3 Types of Hypothesis Test Using the t Statistic (t Tests)
1) The 1-sample t-Test
Similar set-up to z-Test we have already done (but uses t instead of z); hypothesis is
about the value of a population mean (µ).
Example: A diet self-help book estimates that the average 1 ounce chocolate chip
cookie contains 110 calories. A nutritionist suspects this estimate is low. She
randomly samples 15 different brands of 1-ounce chocolate chip cookies. The calorie
counts are shown below. Is there evidence at α = .05 that the average calorie content
is greater than 110 calories per cookie?
100 125 150 160 185 125 90 145 160 100 150 120 85 105 110
2) The matched pairs t-Test (a.k.a. 2 dependent samples)
In these scenarios, two sets of data are collected, but each value in the first data set is
linked in some way to a value in the other data set. Hypothesis is about the average
difference between the two values (µdif).
a) Is there evidence that on b) Is there evidence that on c) Is there evidence that on
average, wives spend average, a certain drug average, more men in
more time per week on lowers cholesterol? city X receive speeding
household chores than tickets each year than do
Sample Data (cholesterol
their husbands spend? women?
level– initial and after 6 weeks
Sample Data (hours/wk): of taking drug): Sample Data (number of
tickets received by each
Couple Wife Husband Patient Before After gender for given year):
1 9.4 3.6 1 270 240
Year Men Women
2 12.5 15.1 2 230 235
2008 28,471 29,002
… (etc.) … (etc.)
2007 24,216 24,105
(Link: matched pairs are from (Link: matched pairs are from
same couple) same patient)
(Link: matched pairs are from
3) The 2-sample t-test (a.k.a. 2 independent samples)
In this scenario, the goal is to compare the means of two different populations.
Therefore, there is a sample from each population, and values from one sample are
not linked in any way to the values from the other sample. Hypothesis is about how
the two means compare to each other (µ1 and µ2)
a) Is there evidence that on average, movie b) Is there evidence that on average, pro
ticket prices are higher in Atlanta than they football players have shorter careers than
are in Dawsonville? pro baseball players?
Sample Data: Sample Data (years in sport before retiring)
Atlanta Dawsonville Football players Baseball players
$8.75 $8.00 8 12
$9.50 $6.75 11 4
$7.50 etc. etc. 9