The two shaded areas each have a probability of 0.005, which adds up to a total probability of 0.01. We can also see if it is statistically significant using the other common significance level of 0.01. Our sample mean (330.6) falls within the critical region, which indicates it is statistically significant at the 0.05 level. The critical region defines how far away our sample statistic must be from the null hypothesis value before we can say it is unusual enough to reject the null hypothesis. If the population mean is 260, we’d expect to obtain a sample mean that falls in the critical region 5% of the time. In statistics, we call these shaded areas the critical region for a two-tailed test. In the graph above, the two shaded areas are equidistant from the null hypothesis value and each area has a probability of 0.025, for a total of 0.05. To graph a significance level of 0.05, we need to shade the 5% of the distribution that is furthest away from the null hypothesis. The significance level determines how far out from the null hypothesis value we'll draw that line on the graph. A picture makes the concepts much easier to comprehend! These types of definitions can be hard to understand because of their technical nature. For example, a significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference. The significance level, also denoted as alpha or α, is the probability of rejecting the null hypothesis when it is true.

Alternative hypothesis: The population mean differs from the hypothesized mean (260).

Null hypothesis: The population mean equals the hypothesized mean (260).We'll use these tools to test the following hypotheses: I left you with a question: where do we draw the line for statistical significance on the graph? Now we'll add in the significance level and the P value, which are the decision-making tools we'll need. The probability distribution plot above shows the distribution of sample means we’d obtain under the assumption that the null hypothesis is true (population mean = 260) and we repeatedly drew a large number of random samples. We want to determine whether our sample mean (330.6) indicates that this year's average energy cost is significantly different from last year’s average energy cost of $260. Here’s where we left off in my last post. It’s easier to understand when you can see what statistical significance truly means! To bring it to life, I’ll add the significance level and P value to the graph in my previous post in order to perform a graphical version of the 1 sample t-test. What do significance levels and P values mean in hypothesis tests? What is statistical significance anyway? In this post, I’ll continue to focus on concepts and graphs to help you gain a more intuitive understanding of how hypothesis tests work in statistics.

P value minitab