Populations and Samples

1
Populations and Samples

• Population a group of individual persons,
  objects, or items from which samples are taken
  for statistical measurement
• Sample a finite part of a statistical
  population whose properties are studied to gain
  information about the whole

(Merriam-Webster Online Dictionary,
http//www.m-w.com/, October 5, 2004)
2
Examples

• Population
• Students pursuing undergraduate engineering
  degrees
• Cars capable of speeds in excess of 160 mph.
• Potato chips produced at the Frito-Lay plant in
  Kathleen
• Freshwater lakes and rivers

• Samples

3
Basic Statistics (review)

• 1. Sample Mean
• Example
• At the end of a team project, team members were
  asked to give themselves and each other a grade
  on their contribution to the group. The results
  for two team members were as follows
• ___________________
• ___________________

Q S
92 85
95 88
85 75
78 92
4
Basic Statistics (review)

• 1. Sample Variance
• For our example
• SQ2 ___________________
• SS2 ___________________

Q S
92 85
95 88
85 75
78 92
5
Your Turn

• Work in groups of 4 or 5. Find the mean,
  variance, and standard deviation for your group
  of the (approximate) number of hours spent
  working on homework each week.

6
Sampling Distributions

• If we conduct the same experiment several times
  with the same sample size, the probability
  distribution of the resulting statistic is called
  a sampling distribution
• Sampling distribution of the mean if n
  observations are taken from a normal population
  with mean µ and variance s2, then

7
Central Limit Theorem

• Given
• X the mean of a random sample of size n taken
  from a population with mean µ and finite variance
  s2,
• Then,
• the limiting form of the distribution of
• is _________________________

8
Central Limit Theorem

• If the population is known to be normal, the
  sampling distribution of X will follow a normal
  distribution.
• Even when the distribution of the population is
  not normal, the sampling distribution of X is
  normal when n is large.
• NOTE when n is not large, we cannot assume the
  distribution of X is normal.

9
Example

• The time to respond to a request for information
  from a customer help line is uniformly
  distributed between 0 and 2 minutes. In one month
  48 requests are randomly sampled and the response
  time is recorded.
• What is the probability that response time is
  between 0.9 and 1.1 minutes?
• µ ______________ s2 ________________
• µX __________ sX2 ________________
• Z1 _____________ Z2 _______________
• P(0.9 lt X lt 1.1) _____________________________