177. One-Sample t-Test

177.0.1. One-sample

Tests if the mean of a single sample differs from a known or hypothesized population mean.

Example

Step 1: State Hypotheses

Step 2: Summarize Data

  • Sample values:
  • Sample size:

Step 3: Calculate Sample Mean ()

Step 4: Calculate Sample Standard Deviation:

  • Find the deviations from the mean and square them
  • Sum of squared deviations
  • Calculate variance of sample
  • Calculate Sample Standard Deviation

Step 5: Calculate the Test Statistic

Step 6: Determine the Degrees of Freedom

Step 7: Find Critical t-value

  • For a two-tailed test at a significance level () of 0.05 and 2 degrees of freedom ()

Step 8: Compare the t-Value to the Critical t-Value

  • If the absolute value of the test statistic is greater than the critical t-value, reject the null hypothesis.
  • If the absolute value of the test statistic is less than the critical t-value, fail to reject the null hypothesis.

Step 8: Find the p-Value

t_test_one_sample.py 
from scipy import stats
rvs = stats.uniform.rvs(size=50)
stats.ttest_1samp(rvs, popmean=0.5)