Use a computer to generate a random sample of 500 values of a normally distributed variable x with a mean of 100 and a standard deviation of 20. Construct a histogram of the 500 values.
a. Use the computer commands on page 90 to randomly generate a sample of 500 data from a normal distribution with mean 100 and standard deviation 20. Construct a histogram using class boundaries that are multiples of the standard deviation 20; that is, use boundaries from 20 to 180 in intervals of 20 (see commands on pp. 52–54). Let’s consider the 500 x values found in part a as a population.
b. Use the computer commands on page 91 to randomly select a sample of 30 values from the population found in part a. Construct a histogram of the sample with the same class intervals used in part a.
c. Repeat part b three times.
d. Calculate several values (mean, median, maximum, minimum, standard deviation, etc.) that describe the population and each of the four samples.
e. Do you think a sample of 30 data adequately represents a population? (Compare each of the four samples found in parts b and c to the population.)