Math 1040 Chapter 9

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bpulsipher
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300124
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Math 1040 Chapter 9
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2015-04-07 04:16:22
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Chapter 9 key terms and principles.
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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

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

    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 :
    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, .
    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, .
    1) the sample is obtained by simple random sampling or through a randomized experiment.

    2)  where 

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

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

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

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