6. Suppose there were 100 bio-medical research teams globally that were mutually in- dependently developing vaccine for COVID-19 virus around May 2020. If we apply t-test with significance level 5% individually to each of them under the null that the developed new vaccine is useless, what is the probability of fasely rejecting that at least one correct null collectively. (5%)

11. Michael wants to examine whether the gender of CEOs affects the probability of default in 2008. Michael collects 200 firm data and estimates the following the logit regression model: where L( ㆍ) is the logistic function is a dummy variable which equals one if firm i defaulted in 2008 and zero otherwise; is a dummy variable which equals one if the CEO of firm i is female in 2007 and zero otherwise. The results are shown below: From the results, Michael argues that the presence of female CEOs would decrease the default probability of the firm by 1.674 percent. Please comment. In addition, the odds ratio of Female is 0.1875. Please explain the meaning of this value and how do we get the value from the estimation results. (10%)

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