sunspot.year is a time series glving the numbers of sunspots from 1700-1988 roun

Question

sunspot.year is a time series glving the numbers of sunspots from 1700-1988 rounded to 1 digit. We may convert the time series to a vector,, with the assignment x - as.vectorfsunspot.year). Let the random variable X representa random observation from the values in sunspot year. Assume X has mean ? and standard deviation ? Answer the 010 ing using R code. a) How many elements does x have? b) Calculate the range of x. (Single number) c) Using the R quantile function calculate the 71st cense of x. d) Calculate the sample mean of x. Call this mean xbar e) Calculate the sample median of x. Calculate the interquartile range ofx g) Calculate the sample standard deviation, s, of x. h) Calculate the critical value to be used to produce an 99% confidence interval for ".eNote that this is a large sample so use a i) Find the lower boundary ror a 99% confidence interval forp norma, critical value. Find the upper boundary for a 99% confidence interval for ?. k) How long is the 99% confidence interval for ?? 1) How many outliers does an R box plot of x show? O 2 03 O 1 O many m) Copy your R script for the above into the text box here.

Explanation / Answer

let the numbers be:-

5,11,16,23,36,58,29,20,10,8,3,0,0,2,11,27,47,63,60,39,28,26,22,11,21,40,78,122,103,73,47,35,11,5,16,34,70,81,111,101,73,40,20,16,5,11,22,40,60,80.9,83.4,47.7,47.8,30.7,12.2,9.6,10.2,32.4,47.6,54,62.9,85.9,61.2,45.1,36.4,20.9,11.4,37.8,69.8,106.1,100.8,81.6,66.5,34.8,30.6,7,19.8,92.5,154.4,125.9,84.8,68.1,38.5,22.8,10.2,24.1,82.9,132,130.9,118.1,89.9,66.6,60,46.9,41,21.3,16,6.4,4.1,6.8,14.5,34,45,43.1,47.5,42.2,28.1,10.1,8.1,2.5,0,1.4,5,12.2,13.9,35.4,45.8,41.1,30.1,23.9,15.6,6.6,4,1.8,8.5,16.6,36.3,49.6,64.2,67,70.9,47.8,27.5,8.5,13.2,56.9,121.5,138.3,103.2,85.7,64.6,36.7,24.2,10.7,15,40.1,61.5,98.5,124.7,96.3,66.6,64.5,54.1,39,20.6,6.7,4.3,22.7,54.8,93.8,95.8,77.2,59.1,44,47,30.5,16.3,7.3,37.6,74,139,111.2,101.6,66.2,44.7,17,11.3,12.4,3.4,6,32.3,54.3,59.7,63.7,63.5,52.2,25.4,13.1,6.8,6.3,7.1,35.6,73,85.1,78,64,41.8,26.2,26.7,12.1,9.5,2.7,5,24.4,42,63.5,53.8,62,48.5,43.9,18.6,5.7,3.6,1.4,9.6,47.4,57.1,103.9,80.6,63.6,37.6,26.1,14.2,5.8,16.7,44.3,63.9,69,77.8,64.9,35.7,21.2,11.1,5.7,8.7,36.1,79.7,114.4,109.6,88.8,67.8,47.5,30.6,16.3,9.6,33.2,92.6,151.6,136.3,134.7,83.9,69.4,31.5,13.9,4.4,38,141.7,190.2,184.8,159,112.3,53.9,37.5,27.9,10.2,15.1,47,93.8,105.9,105.5,104.5,66.6,68.9,38,34.5,15.5,12.6,27.5,92.5,155.4,154.7,140.5,115.9,66.6,45.9,17.9,13.4,29.2,100.2

(a) x has 289 elements.

(b) Lowest value: 0
Highest value: 190.2
Range: 190.2

(c) the 71th percentile is 323/5=64.6

(d)

(e)Median: 39

(f) Lower quartile (xL): 15.55
Upper quartile (xU): 68.95
Interquartile range (xU-xL): 53.4

(g)

39.474102681829

(h) for 99% critical value=2.58

(i)Lower bound 42.64

(j)Upper bound 54.59

(k) Confidence interval (±) 5.973

(l) no outlier

4.08322535397

Mean (Average)=x-bar= 48.613494809689

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