Final answer:
The decision is to fail to reject the null hypothesis when the p-value is greater than the predetermined alpha level (usually 0.05), indicating insufficient evidence to suggest the null hypothesis is incorrect.
Step-by-step explanation:
If the p-value obtained is greater than the alpha level (designated significance level), the appropriate decision is to fail to reject the null hypothesis. This means that there is not enough evidence in the sample data to conclude that the null hypothesis is incorrect. The alpha level is a threshold for determining the significance of the test, commonly set at 0.05 for a 5% significance level. When the p-value exceeds this level, it indicates that the probability of observing the data, if the null hypothesis is true, is too high to warrant rejection.
The p-value has to be less than the alpha level in order to reject the null hypothesis. If this is not the case, as stated by "The p-value is greater than 0.05," we retain the null hypothesis. It's essential to remember that failing to reject the null hypothesis does not mean that we confirm it as true, only that there is insufficient statistical evidence to reject it.