Statistics Chap6

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  1. A continuous random variable has a ________ _________ if its values are spread evenly over the range of possibilities. The graph results in a ____________ shape.
    • Uniform Distribution
    • Rectangular
  2. The graph of a continuous probability distribution is called a _________ _______.
    density curve
  3. The distance along the horizontal scale of a standard normal distribution is the _________
    z score.
  4. What is the procedure for finding a z score (or nth percentile) from a known area?
    • 1. Draw a bell shaped curve and identify region that corresponds to the given probability.
    • 2. Locate the closest probability in the table and identify the corresponding z score.
  5. The z score on the borderline separating the z scores that are likely to occur from those that are unlikely to occur is called the ________ __________
    Critical Value
  6. The expression Image Upload 1  denotes the _________ with an area of Image Upload 2 to its right.
    z score
  7. We can convert nonstandard normal distribution values to standard z-scores using the formula _______  . This is rounded to ___ decimal places.
    Image Upload 3

    2 decimal places
  8. What is the formula for finding x values using the z score?
    Image Upload 4
  9. The ____________ is the distribution of sample means, with all samples having the same sample size n taken from the same population.
    sampling distribution of the mean.
  10. The ______________ is the distribution of sample variances, with all samples having the same sample size n taken from the same population.
    Sampling distribution of the variance.
  11. Image Upload 5  is the _____________________
    Population standard deviation
  12. Image Upload 6      is the
    Population variance
  13. The __________________ is the distribution of sample proportions, with all samples having the same sample size n taken from the same population.
    sampling distribution of the proportion
  14. Notations for Proportions:
    p =
    Image Upload 7=
    • p = Population proportion
    • Image Upload 8= sample proportion
  15. Two important properties of the sampling distribution of the proportion:
    • 1, The sample proportions target the value of the population proportion. (equal to the expected value)
    • 2. The distribution of sample porportions tends to be a normal distribution.
  16. What are the unbiased estimators? (4)
    What are the biased estimators? (2)
    • Unbiased:
    • 1. Mean
    • 2. Variance
    • 3. Proportion
    • 4. Standard deviation

    • Biased:
    • 1. Median
    • 2. Range
  17. What is an unbiased estimator?
    They target the value of the population parameter.
  18. What is a biased estimator?
    They do NOT target the population parameter.
  19. What are the 2 reasons for sampling with replacement?
    1. when selecting a relatively small sample from a large population, it makes no significant difference whether we sample with replacement or without replacement.

    2. Sampling with replacement results in independent events that are unaffected by previous outcomes, and independent events are easier to analyze and result in simpler calculations and formulas.
  20. For a population with any distribution, n > 30, then the sample means have a distribution that can be approximated by a normal distribution with mean Image Upload 9 and standard deviation _________.
    Image Upload 10
  21. If n Image Upload 11 30 and the original population has a normal distribution, then sample means have a normal distibution with mean Image Upload 12 and standard deviation ________
    Image Upload 13
  22. If n  Image Upload 14 30 and the original population does not have a normal distribution, then ____________
    ...the distribution cannot be approximated with mean Image Upload 15 and the standard deviation   Image Upload 16
  23. If all possible random samples of size n are selected from a population with mean Image Upload 17 and standard deviation Image Upload 18, the mean of the sample means is denoted by ______ and the standard deviation of the sample means is denoted by  ______.
    • sample means =  Image Upload 19
    • standard deviation = Image Upload 20
  24. Image Upload 21 is called the
    standard error of the mean
  25. When working with an individual value from a normally distributed population use z = ?
    Image Upload 22
  26. When working with a mean for some sample (or group), use z = ?

