Suppose you have a population of size 7 [i.e. N=7]. You measure some quantity (Y ) and the corresponding numbers are: 11, 12, 13, 14, 15, 16, 17 Show hand calculation for each of the following parts of the question a) Calculate the population mean (). b) Calculate the population variance ( 2 ). c) By using random numbers from the text book (page 14) or from R, draw two samples without replacement. Then i. calculate the sample mean ii. calculate the sample variance iii. calculate V [y] iv. calculate estimated variance of y d) Create a table of all possible combination of two samples (without replacement) from this population. i. calcualte the sample mean for each of these combinations ii. calculate the sample variance for each of these combinations iii. construct 95% confidence intervals for the population mean using each of the sample mean and sample variance from the previous two steps. iv. calculate the proportion of the intervals that truely captures the population mean that you calcualted in part (a). v. What value did you expect to see as an answer to part d)iv? Why is your calculated number different from the expected number? Explain briefly. e) By using the sample variances that you have calculated in part d)ii, i. calculate their mean and comapare it to your answer from part(b). ii. What comment can you make about sample variance based on this comparison