T statistic The t-statistic, t, is used for inference of the mean of a population, when is unknown. –This test statistic has a t distribution with n 1 degrees of freedom. –The margin of error, m, for a CI is where t * is the appropriate value from the t distribution with n 1 degrees of freedom.
Assumptions When we use the t distribution, we assume the population from which we’re sampling is normally distributed. However, hypothesis tests and CIs using the t distribution are “robust” inference techniques. –They can often be used for even very non-normal populations if n 40. –If n <15, we must be sure that population distribution is very close to normal.
You want to rent an unfurnished one bedroom apartment. You take a random sample of 10 apartments advertised in the Mount Vernon News and record the rental rates. Here are the rents (in $ per month): 500, 650, 600, 505, 450, 550, 515, 495, 650, 395 –Find a 95% CI for the mean monthly rent for unfurnished one bedroom apartments in the community. –Do these data give good reason to believe that the mean rent of all such apartments is greater than $500 per month?
Example: Typing Speeds Randomly selected secretaries are given typing tests on an electric typewriter and on a computer using word processing software. On average, is there a difference between typing speeds?
Typing Speed Data (in wpm)
Matched/paired samples We have two measurements or observations on each individual. –Often, but not always, these are “before” and “after” measurements. We want to examine the change from the first to the second measurement. Compute the difference between the two measurements for each individual, and analyze this difference using the one-sample t procedures we’ve discussed.
Typing Speed Data
Example: Typing Speeds On average, is there a difference between typing speeds? –What are our null and alternative hypotheses? –Test at = –What assumptions do we need for this test? In addition, find a 95% CI for the mean difference between typing speeds on typewriters vs. word processors.