    This is called the ______________
    Image Upload 23

    The Central Limit Theorem
  27. According to the ______________, for a large sample size, the sampling distribution of the sample mean is approximately normal, irrespective of the shape of the population distribution.  The sample size is usually considered to be large if _______.
    Central Limit Theorem

    Image Upload 24
  28. What is the Rare Event Rule for Inferential Statistics?
    If, under a given assumption, the probability of a particular observed event is exceptionally small (less than 0.05), we conclude that the assumption is probably not correct.
  29. When sampling

    - without replacement
    - sample size n > 5% of the finite population size N (n > 0.05N)

    adjust the standard deviation of sample means Image Upload 25
    by multiplying it by the ________________:
    finite population correction factor:

    Image Upload 26
  30. If    Image Upload 27   then  Image Upload 28 =  ______

    If   Image Upload 29  then Image Upload 30 = _______
    Image Upload 31

    Image Upload 32
  31. A binomial probability distribution has what 4 requirements?
    • 1. Fixed number of trials
    • 2. Trials are independent
    • 3. Outcome of Success or Failure
    • 4. P(success) is same for each trial
  32. What are the following notations in a Binomial probability distribution: n, x, p, q?
    • n = fixed number of trials
    • x = specific number successes in n trials
    • p = probability of success in one of the n trials
    • q = probability of failure in one of the n trials
  33. How is the mean, standard deviation, and variance calculated in a binomal probability distribution?
    • Mean = Image Upload 33 = np
    • Variance = Image Upload 34 = npq
    • Std. Deviation = Image Upload 35 = Image Upload 36
  34. What are the requirements for a Normal Distribution as an Approximation to the Binomial Distribution?
    1. Sample is a simple random sample of size n which the proportion of successes is p.

    2. np Image Upload 37 5 and nq Image Upload 38 5
  35. What are the steps for the Normal distribution as approximation to the Binomial Distribution?
    • 1. Verify np Image Upload 39 5 and nq Image Upload 40 5.
    • 2. Calculate   Image Upload 41  and   Image Upload 42
    • 3. Calculate the z score Image Upload 43
    • 4. identify the discrete value of x (number of successes)
    • 5. Adjust the value x by using a continuity correction:
    •     x - 0.5 and x + 0.5
    • 6. Draw curve and label
  36. 1. x successes among n trials is an unusually _________ number of successes if P(x or more) is very small (such as 0.05 or less)

    2. x successes among n trials is an unusually _________ number of successes if P(x or fewer) is very small (such as 0.05 or less).
    • 1. high
    • 2. low
  37. What is a normal quantile plot (normal probability plot)?
    What values do x and y represent?
    1. A normal quantile plot is a graph of (x,y) points to determine normality.

    • 2. x is the original set of data values.
    •    y is the corresponding z-scores that is a quartile value expected from the standard normal distribution.
  38. How is normality determined?
    • 1. Construct a histogram
    • 2. Outliers - reject if more than one.
    • 3. Construct a normal quantile plot
  39. In a normal quartile plot how is normality determined?
    • Normal
    • - pattern of points reasonably close to a straight line.

    • Not Normal
    • - points do not lie reasonably along a straight line.
    • - show systematic pattern that is not a straight-line.
  40. What are the steps to manually constructing a Normal Quantile Plot
    • 1. Sort data
    • 2. Calculate proportion for each value.
    • 3. Find z scores corresponding to the cumulative left areas found in step 2.
    • 4. Plot points on scatterplot
    • 5. determine if normal.
  41. What is Data Transformations?
    When a distribution is not normal, it can be transformed by replacing each value of x with log(x+1), which is referred to as a lognormal distribution.  Other transformations, such as Image Upload 44, 1/x, or Image Upload 45 can be used.
  42. The population proportion, p is calculated as:
    • Image Upload 46
    • where
    • x = number of elements in the population with a specific characteristic

    N= total number of elements in the population.
  43. The sample proportion,Image Upload 47  is calculated as:
    • Image Upload 48
    • where
    • x = Number of elementsin the sample with a specific characteristic.
    • n = total number of elements in the sample.
Author:
clkottke
ID:
165856
Card Set:
Statistics Chap6
Updated:
2012-08-16 14:42:43
Tags:
Triola Statistics
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Triola Statistics Chapter 6
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