## Statistcs

Statistcs

An experiment involved 3-day-old infants in the newborn nursery. Systolic and diastolic blood pressure were measured in 99 infants. Data are presented in data set

INFANTBP.DAT.xls (columns B and C for systolic and diastolic blood pressure, respectively). Excel file INFANTBP.DAT.xls

1. Compute appropriate descriptive statistics for systolic and diastolic blood pressure of the infants, using both numeric and graphic measures studied during the

course.

2. Group all data into categories, as described in chapter 2.7. Create tables of the corresponding grouped data.

3. Assuming that number 99 is very large, i.e., “population” (we know that this number must be of the order of 1,000,000, but for the purpose of this project we will

limit this number to 99), compute discrete probability distribution functions for systolic and diastolic blood pressure using grouped data tables, where the discrete

random variable X represents the interval number (0, 1, 2, …, N). Draw discrete probability distribution functions as bar graphs.

4. Using discrete probability distribution functions obtained from the grouped data, compute expected values, variances, and standard deviations for systolic and

diastolic blood pressure.

5. Compare obtained discrete distribution functions to the Binomial and Poisson distributions with the same values of mean and variance. How well the data fit the

Binomial and the Poisson distributions?

6. From the original data set obtained from 99 infants, assuming normal (continuous) distributions for systolic and diastolic blood pressure, determine parameters of

the continuous probability distribution functions for systolic and diastolic blood pressure for the full dataset of 99 samples. Let consider these distribution

functions as continuous “population” distributions.

7. Using calculated normal continuous distribution functions, define, how many infants have unusually high systolic blood pressure and how many of them have unusually

low systolic blood pressure taking into account their percentiles as 0.975 and 0.025, respectively. Provide similar estimations for diastolic blood pressure.

8. Randomly choose data sets of 5 and 20 samples from the complete table of 99 samples for systolic and diastolic blood pressure. Compute estimations of the mean and

the standard errors of the means for the data samples and compare them to the continuous “population” mean and variance. What conclusion can be drawn from these

calculations?

9. Calculate 95% confidence intervals for the estimations of the means μ for 5 and 20 sample sets (Student’s t distribution, assuming that σ is not known). How good

these estimations?

10. Calculate 95% confidence intervals for the estimations of the variances σ2 for 5 and 20 sample sets (χ2 distribution). How good these estimations?

11. Compare statistical data and estimations for systolic and diastolic blood pressures and make conclusions.

Project results must be provided in the form of the project report (a MS Word file with the report and an Excel file with calculations) sent by . In the Excel file,

use a separate sheet for each problem of the project. The report should include: – name of the student; – all required equations, graphs, tables, and descriptions; –