Question

Using the data, find the sample skewness and excess kurtosis of Michelson data on the speed of light (light.txt). Is this data set nrmally distribuited, based on this normal probability plot? 850 740 900 1070 930 850 950 980 980 880 1000 980 930 650 760 810 1000 1000 960 960 960 940 960 940 880 800 850 880 900 840 830 790 810 88 880 830 800 790 760 800 880 880 880 860 720 720 620 800 970 950 800 910 850 870 840 840 850 840 840 840 890 810 810 820 800 770 740 760 750 760 910 920 890 860 880 720 840 850 850 780 890 840 780 810 760 810 790 810 820 850 870 870 810 740 810 940 950 800 810 870. a) Find the sample skewness of Michelson data of the speed of light. b)find the excess kurtosis of Michelson data of the speed of light.

Answer 1

Here I attach the R code used:

x=c(850,740,900,1070,930,850,950,980,980,880,1000,980,930,650,760,810,1000,1000,960,960,960,940,960,940,880,800,850,880,900,840,830,790,810,88,880,830,800,790,760,800,880,880,880,860,720,720,620,800,970,950,800,910,850,870,840,840,850,840,840,840,890,810,810,820,800,770,740,760,750,760,910,920,890,860,880,720,840,850,850,780,890,840,780,810,760,810,790,810,820,850,870,870,810,740,810,940,950,800,810,870)
library(timeDate)
skewness(x)
kurtosis(x)
qqnorm(x)
qqline(x)

shapiro.test(x)

Skewness value obtained is -3.114021. it is negatively skewed. The Kurtosis value obtained is 20.08714, that it is  platykurtic

The normal plot obtained is

It is not normally distributed. it is confirmed by normality test Shapiro-Wilk's test.