calculations and define notation used