You are the CEO of a dairy company. You are planning to expand milk production by purchasing additional cows, lands and hiring more workers. A random sample of 50 farms owned by your company is collected on total milk production {In liters], the number of milking cows, land size (in acres) and the number of laborers. The data collected are contained in the Excel file milkproductlonadsx. Question 1: Estimate the mean milk production for all farms (30 points] a. Construct the 95% condence interval estimate for the mean milk production for all farms and provide your interpretation. b. What assumptions must you make about the population distribution in order to construct the condence interval estimate in (a)? c. Test a claim at 5% significance level that the true mean milk production is at least 120K. Question 2: Study the impact of land size and labor number on milk production. (30 points] Among the existing farms, 27 farms were randomly selected with different levels of land size and labor number as shown in Excel. Use ANOVA to indicate the importance of each of the two factors and their interactions on the milk production. a. Display your Excel ANOVA table. b. What test would you perform and what are your test statistics? c. What is your conclusion? Please justify. Question 3: Investigate the relationships between all the variables. {40 points] You believe that the number of cows, land size and the number of laborers are the best predictors for total milk production on any given farm. Perform a multiple regression in Excel and provide your interpretations. a. Display your Excel output. b. Write down the regression equation and interpret all the coefficients. c. Write down the coefcient of determination and interpret its meaning. d. Analyze the residual plots of your multiple regression model. e. What is the predicted milk production for a 30-acre farm with 20 milking cows and 3 labors? f. What is the null hypothesis to determine whether there is significant relationship between total milk production and each explanatory variable? What are your conclusions? Bonus Question: what is the relationship between one-sample test, two-sample test. analysis ofvarlance (ANDVA) and regression? How do you decide on which test to perform? (5 points]