### Problem 3 The best-paid 20 tennis players in the world have earned millions
ID: 3316926 • Letter: #
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### Problem 3 The best-paid 20 tennis players in the world have earned millions of dollars during theircareers and are famous for havina won some of the four "Grand Slam" tournaments. Somewhat less famous players who are in positions 20 through 100 irn the earnings' rankings have also aarnered large sums, Thefollowing data (in millions of dollars) correspond to the earnings of 15 randomly selected players classified somewhere in positions 20 through 100 10.10, 8.80, 8.64, 7.67, 6.34, 6.03, 5.90, 5.68, 5.51, 5.38, 5.31, 4.92, 4.54, 4.02, 3.86 a) Find the mean and standard deviation of the sample by considering the finite population correction. trJ # Insert R code below this line b) Compute the $94 %$ confidence interval for the average earnings of players classified between positions 20 and 100 of the ranking (Source: http://www.atptennis.com/en) try # Insert R code below this lineExplanation / Answer
Using R software:
> #a)
> x=c(10.10,8.80,8.64,7.67,6.34,6.03,5.90,5.68,5.51,5.38,5.37,4.92,4.54,4.02,3.86)
> length(x)
[1] 15
> mean(x)
[1] 6.184
> var(x)
[1] 3.353497
> sd=sqrt(var(x))
> sd
[1] 1.831256
> #b)
> #94% Confidence interval
> #Here we use t-distribution confidence interval
> n=15;mean(x);sd
[1] 6.184
[1] 1.831256
> t1=qt(0.03,14) # quantile point at 94% CI and (n-1) degrees of freedom.
> t1
[1] -2.046169
> t2=qt(0.97,14)
> t2
[1] 2.046169
> lower_limit=mean(x)+t1*(sd/sqrt(n))
> lower_limit
[1] 5.216514
> upper_limit=mean(x)+t2*(sd/sqrt(n))
> upper_limit
[1] 7.151486
conclusion : 94% confidence interval =(5.216514,7.151486)
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