Statistics Chapter 7 - Sampling Distributions

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honestkyle
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210024
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Statistics Chapter 7 - Sampling Distributions
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2013-04-11 14:46:36
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sampling stats
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Sampling and Sampling Distributions
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  1. What is a parameter?
    A numerical characteristic of a population.
  2. What is a statistic?
    A numerical characteristic of a sample
  3. How is the method for Simple Random Sampling determined?
    Depends on whether the population is infinite or finite.
  4. A Simple Random Sample of size n from a finite populate of size N is one selected such that...?
    Each possible sample of size n has the same probability of being selected.
  5. What are Computer-Generated random numbers?
    • Automate random sampling
    • Facilitate large projects
  6. What is Sampling Without Placement?
    An item can not appear more than once in a sample.
  7. What is Sampling With Placement?
    An item can appear more than once in a sample.
  8. What are the two criteria for infinite populates in a Simple Random Sample?
    • Each element selected comes from the population
    • Each element is selected independently
  9. What is a Sampling Distribution?
    • There is a distribution of different values for each statistic.
    • Different values for each sample
  10. What is a sampling distribution of ?
    • Probability distribution of all possible values of 
    • Unbiased estimator
  11. What is the expected value of  equal to?
  12. The variance of the sampling distribution of  is directly proportional to what?
    The variance of the population
  13. The variance of the sampling distribution of  is inversely proportional to what?
    The sample size
  14. The standard deviation of the sampling distribution of  is called what?
    The standard error of the mean
  15. What is the standard error of the mean equation?
  16. What happens to a normal distribution as n increases?
    The spread becomes narrower.
  17. The formulas for  and  hold if?
    The sampled population is infinite
  18. What is the condition for the standard error formulas to hold approximately for large finite populations?
    • If N is much larger than n
    • (at least 20 times larger)
  19. What is the finite population correction if ?
  20. What is the standard error equation for a finite population where ?
  21. True or False
    The mean, , of the population of all possible sample means is not equal to .
    • False
    • They ARE equal.
  22. True or False
    The standard error, , of the population of all possible sample means is less than .
    • True
  23. What does the Central Limit Theorem (CLT) say?
    •  is normally distributed if 
    • the population is normally distributed (or close)
  24. What percent of all possible sample means are within one  of ?
    • 68.26%
    • Empirical rule
  25. What percent of all possible sample means are within two  of ?
    • 95.44%
    • Empirical rule
  26. What percent of all possible sample means are within three  of ?
    • 99.73%
    • Empirical rule
  27. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports 
    They sample 121 students.
    What is the standard error of the sample mean?
    • 0.2
  28. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports
    They sample 121 students.
    What is the chance they will find a sample mean b/w 5 and 6 hrs?
    • 0.9876
    • Look up values on chart and find difference.
    • 0.9938 - 0.0062 = 0.9876
  29. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports 
    They sample 121 students.
    Calculate the probability that the sample mean will be between 5.3 and 5.7 hrs?
    • 0.6826
    • 5.3 = z-score of -1
    • 5.7 = z-score of 1
    • Empirical rule says 68.26%
  30. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports 
    They sample 121 students.
    How strange would it be to obtain a sample mean greater than 6.5 hours?
    • It would be somewhat strange.

    • 5 is an outlier.
  31. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports 
    They sample 121 students.
    What is the probability that the sample mean will be exactly 5.5 hours?
    • Can't answer that.
    • You can't find the exact value, only the probability.
  32. What is the Expected Value equation of the sampling distribution of ?
  33. What is the standard error equation of the sampling distribution of  for an infinite population?
  34. What is the standard error equation of the sampling distribution of  for a finite population?
  35. How large does n need to be for the Central Limit Theorem to apply to a sampling distribution of ?
     and

  36. The President of Doerman Dist. believes that 30% of the firm's orders come from first-time customers.
    To verify his claim, he takes a s.r.s. of 100 orders.
    Assume the President of Doerman is correct and p = 0.30. 
    What does the sampling distribution of  look like?
    What is the expected value?
    The standard error?
    • Check, if this is true - 
    • 100(0.3) = 30 - Yes
    • Check if this is true - 
    • 100(1-0.30)=70 - Yes
    • Not finite, so no correction factor.
  37. The President of Doerman Dist. believes that 30% of the firm's orders come from first-time customers.
    To verify his claim, he takes a s.r.s. of 100 orders.Assume the President of Doerman is correct and p = 0.30. 
    What is the probability that the sample proportion will be between 0.20 and 0.40?
    • 0.9708
  38. Probability sampling is based on what?
    Randomness
  39. Non-probability sampling is based on what?
    Not being based on randomness.
  40. What is stratified random sampling?
    The population is divided into close homogeneous groups and a s.r.s. is taken from each strata.
  41. What is the advantage of stratified random sampling?
    You don't have to use such a large sample size.
  42. What are examples of strata groups for stratified random sampling?
    age, location, department, industry type, etc.
  43. What is Cluster Sampling?
    Population is divided into groups (clusters), a s.r.s. is taken from the clusters, and all elements within each chosen cluster form the sample.
  44. What is an example of Cluster Sampling?
    Clusters are city blocks or other well-defined areas.
  45. What is the advantage of Cluster Sampling?
    Close proximity of elements is cost-effective (many sample values can be obtained in a short time)
  46. What is the disadvantage of Cluster Sampling?
    Usually requires a larger sampling size than s.r.s. or stratified random sampling
  47. What is systematic sampling?
    Pick the first element at random, then select every n/N elements that follow.
  48. What is the advantage of Systematic Sampling?
    • Sample easier to identify than s.r.s.
    • (pick every 100th listing of a phone book after picking the first one at random)
  49. What is Convenience Sampling?
    • Sample elements selected based on convenience (easy access)
    • Example: A professor uses student volunteers to constitute a sample
  50. What are the advantages and disadvantages of Convenience Sampling?
    • Advantage: Sample selection and data collection are relatively easy
    • Disadvantage: Impossible to determine how representative of the population the sample is
  51. What is Judgement Sampling?
    • A person most knowledgeable on the subject of the study selects elements of the population that (s)he feels are most representative of the population.
    • Example: A journalist may select certain senators, judging them as reflecting the general opinion of the senate
  52. What are the advantages and disadvantages of Judgement Sampling?
    • Advantage: Easy
    • Disadvantage: Quality of the sample depends on judgement of person selecting the esample

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