1. (Flight arrivals & two-sided test) Based on past historical data, the (benchmark) mean arrival rate of flights between 5pm and 6pm at Chicago’s O’Hare Airport is 196 flight arrivals per hour. To...

1. (Flight arrivals & two-sided test) Based on past historical data, the (benchmark) mean arrival rate of flights between 5pm and 6pm at Chicago’s O’Hare Airport is 196 flight arrivals per hour. To increase arrivals, a new air traffic control procedure is implemented by the airport. A random sample consisting of 40 days after the installation of the new procedure was used to collect data on the number of arrivals per hour between 5pm and 6pm. The dataset “Flights.xls” contains these data. Using these data: a) Test the null hypothesis at the 5% significance level that the arrival rate under the new procedure is equal to the mean arrival rate of 196 flights, against the two-sided alternative hypothesis that it is not equal to the mean arrival rate. Explain your results. b) Do your results hold at the 1% significance level? Explain. 2. (Earnings “gender gap” & one-sided test) A widely-researched topic by economists is the determinants of the “gender gap” in earnings, i.e., the difference in earnings by males vs. females. Past historical data indicates that the (benchmark) mean wage rate of full-time, urban, non-unionized male workers in the Northeast part of the U.S. is $10.25 (inflationadjusted). The dataset “cps_NE_2008.xls” (which is an extract from the main CPS dataset that you studied in Chapter 2) contains a random sample from the year 2008 for 589 full-time, urban, non-unionized workers (males and females) from the Northeast part of the U.S. For each sampled worker, the dataset contains information on hourly wage, years of education, age, years of work experience, gender, and marital status. Using this dataset: a) Test the null hypothesis at the 5% significance level that in 2008 the mean wage of women was greater than the benchmark wage rate of men ($10.25), against the one-sided alternative hypothesis that it was below $10.25. Explain your results. b) Do your results hold at the 1% significance level? Explain. 3. (Proportions & Bernoulli & one-sided test) It is believed that the (benchmark) percentage of women that are married in the U.S. is 46%. Using the dataset “cps_NE_2008.xls”: a) Test the null hypothesis at the 5% significance level that in 2008 the mean proportion of women that were married in the Northeast part of the U.S. was smaller than the U.S. benchmark rate, against the one-sided alternative hypothesis that it was greater than the benchmark proportion. Explain your results. b) Do your results hold at the 1% significance level? Explain.