Inferences using the Standard Normal Distribution
Notes
Confidence Interval for the Mean –
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Notes ./ConfidenceIntervalNotes.pdf
Calculations by hand and with Excel and TI-84 ./ConfidenceInterval.xlsx
ConfidenceInterval.pdf
Hypothesis Testing –
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Notes ./HypothesisTestingNotes.pdf the steps listed with brief explanations on one sheet,
front and back
OutcomesAndErrorTypes.pdf Type I and Type II errors and Type I and Type II correct decisions
defined and briefly discussed.
SampleSizeNeeded.xlsx and SampleSizeNeeded.pdf what sample size is needed to produce a
given quality of result?
Excel worksheet with all the steps, just fill in numbers: HypothesisTesting.xlsx and also includes
other documentation on other sheets, but separate PDFs are provided for those sheets.
Blank worksheet to follow along step-by-step: HypothesisTestingWorksheet.pdf
Excel instructions for the =ZTEST() function: HypothesisTestingExcel.pdf
TI-84 Instructions for STAT TESTS 1:Z-Test with the “Data” option, where sample data is stored in
a TI-84 List: HypothesisTestingTI84Data.pdf
TI-84 Instructions for STAT TEST 1:Z-Test with the “Stats” option, where you give sample mean
and sample size numbers directly, not the underlying data set: HypothesisTestingTI84Stats.pdf
Calculations by hand and with Excel and TI-84 HypothesisTesting.xlsx HypothesisTesting.pdf
Definitions that most of us will skim by and ignore at first reading
[JK10 p. 397] Definition: Point estimate for a parameter: A single number designed to estimate a
quantitative parameter of a population, usually the value of the corresponding sample statistic.
[JK10 p. 397] Definition: Unbiased statistic: A sample statistic whose sampling distribution has a mean
value equal to the value of the population parameter being estimated. A statistic that is not unbiased is
a biased statistic.
[Blu4 p. 345] Definition: Consistent estimator: As the sample size increases, the value of the estimator
approaches the value of the parameter estimated.
[Blu4 p. 345] Definition: Relatively efficient estimator: All of the statistics that can be used to estimate
a parameter, the relatively efficient estimator has the smallest variance.
[JK10 p. 399] Interval Estimate: An interval bounded by two values and used to estimate the value of a
population parameter. The values that bound this interval are statistics calculated from the sample that
is being used as the basis for the estimation.
[JK10 p. 399] Level of Confidence, −𝜶 : The portion of all interval estimates that include the parameter
being estimated.
[JK10 p. 399] Confidence Interval: An interval estimate with a specified level of confidence.
Differences among textbooks
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[JK10] σ, the population’s (not just the sample’s) standard deviation, is assumed to be known.
[Blu4] seems to be using this also for cases where sample size 𝑛 ≥ 30, as well as cases where
the population 𝜎 is known. (Section 7.2, pages 345-357).
But [JK10 pp. 402-403] has this note: The assumption is that the sampling distribution of 𝑥̅ has a
normal distribution… There is no hard and fast rule defining “large enough”; the sample size
that is “large enough” varies greatly according to the distribution of the population.
[vias.org] focuses on t-distribution only. “In many textbooks the confidence interval of the
mean is derived by discussing populations and large samples. Consequently the ztransformation is introduced without payming much attention to the t-distribution. In fact, as
the t-distribution approaches the normal distribution for large sample sizes, it is much more
convenient to use the t-distribution for both small and large samples.
Miscellaneous
[Blu4 p 347] When you are computing a confidence interval for a population mean by using raw data,
round off to one more decimal place than the number of decimal places in the original data. When you
are computing a confidence interval for a population mean by using a sample mean and standard
deviation, round off to the same number of decimal places as given for the mean.