[EX02-212] When the Internet study “You and the Internet” (Section 2.1, p. 39) was performed, it appeared that the variable x, the number of Internet activities in a week, had an approximately normal distribution. That distribution is approximated by this relative frequency distribution:

Internet Activities/ Relative Internet Activities/ Relative Week, x Frequency Week, x Frequency 1 0.01 8 0.14 2 0.03 9 0.11 3 0.05 10 0.08 4 0.09 11 0.05 5 0.10 12 0.04 6 0.14 13 0.03 7 0.13

a. Select a random sample of size 40 from this relative frequency representation of the population of all Internet users.

b. Construct a histogram of the sample obtained in part

a. Do not group the data. (See instructions that follow.)

MINITAB (Release 14)

Input the x values into C1 and the corresponding relative frequencies into C2; then continue with:

Choose: Calc  Random Data  Discrete Enter: Generate: 40 rows of data Store in column(s): C3 Values (of x) in: C1 Probabilities in: C2  OK Excel Input the x values into column A and the corresponding relative frequencies into column B; then continue with:

Choose: Tools  Data Analysis  Random Number Generation  OK Enter: Number of Variables: 1 Number of Random Numbers: 40 Distribution: Discrete Value & Prob. Input Range:

(A2:B5 select data cells not labels)

Select: Output Range Enter: (C1 or select cell)

c. Find the mean, median, and standard deviation of the sample obtained in part a.

d. Repeat parts a–c three more times, being sure to keep the answers for each set of data together.

e. Describe the similarities and differences between the distributions shown on the four histograms.

f. Make a chart displaying the numerical statistics for each of the four samples and describe the variability from sample to sample of each statistic.

g. The four samples were all drawn randomly from the same distribution. Write a statement describing the overall variability between these four random samples.