8.6: OneSample ttests and CIs Exercises
 Page ID
 18056
Practice Calculating ttests
Exercise \(\PageIndex{1}\)
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 \(\overline{X} = 1.10\) and the spread was \(s = 0.40\), and you test for a difference from 0 at the \(α\)=0.05.
 Answer

Based on opinions from 55 people, we can conclude that the average opinion of craft beer (\(\overline{X}\)=1.10) is positive, \(t(54)\)=22.00, \(p < .05\).
Practice with Confidence Intervals
Exercise \(\PageIndex{1}\)
What is the relationship between a chosen level of confidence for a confidence interval and how wide that interval is? For instance, if you move from a 95% CI to a \(90\%\) CI, what happens? Hint: look at the ttable to see how critical values change when you change levels of significance.
 Answer

As the level of confidence gets higher, the interval gets wider. In order to speak with more confidence about having found the population mean, you need to cast a wider net. This happens because critical values for higher confidence levels are larger, which creates a wider margin of error.
Exercise \(\PageIndex{1}\)
You hear a lot of talk about increasing global temperature, so you decide to see for yourself if there has been an actual change in recent years. You know that the average land temperature from 19511980 was 8.79 degrees Celsius (this is your population mean, \( \mu \). You find annual average temperature data from 19812017 (N=37) of 9.44 degrees Celsius with a standard deviation of 0.35 degrees Celsisum. You decide to construct a \(99\%\) confidence interval (because you want to be as sure as possible and look for differences in both directions, not just one) using the information to test for a difference from the previous average. You can just do the math and report a statistical sentence.
 Answer

CI = (9.28, 9.60); CI does not bracket \(μ\), reject null hypothesis
Contributors and Attributions
Foster et al. (University of MissouriSt. Louis, Rice University, & University of Houston, Downtown Campus)
