Load “Lock5Data” into your R console. Load “OlympicMarathon”data set in
“Lock5Data”. This data set contains population of all times tofinish the 2008
Olympic Men’s Marathon.
a) What is the population size?
b) Now using “Minutes” column generate a randomsample of size 5.
c) Calculate the sample mean and record it (createa excel sheet or write a
direct R program to record this)
d) Continue steps (b) and (c) 10,000 time (thatmean you have recorded 10,000
sample means)
What you have in step (d) is closely resemble to distribution ofsample means
with sample size 5.
e) Calculate the mean of 10,000 samplemeans.
f) Calculate the population mean (that mean usingall data in “Minutes” column)
g) According to the central limit theorem, ifconditions satisfied, then the mean of
distribution of sample mean should be close to the population mean.Now
compare your results for part (e) and (f). Are they same or atleast close to
each other?
h) Calculate the standard deviation for 10,000data points you have from above.
i) Now calculate theoretical standard error usingthe formula !
√! . Here ? is the
standard deviation using all “Minutes” data and ? is the samplesize (which is
equal to 5 in this case)

j) Comment about your results in part (h) and(i)
k) Graph your 10,000 records in a histogram
l) Is your histogram close to a normaldistribution shape?
m) According to the central limit theorem, ifsample size is large enough then
distribution of sample means is close to normal distribution. Letincrease the
sample size to see whether this is true or not. Use sample size 40and repeat
steps (b), (c) and (d) again. Create a histogram for this new dataset. Is your
histogram shape look like normal distribution?