is it true that it is more difficult to reject a null hyputhesis if we use a 10 %level of significance compared with a 5% level of significance?
No, it is more likely to reject with 10%.
Yes, it is true that it is generally more difficult to reject a null hypothesis if we use a higher level of significance (such as 10%) compared to a lower level of significance (such as 5%).
To understand why this is the case, let's first clarify what the level of significance represents. In hypothesis testing, the level of significance (often denoted as α) is the probability of rejecting the null hypothesis when it is actually true. It determines how willing we are to make a Type-I error, which is the incorrect rejection of a true null hypothesis.
With a 5% level of significance, we are saying that we are willing to accept a 5% chance of making a Type-I error. In other words, we are quite cautious in concluding that the null hypothesis is false. On the other hand, with a 10% level of significance, we are willing to accept a higher 10% chance of making a Type-I error. This indicates that we are more open to rejecting the null hypothesis, even when there might be a higher probability that it is true.
By using a higher level of significance, we're effectively widening the acceptance region and decreasing the rejection region in the statistical test. This means that more data falls within the acceptance region, making it more difficult to reach the threshold for rejecting the null hypothesis. Consequently, we become less likely to reject the null hypothesis, even when there might be evidence to suggest otherwise.
However, it's important to note that the choice of the level of significance depends on various factors, including the field of study, the consequences of making errors, and the significance of the research question. In general, a 5% level of significance is commonly used as a standard to strike a balance between Type-I and Type-II errors. Nonetheless, the choice of the level of significance should be justified based on the specific context of the study.