Note: Although the labs only cover part of the learning objectives your exams will cover
the full list of learning objectives that are given here. Objective in boldface is to be used
this quarter for the lab report.
Lab 13. Learning objectives.
80. Learn how to carry out and interpret significance tests for null hypotheses
about population proportions and population means.
81. The statement being tested is called the null hypothesis. Usually the null
hypothesis is a statement of no difference or no effect. A significance test is
designed to answer the question - "Does the null hypothesis provide a
reasonable explanation of the data?"
82. A test statistic is used to measure how far the results are from what would be
expected if the null hypothesis was true.
83. The probability of getting outcomes at least as far from what we would
expect if the null hypothesis were true is called the P-value. It depends on
the sampling distribution of the test statistic. The smaller the P-value, the
stronger the evidence against the null.
84. The alternative hypothesis may be one-tailed or two-tailed. The P-value is
calculated in the direction(s) of the alternative hypothesis.
85. To test Ho: p = p0 versus Ha: p > p0 for a specified value p0, we can use the
test statistic z =
ˆ
p - po
po(1!po) / n
and compute the P-value as the percentage of
the normal curve that is above z.
86. To test Ho: µ = µ0 versus Ha: µ > µ0 for a specified value µ0, and a known
standard deviation σ, we can use the test statistic z =
x !
µ
o
"
/n
and compute
the P-value as the percentage of the normal curve that is above z.
Understand some of the key caveats about significance testing:
87. P-values are strongly related to sample size. Thus, statistical significance is
not the same as practical significance. Also, finding a lack of significance
should not be ignored.
88. Carrying out the mechanics of a significance test cannot make up for a poorly
designed study. A valid significance test is based on the randomization used
to collect the data.
89. Beware of searching for significance.
90. Cutoff values of 1% or 5% are commonly used. However, there is no sharp
border between significant and insignificant, only increasingly strong
evidence as the P-value decreases. There is no practical distinction between
the P-values .049 and .051.
