Significance Test and Confidence Intervals In General:

Is the result with P-value 0.045 significant at the 1% level?

To determine the significance of a result with a given p-value, we need to compare it to a pre-determined threshold, called the significance level. In this case, we are asked to determine the significance at the 1% level.

The significance level, often denoted by α, is the probability of rejecting the null hypothesis when it is true. In other words, it represents the maximum tolerable rate of incorrectly rejecting a true null hypothesis.

If the p-value is smaller than the significance level (p-value < α), then we reject the null hypothesis and consider the result to be statistically significant. On the other hand, if the p-value is greater than the significance level (p-value > α), we fail to reject the null hypothesis and do not consider the result to be statistically significant.

In this case, we are given a p-value of 0.045 and asked to determine significance at the 1% level. Since 0.045 is greater than 0.01 (1% written as a decimal), we conclude that the result is not statistically significant at the 1% level.