If all of the tickets purchased in this week's state lottery is considered the population, the five winning tickets drawn on Saturday constitute the sample. If the lottery is not "fixed," why is this a probability sample? (Select all that apply.)
a. Because according to the laws of probability, the group of five people who won is exactly representative of all of the persons who purchased tickets
b. Because each ticket purchased has a chance of being included in the sample
c. Because the tickets drawn have a high probability of being representative of all tickets purchased
d. Because use of random sampling increases the probability that those persons whose tickets win will play the lottery again
e. Because each ticket probably has an equal chance of being included in the winning group, whether or not random sampling is used
ANS: B, C
Probability sampling methods have been developed to ensure some degree of precision in estimations of the population parameters. Thus, probability samples reduce sampling error. The term probability sample refers to the fact that every member (element) of the population has a probability higher than zero of being selected for the sample. Since all tickets have a greater than zero chance of winning, and since the tickets drawn have a very good probability of being representative of all tickets purchased, this is a probability sample.
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