Question

I would like to see a very well documented pdf file with your comments on the steps, and the complete information on your generated sample. Thank you! NOTE for R users: Please export your generated sample as a .csv file (or Rdata file if you prefer). You can find some useful info here.

Exercise 2.

Use R script please

Advanced Math

use R studio

Answer 1

numeric (0) We can generate random sample in R from distribu- tion by "rnorm" command but we will have to set.seed so does not generate new sample every time. We have n=25 that mean degree of freedom will be 24. $group numeric (0) It is done in R as follows: $names [1] "1" > ## t table value > t.table=qt (0.975, 24) > t.table [1] 2.063899 > boxplot.data$out ## for checking outliers numeric (0) > # #Random sample generation in R > set.seed (123) > data=rnorm (n=25, mean=150, sd=10) ## random sample generation > data [1] 144.3952 147.6982 165.5871 150.7051 151.2929 167.1506 154.6092 137.3494 143.1315 145.5434 162.2408 153.5981 [13] 154.0077 151.1068 144.4416 167.8691 154.9785 130.3338 157.0136 145.2721 139.3218 147.8203 139.7400 142.7111 [25] 143.7496 we can see there is not outlier in randomly generated data. The 95% confidence interval of population mean is given by + * (0.975.24) Answer(2): In R it can be done as below: The sample mean in R can be obtained by "mean" command. Answer(1): > ## mean > xbar=mean (data) > xbar [1] 149.6667 > boxplot.data=boxplot (data) ## plotting box- plot > boxplot.data ## stats of boxplot $stats (,1) [1, ] 130.3338 [2,] 143.7496 [3,] 147.8203 [4, ] 154.6092 [5,] 167.8691 > ## confidence interval of population mean > n=length(data) > lower.limit=xbar-((s/sqrt (n)) *t.table) ## lower limit > lower.limit [1] 145.7588 > upper.limit=xbar+ ((s/sqrt (n)) *t.table) ## upper limit > upper.limit [1] 153.5746 The sample standard deviation in R can be obtained by "sd" command. > ## standard deviation > S=sd (data) > S [1] 9.467324 $n [1] 25 End of document I $conf [,1] [1,] 144.3886 [2,] 151.2519 Answer(3): Here we have to find 95 % confidence interval for the population mean so we need table value of t distribu- tion. $out