1.A humanitarian agency wants to check if children in a certain country are not eating enough calories. Suppose that the calories intake of children in that country had a distribution which is left skewed. The agency randomly selects 55 children from this country and measure the amount of calories they consumed on a particular day. Which of the following statements is true? A. The distribution of the data would be approximately normal by the central limit theorem B. The distribution of the data would be approximately normal by the law of large numbers C. The distribution of the sample mean would be approximately normal by the central limit theorem D. The distribution of the sample mean would be approximately normal by the law of large numbers. Part 2: Researchers calculate a 90% confidence interval for the regression slope to be (-0.41, 0.89). What is the best way to interpret the interval? A. We are 90% confident that the sample regression slope lies between-0.41 and 0.089 B. 90% of the regression data falls between-0.41 and 0.89 C. There must be something wrong because the slope can't be negative D. There is a 90% chance the true regression slope is lies between -0.41 and 0.89 E. We are 90% confident that the true regression slope lies between-0.41 and 0.89 F. We are 90% confident that the true mean lies between-0.41 and 0.89 Part 3: which of the following requirements must be met before using the results of the confidence interval above? (Check all that apply) A. Check that the largest residual is no more than 4 times the smallest residual B. Examine a scatter plot to see if there's a linear relationship between the explanatory and response variables C. Examine a histogram of the residuals to see whether the error term is normally distributed D. Check that you have a sample size , n greater than 30 E. Check that the population standard deviation is known F. Examine a residual plot to see whether the variance of the error term is constant for all values of the explanatory variables. Additional question A certain student wanted to estimate the average number of friends people have on Facebook. The student took a simple random sample of 50 students out of all her Facebook friends. She then recorded how many friends each of the selected 50 friends had and found an average of 340 friends. Let's assume that the population standard deviation of the number of fb friends that people have is 120. What is the margin of error for a 95% confidence interval of the true mean number of Facebook friends for all friends of this student