You are curious about how people feel about craft beer, so you gather data from 55 people in the city on whether or not they like it. You code your data so that 0 is neutral, positive scores indicate liking craft beer, and negative scores indicate disliking craft beer. You find that the average opinion was X = 1.10 and the spread was = 0.40, and you test for a difference from 0 at the α = 0.05 level.

Test type: Since you're comparing the mean (average) opinion (1.10) to a hypothesized value (0) and you have only one sample, you'll likely be conducting a one-sample t-test.

Statistical Software: Many statistical software packages or online calculators can perform this test. Here, we won't delve into the specific calculations, but we can discuss the interpretation of the results.

Interpretation: The software will provide a p-value. This value represents the probability of observing a sample mean as extreme as 1.10 (or more extreme) if, in reality, the true average opinion is neutral (0).

Decision Rule:

If the p-value is less than α (0.05), you would reject the null hypothesis (that the average opinion is 0). This suggests there's evidence to believe people's average opinion on craft beer is statistically different from neutral.

If the p-value is greater than α (0.05), you would fail to reject the null hypothesis. In this case, you wouldn't have enough evidence to conclude a significant difference from a neutral opinion based on this sample.

Confidence Level: The α level (0.05) signifies a 5% chance of making a Type I error (rejecting a true null hypothesis). This means there's a 5% risk of concluding people have a different opinion from neutral when they actually don't, based on random sampling variation.

In conclusion, by performing a one-sample t-test and considering the p-value, you can determine if there's a statistically significant difference between the average opinion on craft beer (1.10) and a neutral opinion (0) in your sample, considering the chosen significance level (α = 0.05).