Suppose that you were told that average hourly wages in State A and State B are different. However, you have your own suspicion that it could be the same. You suggest to your brother, who is attending a school in State B to collect data on hourly wage as part of your project You do the same for State A as your school is located in State A. The accompanying table shows your and your brother's findings. Average Hourly Wages in State A and State B, in dollar State A State B Ystate a Sstate a | nstate A Ystate B Sstate B Nstate B 58.7 155 57.8 3.9 4.2 157 (a) Let your null hypothesis be that there is no difference in the average hourly wage in the two states. Specify the alternative hypothesis. (b) Find the difference in average hourly wage and the standard error of the difference. Generate a 95% confidence interval for the difference in average hourly wage. Calculate the t-statistic for comparing the two means. Is the difference statistically significant at the 1% level? Which critical value did you use? Why would this number be smaller if you had assumed a one-sided alternative hypothesis? What is the intuition behind (d) this? What about at 5% level? (e)