Engineering

Computer ScienceQ&A LibraryLoad “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

Load “Lock5Data” into your R console. Load “OlympicMarathon” data set in

“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)

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