Question 8.I.2: Calculating the p-value for a Two-tailed Hypothesis Test Fin......

The p-value associated with this sample test statistic is the combined tail area of the z-distribution below z = −1.06 and above z = 1.06.

Thus: p-value = P(z < −1.06) + P(z > 1.06)

= (0.5 – 0.3554) + (0.5 – 0.3554) = 0.1446 + 0.1446 = 0.2892 (Table 1, Appendix 1)

Then the p-value is 0.2892 (28.92%).

Statistical Conclusion

Since the p-value for this hypothesis test is greater than 5% (i.e. p-value = 0.2892 > 0.05), there is insufficient evidence to reject H_0. (Refer to Figure 8.11 for the decision rule for the p-value.)

Stated pragmatically, there is a 28.92% chance that the null hypothesis is true. Since this is a relatively high probability (significantly more than 5%), H_0 is accepted.

Management Conclusion

From a management point of view, the p-value of a hypothesis test provides a measure of the intensity with which the sample evidence (as reflected in the sample test statistic) supports the alternative hypothesis. Low p-values (below 5%) show strong-tooverwhelming support for the alternative hypothesis, H_1, while high p-values (above 5% and certainly above 10%) show weak-to-no support for the alternative hypothesis, H_1.