236 Fundamentals of Statistics
If that were the case, we would not need to double the probability, and the
p value would be 0.0478, so the sample average lies outside the acceptance
region if a5 0. 0 5. We would call this result statistically significant and
would reject the null hypothesis, accepting the hypothesis that the new pro-
cess reduces the number of defective resistors.
It sounds like we’ve got something for nothing, but we haven’t. We’ve at-
tained signifi cant results at the cost of assuming something that we hadn’t
assumed before. Because it’s easier to achieve “signifi cant” results in one-
tailed tests, they should be used with extreme caution and only when war-
ranted by the situation. You should always state your alternative hypothesis
before doing your analysis (rather than deciding on a one-tailed test after
seeing the results with the two-tailed test).EXCEL TIPS
To calculate the p value with Excel, fi rst calculate the value of
the z test statistic using the Excel function z 51 AVERAGE^1 data
range^2 2m 02 /^1 s/SQRT^1 n^22 , where data range is the range of cells
in your worksheet containing the sample values, m 0 is the mean
under the null hypothesis, s is the standard deviation of the
probability distribution, and n is the sample size.
For a one-tailed test where z is negative, the p value 5
NORMSDIST^1 z^2.
For a one-tailed test where z is positive, the p value 5
12 NORMSDIST 1 z 2.For a two-tailed test where z is negative, the p value 5
23 NORMSDIST^1 z^2.
For a two-tailed test where z is positive, the p value 5
23112 NORMSDIST^1 z^22.CONCEPT TUTORIALS
Hypothesis Testing
You can get a visual picture of the principles of hypothesis testing by open-
ing the Hypothesis Testing workbook.To use the Hypothesis Testing workbook:1 Open the Hypothesis Testing workbook, located in the Explore
folder. Enable any macros in the workbook.
2 Move through the workbook, reviewing the material on hypothesis
testing.