is it more difficult to reject a null hyputhesis if we use a 10% level of significance compared to 5% level of significance.?
No, it is easier to reject the null at 10% versus 5% level of significance. If you look at a z-table (for example), you will see why.
Yes, it is generally more difficult to reject a null hypothesis when using a 10% level of significance compared to a 5% level of significance. The level of significance, also known as alpha (α), represents the maximum probability of making a Type I error, which is rejecting a true null hypothesis.
When we use a 5% level of significance, we are setting the threshold for rejecting the null hypothesis at 5%. This means that we are willing to accept a 5% chance of making a Type I error.
On the other hand, when we use a 10% level of significance, we are setting a higher threshold for rejecting the null hypothesis at 10%. This means that we are willing to accept a higher chance, 10%, of making a Type I error.
Since we are setting a more lenient or relaxed threshold for rejecting the null hypothesis at a 10% level of significance, it becomes easier to reject the null hypothesis. In other words, there is a higher probability of obtaining statistically significant results, which may lead to rejecting the null hypothesis.
However, it is important to note that using a higher level of significance also increases the likelihood of making a Type I error. Therefore, it is crucial to carefully consider the appropriate level of significance to minimize the risk of false positives while maintaining the power to detect meaningful differences or effects.