Q3. How Do Locust Outbreaks Affect Children's Health? While we were unpleasantly distracted with the COVIDIQ pandemic, several countries also had to deal with one the worst locust outbreaks in recent years.7 Even though we have been able to control and prevent many locust outbreaks from reaching plague conditions, every once in a while we still experience environmental conditions that lead to a very large surge in locust swarms, and with climate change, we expect those surges to occur more frequently.8 To learn more about the impacts of locust outbreaks on human wellbeing, a team of researchers collected data from the Food and Agriculture Organization (FAQ) on the detection of locust swarms, and merged the data with measurements of children in the Demographic and Health Surveys (DHS). Through a process we will not go into detail here, the researchers match each child with a binary variable for being exposed to a locust swarm around the timing of their birth. Specically, the researchers are focusing on the time period during the 9 months before birth (what is referred to as inutem). The main outcome the researchers are examining is heightforage which is a standardized score that compares the height of a child to the distribution of height for children of the same age.9 The researchers run a regression of the heightforage dependent variable on the binary independent variables for locust swarm exposure: exposure in the 9month period before birth. The regression includes many other control variables that are not of interest for this question. Think of this regression as comparing children that experienced exposure to a locust swarm around the time they were in-utero to children that did not experience a locust swarm in-utero (but might have experienced it later in life). The two population coefficient that the research team is interested in learning about as 39m-pre-birth. The researchers report the following regression output from the regression described in part (1): Coefficient Estimate Estimated Std. Error t-statistic Bom -pre -birth -0.36 0.08 -4.5 Sample size (n): 341,862 While the researchers scratch their heads as how to interpret the results, they ask for your help to determine whether they can reject that their findings are likely to be observed just due to random chance. For simplicity, you tell them you are also going to focus only on a two-sided test. 1. State the null and alternative hypotheses for a test that seeks to evaluate whether locust exposure in the 9 months before birth change the prediction for the height-for-age of children. [1pt] 2. Using the critical value approach, can you reject the null hypothesis at the 5% significance level? [1pt] 3. Calculate the p-value of observing the t-statistic of -4.5. Based on this p-value alone, can you reject the null hypothesis at the 5% significance level? [1pt] 4. Construct a 95% confidence interval for the first coefficient, Bom-pre-birth. Based on this 95% confidence interval alone, can you reject the null hypothesis at the 5% significance level? [2pts]