Final answer:
To be very conservative against accepting a given claim, one would tend to choose a small alpha like 0.01, which reflects a stringent threshold for evidence before rejecting the null hypothesis and thus reduces the chances of a Type I error.
Step-by-step explanation:
If you are very conservative against accepting a given claim (an alternative hypothesis), you would tend to choose a small alpha. The alpha level (significance level) in hypothesis testing reflects the threshold for how extreme the data must be before we reject the null hypothesis. By choosing a smaller alpha, such as 0.01, you are saying that you require more evidence against the null hypothesis before you reject it; you are less willing to make a Type I error, which is rejecting the null hypothesis when it's actually true.
For instance, if an alpha of 0.05 is set and the calculated p-value is greater than 0.05, you would not reject the null hypothesis. This implies that there is insufficient evidence at the 5% significance level to support the alternative hypothesis. Similarly, if you set an even more stringent alpha of 0.01 and the p-value is greater than this, then there is not enough evidence at the 1% significance level.
Traditional practices in various fields have involved setting a threshold probability, like 0.05 or 0.01, to determine the significance level, though this choice can be somewhat subjective and based on the specific standards or preferences within a field. A more conservative alpha reflects a more stringent criterion for evidence and reduces the likelihood of a Type I error.