Math 1040 Chapter 9

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  1. 9.2

    Remember, the ____ of statistical inference is to use information obtained from a ______ and __________ the results to the population being studied. As with estimating the population proportion, the first step is to obtain a _____ ________ of the parameter.The _____ ________ of the population mean, μ, is the sample mean, x¯.
    goal, sample, generalize, point estimate, point estimate
  2. 9.2

    Suppose that a simple random sample of size n is taken from a population. If the population from which the sample is drawn follows a normal distribution, the distribution of

    Image Upload follow?
    Student’s t-distribution with n−1 degrees of freedom, where x¯ is the sample mean and s is the sample standard deviation.
  3. 9.2

    The six steps of Properties of the t-Distribution are:
    1) The t-distribution is different for different degrees of freedom.

    2) The t-distribution is centered at 0 and is symmetric about 0.

    3) The area under the curve is 1. The area under the curve to the right of 0 equals the area under the curve to the left of 0, which equals 1/2.

    4) As t increases or decreases without bound, the graph approaches, but never equals, zero.

    5) The area in the tails of the t-distribution is a little greater than the area in the tails of the standard normal distribution because we are using s as an estimate of σ, thereby introducing further variability into the t-statistic.

    6) As the sample size n increases, the density curve of t gets closer to the standard normal density curve. This result occurs because as the sample size increases, the values of s get closer to the value of σ by the Law of Large Numbers.
  4. 9.2

    What does Image Upload represent?
    The notation Image Upload is used to represent the z-score whose area under the normal curve to the right of Image Upload is Image Upload. Similarly, we let Image Upload represent the t-value whose area under the t-distribution to the right of Image Upload is Image Upload.

    The shape of the t-distribution depends on the sample size, n. Therefore, the value of tα depends not only on α, but also on the degrees of freedom, n−1.
  5. 9.2

    List the three conditions required for constructing a confidence interval for a population mean Image Upload:
    Provided....

    sample data come from a simple random sample or randomized experiment,

    sample size is small relative to the population size (n≤0.05N),

    the data come from a population that is normally distributed, or the sample size is large
  6. 9.3

    List two things you should look for that tell you to construct a confidence interval for a population proportion, Image Upload.
    1) sample data that are qualitative with 2 outcomes (e.g., true/false, yes/no, 0 or 1)

    2) summary information that includes a sample proportion - the number of successes x out of n trials.
  7. 9.3

    List the three conditions that must be met when constructing a confidence interval for a population proportion, Image Upload.
    1) the sample is obtained by simple random sampling or through a randomized experiment.

    2) Image Upload where Image Upload

    3) the sample size can be no more than 5% of the population size Image Upload.
  8. 9.3

    list two things you should look for that tell you to construct a confidence interval for a population mean, Image Upload.
    1) raw data that are quantitative,

    2) summary information that includes a sample mean (Image Upload), sample standard deviation (Image Upload), and sample size (Image Upload).
  9. 9.3

    Besides the facts that...

    (1) the sample must be obtained by simple random sampling or through a randomized experiment and

    (2) that the sample size must be small relative to the size of the population,

    what other condition must be met?
    The data come from a population that is at least approximately normal with no outliers.

    This condition is verified using a normal probability plot (to check for normality) and a boxplot (to check for outliers).
  10. 9.3

    See below for a table of
    The steps listed in the flowchart are as follows:

    (1) Which parameter are we estimating?

    If “Proportion, p,” forward to Image Uploadand Image Upload and construct a confidence interval for p.

    If “mean, μ,” forward to "Is n ≥ 30?"

    (2) Is n ≥ 30?

    If “Yes”, forward to "Compute t-interval"

    If “No”, "Do the data come from a population that is approximately normal with no outliers?"

    (3) Do the data come from a population that is approximately normal with no outliers?

    If “Yes”, Compute t-interval

    If “No”, Use nonparametric methods
  11. 9 - Video

    In general, how are data used to test hypotheses?
    If the data are unusual, the null hypothesis is rejected.
Author:
bpulsipher
ID:
300124
Card Set:
Math 1040 Chapter 9
Updated:
2015-04-07 08:16:22
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Description:
Chapter 9 key terms and principles.
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