Modeling the Height of the U.S. Population II 1 point possible {graded} Continuing from the problem above, your goal is to answer the question of interest "Were people in the U.S. taller in 2018 than in 1920?" You do so by sampling 106 individuals labeled 1, 2, . . .,16 chosen randomly from the US. population. Let X,- denote the height of the i-th individual. We will treat X; as a random variable, and use the sample X1, . . . .f X\" to answer the question of interest. In addition to the initial modeling assumptions on X1, . . . ,XT1 discussed in the previous problem, we further assume: . X1; is Gaussian; . Var (Xi) = 1.3. These assumptions were derived by fitting the data from the 1920 census. Having established these assumptions, we decide on the following protocol for answering the question of interest. If ,u. 2 IE [Xi] > 5.5 [and the goal of this lecture is to tackle the question "Is p. > 5.5?"), then we respond by "Yes, the 2018 US. population was taller as a whole than the 1920 population". Otherwise, we respond by "No." Which of the following are true statements regarding the two additional assumptions above? [Choose all that apply.) D Theyr place restrictions on the different possible distributions that X1, . . . . Xn could follow. D For the purposes of hypothesis testing, they allow us to interpret the question of interest as a very specific mathematical question about the mean of X;. Another Example: Modeling the Height of the U.S. Population I 1/1 point (graded) You have access to U.S. census data for the height of individuals from the year 1920. The dataset shows that the average height of the U.S. was 5.5 feet. For simplicity, let's assume that the 1920 dataset included the heights of a// people residing in the U.S. at that time. Your goal as a statistician is to provide a response to the question of interest: "Were people in the U.S. taller in 2018 than in 1920?". The company that you work for has limited resources, so you will not be able to survey the entire U.S. population, but you still would like to assess the heights of individuals in the U.S. Therefore, you decide to take the following sampling approach: Pick 1 million people (with replacement, for simplicity) randomly from the U.S. population and record their heights. Let X denote the random variable equal to the height of the i-th person chosen. Assume that any particular individual's height does not influence anyone else's and that there is a common underlying distribution which describes the random variables X1, . . ., Xn. Which mathematical property of X1, . . ., An most accurately captures all assumptions made in the previous paragraph? O X1, . .., Xn all have the same distribution, but some of them are correlated. O X1, . .., Xn are independent, but may not all have the same distribution. The random variables X1 , . .., Xn are iid.In hypothesis testing of mean we need population to come from the normal distribution as well as we need variance of the population otherwise we are using the estimate of variance so as we are testing the hypothesis that mean height of 2018 Us population is higher than that of 1920 hence Option [2) is correct Was this answer helpful? (17 2 Q 10