Using R Script please show the coding/steps to find the 95% confidence interval for the mean change in percent return to investors.

Question

Thanks in advance!!! Please show all work/ coding in R Script, so I can try to understand how to solve problems like this later on.

Fortune magazine (March 1997) reported the total returns to investors for the 10 years prior to 1996 and also for 1996 for 431 companies. The total returns for 10 of the companies are listed below.

Find a 95% confidence interval for the mean change in percent return to investors.

It is listed as Company. 1986–96    1996 

Coca-Cola.  29.8%  43.3% 

Mirage Resorts.  27.9%  25.4%  

Merck. 22.1% 24.0%

Microsoft. 44.5%  88.3% 

Johnson & Johnson.  22.2%  18.1%  

Intel. 43.8%  131.2%  

Pfizer. 21.7%  34.0%  

Procter & Gamble.  21.9%  32.1% 

Berkshire Hathaway.  28.3%  6.2%  

S&P 500.  11.8%  20.3% 

Answer 1

library(clipr)

#Import data from clipboard

mydat<-read_clip_tbl()

head(mydat)

#calculate vector of differences

dif<-mydat$Yr1996-mydat$Old

CL=.95 ## set constant for conficence level

n = length(dif) ## set sample size

## The Hard way (using t distribution and separate calculations)

MOE=abs(qt(((1-CL)/2),n-1)*(sd(dif)/sqrt(n))) ## margin of error

UCL=mean(dif)+MOE

LCL=mean(dif)-MOE

sprintf("95 percent CI for mean change is [%.3f %.3f]",LCL,UCL)

## the easy way

t.test(dif,alternative = c("two.sided")) #default is CL=95%