Statistics Chapter 7 - 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 Image Upload?
    • Probability distribution of all possible values of Image Upload
    • Unbiased estimator
  11. What is the expected value of Image Upload equal to?
    Image Upload
  12. The variance of the sampling distribution of Image Upload is directly proportional to what?
    Image Upload
    The variance of the population
  13. The variance of the sampling distribution of Image Upload is inversely proportional to what?
    Image Upload
    The sample size
  14. The standard deviation of the sampling distribution of Image Upload is called what?
    The standard error of the mean
  15. What is the standard error of the mean equation?
    Image Upload
  16. What happens to a normal distribution as n increases?
    The spread becomes narrower.
  17. The formulas for Image Upload and Image Upload 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)
    • Image Upload
  19. What is the finite population correction if Image Upload?
    Image Upload
  20. What is the standard error equation for a finite population where Image Upload?
    Image Upload
  21. True or False
    The mean, Image Upload, of the population of all possible sample means is not equal to Image Upload.
    • False
    • They ARE equal.
  22. True or False
    The standard error, Image Upload, of the population of all possible sample means is less than Image Upload.
    • True
    • Image Upload
  23. What does the Central Limit Theorem (CLT) say?
    • Image Upload is normally distributed if 
    • the population is normally distributed (or close)
    • Image Upload
  24. What percent of all possible sample means are within one Image Upload of Image Upload?
    • 68.26%
    • Empirical rule
  25. What percent of all possible sample means are within two Image Upload of Image Upload?
    • 95.44%
    • Empirical rule
  26. What percent of all possible sample means are within three Image Upload of Image Upload?
    • 99.73%
    • Empirical rule
  27. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports Image Upload
    They sample 121 students.
    What is the standard error of the sample mean?
    • 0.2
    • Image Upload
    • Image Upload
  28. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports Image Upload
    They sample 121 students.
    What is the chance they will find a sample mean b/w 5 and 6 hrs?
    • 0.9876
    • Image Upload
    • Image UploadImage Upload
    • Image Upload
    • 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 Image Upload
    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 Image Upload
    They sample 121 students.
    How strange would it be to obtain a sample mean greater than 6.5 hours?
    • It would be somewhat strange.
    • Image Upload

    • Image Upload
    • 5 is an outlier.
  31. Student records at a university suggest that students spend an average of 5.5 hrs/wk playing sports Image Upload
    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 Image Upload?
    Image Upload
  33. What is the standard error equation of the sampling distribution of Image Upload for an infinite population?
    Image Upload
  34. What is the standard error equation of the sampling distribution of Image Upload for a finite population?
    Image Upload
  35. How large does n need to be for the Central Limit Theorem to apply to a sampling distribution of Image Upload?
    Image Upload and

    Image Upload
  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 Image Upload look like?
    What is the expected value?
    The standard error?
    • Check, if this is true - Image Upload
    • 100(0.3) = 30 - Yes
    • Check if this is true - Image Upload
    • 100(1-0.30)=70 - Yes
    • Not finite, so no correction factor.
    • Image Upload
    • Image Upload
  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
    • Image Upload
    • Image Upload
    • Image Upload
    • Image Upload
  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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honestkyle
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210024
Filename:
Statistics Chapter 7 - Sampling Distributions
Updated:
2013-04-11 18:46:36
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sampling stats
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Sampling and Sampling Distributions
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