Statistics 101: Section L - Laboratory Assignment 9
This week’s lab consists of activities dealing with the sampling distribution of the sample mean.
1. Group Activity The accompanying table lists distances from Ames to home towns of 200 students
who took Stat 101 in a previous semester. There are 20 rows (00 to 19) and 10 columns (0 to 9). Row
05, column 2 has the distance 77 miles. The purpose of this exercise is to use sampling to estimate
the average distance from Ames to home towns of the 200 Stat 101 students. Record all information
on the accompanying form and record your information on the blackboard (in parts (b), (c) and (e))
so that the entire lab can examine all of the sample results. Hand in one answer sheet for each group
and attach your individual data collection sheets.
(a) Tell how you can use Table B, the table of random digits to select distances at random.
(b) Each member of your group should select one distance at random. Record the column number,
row number, and distance on the line provided. Also record your groups sample values on the
blackboard under the heading n = 1. Do you think selecting one distance is a reasonable procedure
for estimating the average distance for all 200 students? Explain briefly why or why not.
(c) Each member of your group should select five distances at random. Record column and row
numbers and distances. Calculate a sample mean value as an estimate of the true mean distance
of all 200 students. Record your group’s estimates on the blackboard under the heading n = 5.
(d) Have each member of your group select a second set of five distances at random. Record column
and row numbers and distances. Calculate the sample mean of these samples. Did you come up
with the same sample mean values? What does this tell you about taking random samples?
(e) Repeat part (c) only this time select 10 distances at random. Record your estimates on the
attached form and on the blackboard. Do you feel this procedure produces a better or worse
estimate of the mean distance than those in (c) and (d)? Explain briefly.
(f) When all of the groups are done (or nearly all) examine the results on the blackboard. Construct
a histogram of the results for each sample size. The true mean of all 200 distances is 197.8 miles.
Each group of estimates (n = 1, n = 5, n = 10) should be centered around that value. Do the
histograms have centers close to this value? Which histogram appears to have the smallest spread
(no calculation required)?
2. Individual Activity In an earlier lab you sampled senators from the 1994 U.S. Senate and noted the
number of years of service. On a separate page is a histogram displaying the years of service for those
100 senators and a histogram giving an empirical sampling distribution for the sample mean years of
service for random samples of 10 senators. Refer to those histograms when answering the following
questions.
(a) Describe the shape of the distribution of the Years in Senate for the 100 senators.
(b) Describe the shape of the distribution of the Sampling Distribution of Average Years in Senate.
(c) If we had taken random samples of size 20 instead of 10, would the sampling distribution of the
average years exhibit less spread, about the same amount of spread or more spread than that
depicted in the histogram? Explain your answer briefly.
(d) Looking at the histogram of the sampling distribution, what is the approximate center and standard deviation of the average years? Hint: six standard deviations would be approximately equal
to the range.
(e) The mean years in the senate for this population is actually µ = 12.4 years and the standard
deviation is σ = 8.7 years. What is the relationship between these values and your guesses in (d)?
Individual Answer Sheet
Name
1. Distance from Home Town to Ames
(b) row #
column #
distance
(c) row #
column #
distance
sample mean distance =
(e) row #
column #
sample mean distance =
(d) row #
column #
distance
sample mean distance =
distance
2. Senators
(a)
(b)
(c)
(d)
(e)
Group Answer Sheet
Group Members:
Histogram: n=1
Histogram: n=5
Histogram: n=10
Do the histograms have centers close to 197.8 miles?
Which histogram appears to have the smallest spread?