Andy C. answered 07/25/17
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Typically, the mean average and standard deviation of a sample data is calculated.
The mean average and standard deviation are used in a test statistic formula, which
produces a test statistic.
The test statistic is then located on the normal bell curve table. If it lies beyond
the specified rejection threshold, the null hypothesis is rejected.
Common Thresholds are 1.95 which is for 95% confidence
2.81 which is for 99% confidence
Yes, it is possible for the null hypothesis to get rejected at one confidence level
but not another.
Once this is done, the researcher can say there is statistical evidence that supports
the claim about the population mean, or there is statistical evidence that
refutes the claim about the population mean.
The process is pretty much the same for testing a population proportion.
Ex. What percent of the student body is taking Calculus.
If the school claims that 20% of the students are taking calculus,
then a sample data should reflect and support that statistically.
Random sampling is required for such research as to eliminate bias.