If all of the tickets purchased in this week's state lottery is ...

[maychende]

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

Question 2

The population parameter for firefighters on Long Island is 79 male. The sample statistic for three fire stations is 73 male. Why wasn't the sample statistic the same as the population parameter?
 
  a. Sampling error was present.
  b. Random variation might have occurred.
  c. Systematic variation might have occurred.
  d. The sample was fairly small.
  e. The sample was not perfectly representative.
  f. The population parameter is inaccurate.

[olivia_paige29]

Answer to Question 1

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.

Answer to Question 2

ANS: A, B, C, D, E
The difference between a sample statistic and a population parameter is called the sampling error. A large sampling error means that the sample is not providing a precise picture of the population; it is not representative. Sampling error is usually larger with small samples and decreases as the sample size increases. Sampling error reduces the power of a study, or the ability of the statistical analyses conducted to detect differences between groups or to describe the relationships among variables. Sampling error occurs as a result of random variation and systematic variation.

[maychende]

Thank you

[olivia_paige29]

Happy to help you