1. Anything in that range that matches our existing condition for
mean costs is the hypothesis H0 (also called the null hypothesis) ?
that the efforts DO NOT change costs.
2. Only those values outside the range would support hypothesis H1 ?
the alternate hypothesis ? that mean costs are now lower.
To calculate the values in the statistical range, we?ll need the mean
and standard deviation, easily done in Excel or many programmable
Mean = $56.42
S.D. = $10.04
3. It is effective to use the Student?s T-distribution for small
sample sizes, as it provides a statistical significance related to the
sample size. Our sample size is 26 ? but the Student?s T-distribution
uses ?degrees of freedom? ? which is N-1 or 25.
What?s the t-critical value? That depends on the confidence level
that we?re trying to get ? and whether we?re dealing with a two-tailed
or one-tailed T-distribution. Here it?s distributed about the mean,
so it?s two-tailed (sometimes samples can vary only one way).
The critical values are determined from the following table:
Surfstat Statistical Tables
?Student?s T Table? (1997)
95% confidence: 2.06
4. You?ll accept the H0 hypothesis based on whether or not the same
falls in the range of:
mean +/- T-crtical * SD
In our case this is:
$56.04 +/- 2.06 * $10.04 = $34.58 to $76.72
With $60 well within that range, there?s no statistical reason to
believe that cost-control efforts changed anything, so you?re accept
H0 ? no change.
?Statements of probability and confidence intervals? (undated)
5. What can you do to enhance your conclusions? You can expand your
sample size, though your critical T never drops below 1.96 ? and you?d
have to get a much tighter standard deviation to judge the
cost-control efforts to be effective.
Google search strategy
t-distribution + critical
t-distribution + ?hypothesis testing?