1. For a sample, table below shows number of people purchased three competing brands of a product, A, B and C, at time t1 and t2(t2>t1). Based on the data beiow, answer the next four questions. Bought at time t1 A B C Total Bought A 976 at time 70? t2 C 141 Total 786 599 438 1823 a) Which brand is the most popular at time, t1? Why? (3 points) b) How many people switched brands between time t1 and t2? Explain how you obtained the answer. {2 points) c) Which brand had the lowest brand loyalty? Why? (3 points) d) If brand A and B had both marketing campaigns from time t1 to t2, and based on numbers provided in the above tabie, which brand (A or B) had a more successful campaign? Explain your reasoning. (2 points) 2. Random variabie X represents marketing budget of competitors of a pen manufacturing company. It has a normal distribution with mean 2 and standard deviation of 2 (both in $ million). a) What is the probability of marketing budget to be greater than $8 million? (Hint: use a standard normal tabie, partially shown at the end of this question book or use Excel) b) What is the probability of marketing budget to be exactly 53 million? (10 points) 3. In an experiment an analyst randomly selected 20 stores and collected sales of a product in one day in each store. From collected sample data he has: I? = 34.32 and 1(Xi X)2 = 309.65. a) What is 90% confidence interval for population mean? {m assume sample size is larger enough and use standard normal table) b) Provide an interpretation of this confidence interval in a few sentences. (10 points) Show All your works. . (a) An analyst wishes to estimate the average annual expenditures per company on high-end coffee maker machine. The estimate must be accurate within plus or minus $80 and the estimated standard deviation in such expenditures is $400. For a 90% confidence interval, what is the required sample size? (Hint: use standard normal table or Excel. ~ You can round up or down to the nearest integer.) (b) On a separate study, this analysis is studying the annual expenditures per company on coffee filter. Through a survey, he collected a sample and observed the following information from that sample: minimum expenditure observed = $600, maximum expenditure observed = $1,100, average expenditure (based on sample) = $1,050. What is an approximate estimate for standard deviation of population for the annual expenditures on coffee filter? (10 points) ~ Show All your works.~ . Table below provides sales data for several stores that are selling a specific laptop type of brand XYZ and the color of sold units in one week: ~ store ~ Sales ($) ~4 Color 1 2400 Grey