This project involves a test of the basic idea behind the bootstrap method. Essentially you will write a program that:
1. Generates a parent population of size 100,000 whose distribution approaches that of a normal distribution,
2. Draw a random sample of size 100 from the parent population,
3. Subject the random sample to a bootstrap procedure, and
4. Generate an output file in which the mean and standard deviation of the parent population are compared to the average mean and average standard deviation from
the bootstrap samples.
? It is recommended that you seed the random number generator by invoking subroutine ranseed.f95 and put a date/time stamp on your output file through use of subroutine timestamp.f95.
Generate the parent population by calculating 100,000 values of the sum of six (6) random numbers. If you are unsure how to approach this, see the sample Fortran source code titled Normal Distribution Source Code - Revised posted under Course Documents.
It would behoove you to store the parent population values in a vector array of size 100,000 as this will make it easier not only to create the initial bootstrap sample but also to calculate the parent distribution's mean and standard deviation. (Hint: Since the parent distribution is composed of the sums of six random numbers whose values are between 0 and 1, the range of the parent distribution should be between 0 and 6.)
? Randomly draw a sample of size 100 from the parent population and store it in a vector array.
Sample with replacement this sample array ns times (I set ns to 10,000). For each bootstrap sample, calculate the mean and standard deviation. Store the calculated values of the bootstrap samples' means and standard deviations so at the end of the bootstrap sampling process you can calculate the average mean and average standard deviation of the bootstrap samples).
Important! Guard the content of the initial sample array from that of the bootstrap samples. You want to draw 100 samples with replacement from the initial sample array each time, but not change its content.
Attach to an email the output files from five cases. (This is why you want to seed the random number generator, otherwise the results of all five cases will be identical.) In the body of the email, state whether or not you believe the results lend confidence to the validity of the resampling bootstrap method.