Welcome! When you get to lab, please pull up the following documents for February 24th for the Single Sample t-test Powerpoint Doc Excel dataset

Difference between z-test and t-test Given both the mean and the standard deviation for the population t-test: Compare data of a sample to an entire population Given just the population mean, not standard deviation for the population (σ) Estimate S from sample (estimated standard deviation for the population)

Scenario 1 A previous study done by Edison Research stated that most Americans listen to 4.08 hours of music on average every day. Using the data from the students in this statistics class, conduct a single sample t-test to see whether Auburn students differ compared to the population. Use an alpha (probability of a Type 1 error, p-level) of .05

Null Hypothesis/ Research Hypothesis

What are the degrees of freedom? Degrees of freedom: the number of scores that are free to vary infinitely when estimating a population parameter from a sample df = N-1 Where N = sample size

How to report t-test results t(df) = t-stat , p-level < or > alpha

Calculating Effect Size (Msample – µpopulation ) / estimated population standard deviation In t-test, the population standard deviation is estimated because we had to infer from the descriptive statistics, while in a z-test, the population standard deviation is given.

Effect Size 0.20 = small; 0.50 = medium; 0.80 = large Include: Who/what is being measured The measurement Identify populations Size of effect At the individual level In terms of standard deviations 0.20 = small; 0.50 = medium; 0.80 = large

Confidence Intervals Lower bound: (- Confidence Level + Msample ) Upper bound: (Confidence Level + Msample)

Statistical Decision From our results, what can we conclude about the study? Do we Fail to Reject the Null or Reject the Null Hypothesis? Why?

Practical Decision Something to think about: How can music be beneficial? Altering your mood; Working out; Memory loss; Help with sleeping Based on the results of the t-test, do you think Auburn University should start a campaign that encourages students to listen to more music? Use the scenario, statistical test results, effect size, and any additional insights.

Example of Practical Decision What should be included: Decision 2 statistical evidences from the study Additional insight

Time to Practice! Using the single-sample t-test, use the collected data to see if Auburn University students change majors more than the national average of times students changes their majors, which is 3 times. Use an alpha (probability of a Type I error, p-level) of .05