# How to do a 1 sample t-test

What it is
• It is a test to see if a mean from a sample is different from the population average
(mean) and we are only given the sample standard deviation.
• It helps determine if there is a meaningful difference between the sample and the
population it was collected from.
Example
• Researchers at Wazamata U are worried about the incoming freshmen's caloric
intake. They are worried about the freshman 15 being a greater amount of weight
gain than other years. They collect the weight gain of 16 students at Wazamata U.
They found that Freshman (sample) gained an average of 10 pounds over the year
with a Sx= 8 and the rest of the college (population) gained a total of 6 pounds.
• We are going to use an Alpha of .05

Steps

1. Identify if 1 or 2 tail
2. Identify Hypothesis
3. Create a chart for all the known and needed information and enter
what is known
4. Calculate Sm (Standard Error of the mean)
5. Calculate Tobt
6. Calculate DF
7. Look up Tcrit
8. Interpret results Decide if you reject the null
9. Conclusuion

Step 1.
Example: Examining if the freshman 15 is true. Do Freshman (sample)
gain more than college students (population).
• 1 tail greater than

Researchers at Wazamata U are worried about the
incoming freshmen's caloric intake. They are worried
about the freshman 15 being a greater amount of
weight gain than other years. They collect the weight
gain of 16 students at Wazamata U. They found that
Freshman (sample) gained an average of 10 pounds
over the year with a Sx= 8 and the rest of the college
(population) gained a total of 6 pounds.
We are going to use an Alpha of .05

Note below you have calculate your standard error of the mean first as you don't have it to calculate your t obtained.

Steps 4 and 5

Step 6 and 7

What you need to calculate t critical

1 or 2 tail (1), alpha (.05), DF= 15

DF= N-1 = 16-1= 15

Notice in the image below we have drawn a rejection region which is based off of our critical value. If our obtained value (2) falls in that region we reject the null and find support for the alternative. Since it does we do reject the null and find support that freshman gain more weight. We always recommend that you draw a normal curve with rejection regions to determine if you should reject the null. Visualizing is key.

APA style

A 1-sample t-test showed that Freshman students
(M = 10 differed significantly from the population, t(15) = 2, p < .05.

Template for APA

t(df) = tobt, p = p-value

Michael FleischerComment