Reference no: EM132855593

1. Develop a random-number generator based upon a normal distribution with µ = 150 and σ = 7.1.

a. Generate a sample consisting of 500 random numbers.

b. Compute the sample mean and sample standard deviation and compare them to the theoretical mean and standard deviation for the distribution. Explain any observed differences between the sample and theoretical means and standard deviations.

Note: The Excel spreadsheet entitled "Random Number Generation Using Excel.xlsx" provides a template for using Excel to generate random numbers based upon the normal distribution. There are two methods you can use to generate a normal distribution, choose either one.

c. Perform a Chi-squared test to measure the degree of agreement between the distribution for the sample and the theoretical distribution at a 95% level of confidence. Comment on your p values and conclusions

Note: The Excel spreadsheet entitled "Chi-Square Goodness-of-Fit Tests Using Excel.xlsx" provides a template for using Excel to perform a Chi-squared test to measure the degree of agreement between the distribution for a set of random generated numbers based upon the normal distribution actual and the theoretical distribution.

2. Develop a random-number generator based upon a Poisson distribution with λ = 4

a. Generate a sample consisting of 200 random numbers.

Note: The Excel spreadsheet entitled "Random Number Generation Using Excel.xlsx" provides a template for using Excel to generate random numbers based upon the Poisson distribution.

b. Compute the sample mean and sample standard deviation and compare them to the theoretical mean and standard deviation for the distribution. Explain any observed differences between the sample and theoretical means and standard deviations.

c. Perform an autocorrelation test to assess whether the 5th, 10th, 15th, 20th (lag=5) and so on, numbers in the sequence of random numbers are autocorrelated using α = 0.05.

Note: The Excel spreadsheet entitled "Autocorrelation Test Using Excel.xlsx" provides a template for using Excel to perform an autocorrelation test.

3. Develop a random-number generator based upon an exponential distribution with µ = 7.8

a. Generate a sample consisting of 500 random numbers.

Note: The Excel spreadsheet entitled "Random Number Generation Using Excel.xlsx" provides a template for using Excel to generate random numbers based upon the exponential distribution.

b. Compute the sample mean and sample standard deviation and compare them to the theoretical mean and standard deviation for the distribution. Explain any observed differences between the sample and theoretical means and standard deviations.

c. Perform a Komolgorov-Smirnov test to measure the degree of agreement between the distribution for the sample and the theoretical distribution at a 95% level of confidence.

Note: The Excel spreadsheet entitled "Kolmogorov-Smirnov Test Using Excel.xlsx" provides a template for using Excel to perform a Kolmogorov-Smirnov test to measure the degree of agreement between the distribution for a set of random numbers based upon the exponential distribution actual and the theoretical distribution.