**Question **# (6) Before they left for the trip, they wanted to estimate the times they needed to makethe deliveries. The houses where the elderly resided in are scattered across the remoteareas, some close to the villages, but some further away. The community center did askthe elderly to call in after they received their letter lunch, so there is a good record of thetimes it took to make these deliveries. (a) Glenda and John browsed through one of theserecords. Twenty random samples of n = 6observations of the time it took to make adelivery from previous activities are stored inthe file letterlunch-question6a.csv. Basedon the data: (i) find the sample mean, X, of each sample (ii) calculate the variance of the statistic in (i)based on the 20 random samples (iii) justify that the variance in (ii) is anestimate of the sampling variation of X.Thereby, estimate SE(X) In(iv) in (i)-(iii), we are able to understand the meaning of the sampling variation and standard error of a statistic through repeated sampling (20 samples).practice, repeated sampling is not possible.Use any of the 20 samples, illustrate another way in which SE(X) can be estimated. Compare and contrast between(iv) and (iii) They noticed that(b) Moving on, they saw another set of, more recent, records.the pattern of data was very different from that in (a). The attached fileletterlunch-question6b.csv contains 20 random samples of n = 12 observationsfrom these more recent deliveries. They were puzzled, so they asked the communitycenter for the reason. The woman who works in the community center said that, up until 6 months ago, the remote areas had only been occupied by the locals. Recently,a German architect called Karl Bengs, who moved to Japan in 1993, had completed reviving a number of derelict kominkas¹. As a result, there has been an influx of retirees from the cities. However, these kominkas are in locations that are further away from the other houses.Use the new data: (i) find the sample mean, X, of each sample (ii) calculate the variance of the statistic in (i) based on the 20 random samplesand thereby estimate SE(X) (c) Select one sample from eachletterlunch-question6b.csvof letterlunch-question6a.csvand (i) estimate the population variance (standard deviation) of X in (a) and (b) and then articulate why these variances are related to the performance of X as an estimator in (a) and (b) (ii) the relevance of the sample size, n, in X as an estimator