New Caledonia is a French territory located in the Pacific Ocean. With your recent work on the state ballot behind you, you've been hired to conduct a poll to determine support for independence. Individuals in New Caledonia are in favor or against independence. Let yk represent the response of individual k from the population. Let yk be coded as follows, yk = 0, if individual k is against independence 1, if individual k supports independence Let p represent the proportion of the population in favor of independence. You plan to collect a random sample (with replacement) of size n, (Y1, Y2, . . . , Yn). (a) Is yk a random variable? Explain. (1 point) (b) One of your colleagues proposes the following estimator p = 1 n Pn i=1 Yi . Show that this estimator is unbiased. (Show and explain your steps). (3 points) (c) From class we know that variance of Y1 is p(1 p). Derive the variance of the estimator from part b. (3 points) (d) Can you compute the variance with your sample? If not, explain and propose an alternative that you can compute. (1 point) (e) Your client wishes to have a margin of error of 5 percent. Using 95 percent confidence and an assumed value of p = 0.5, calculate the sample size required for the margin of error. (1 point) (f) Unfortunately, you have already collected a sample of 200 responses. It's now one month later, but you proceed by collecting a new sample of 185 responses. Your colleague proposes combining the samples to achieve your desired margin or error. Can you use the combined sample to obtain an unbiased estimate of the level of support on the day you conducted the first poll? Explain. (1 point)