Below is a table from a scientific study in Tennessee called Project STAR (Schanzen- bach, 2006, Table 2). The table contains averages for the treatment and control groups over various characteristics. The final column reports the p-value from a t-test for equality of the two means. The experiment sought to document educational gains from students in small-sized classes. The outcome variable is reported in the final row, while the treatment variable is listed in the penultimate row. The other rows are pre-treatment (a.k.a. control) variables. Econ 4523-Fall 2022 Characteristic Free lunch White or Asian Age in 1985 Female Attrition rate Problem Set 2 Days absent Class size in kindergarten Standardized test score in kindergarten Treatment 0.47 0.68 5.44 0.49 0.49 10.00 15.10 0.17 Due: Sep. 6 beginning of class Control P value 0.48 0.67 5.43 0.49 0.52 10.50 22.40 0.00 0.46 0.66 0.38 0.87 0.01 0.01 0.00 0.00 a. What is the ATE in this study? b. What is the average difference in the treatment value? (Hint: This is not the ATE. In most studies, this value is 100% [for cases where treatment is a 0/1 variable]) c. Do you think this experiment did a good job of randomizing the two groups? Why or why not? Total costs + Equivalent units of production Cost per equivalent unit of production d. Do you think this experiment is internally valid? Externally valid? Explain. 7. Rainfall in Sonoma County, California (a part of Silicon Valley) is highly correlated with eBay's worldwide total gross merchandise volume (i.e. the number of products eBay sells). Which of the following answers could support a causal explanation for this relationship? Explain why. a. Across the world, people prefer to buy more eBay products on rainy days. b. Climate change has caused Sonoma County to have increased rainfall and has encouraged the global population to do more shopping from home. c. eBay sales and rainfall in Sonoma County have both been increasing at similar rates in recent years d. Rainfall motivates residents of Sonoma County to buy and sell goods on eBay at extraordinarily high rates