# Load “Lock5Data” into your R console. Load “OlympicMarathon” data set in“Lock5Data”. This data set contains population of all times to finish the 2008Olympic Men’s Marathon.a. What is the population size?b. Now using “Minutes” column generate a random sample of size 5.c. Calculate the sample mean and record it (create a excel sheet or write adirect R program to record this)d. Continue steps (b) and (c) 10,000 time (that mean you have recorded 10,000sample means)What you have in step (d) is closely resemble to distribution of sample meanswith sample size 5. e. Calculate the mean of 10,000 sample means.f. Calculate the population mean (that mean using all data in “Minutes” column)g. According to the central limit theorem, if conditions satisfied, then the mean ofdistribution of sample mean should be close to the population mean. Nowcompare your results for part (e) and (f). Are they same or at least close toeach other?h. Calculate the standard deviation for 10,000 data points you have from above.i. Now calculate theoretical standard error using the formula !√! . Here sd/ square root od n  is thestandard deviation using all “Minutes” data and n is the sample size (which isequal to 5 in this case)

Question

“Lock5Data”. This data set contains population of all times to finish the 2008
Olympic Men’s Marathon.
a. What is the population size?
b. Now using “Minutes” column generate a random sample of size 5.
c. Calculate the sample mean and record it (create a excel sheet or write a
direct R program to record this)
d. Continue steps (b) and (c) 10,000 time (that mean you have recorded 10,000
sample means)
What you have in step (d) is closely resemble to distribution of sample means
with sample size 5.

e. Calculate the mean of 10,000 sample means.
f. Calculate the population mean (that mean using all data in “Minutes” column)
g. According to the central limit theorem, if conditions 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 at least close to
each other?
h. Calculate the standard deviation for 10,000 data points you have from above.
i. Now calculate theoretical standard error using the formula !
√! . Here sd/ square root od n  is the
standard deviation using all “Minutes” data and n is the sample size (which is
equal to 5 in this case)